TSTP Solution File: ITP366_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% 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 : n003.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 23:10:00 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 757
% Syntax : Number of formulae : 1662 ( 513 unt; 218 typ; 0 def)
% Number of atoms : 3308 ( 747 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 3000 (1136 ~; 990 |; 356 &)
% ( 421 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 3059 ( 784 atm; 778 fun; 954 num; 543 var)
% Number of types : 27 ( 25 usr; 1 ari)
% Number of type conns : 332 ( 177 >; 155 *; 0 +; 0 <<)
% Number of predicates : 360 ( 355 usr; 301 prp; 0-4 aty)
% Number of functors : 145 ( 137 usr; 21 con; 0-4 aty)
% Number of variables : 2181 (2081 !; 100 ?;2181 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_bool_fun$': $tType ).
tff(type_def_6,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'A_ltln_a_ltln_fun$': $tType ).
tff(type_def_8,type,
'Int_int_fun$': $tType ).
tff(type_def_9,type,
'Nat_a_set_fun_bool_fun$': $tType ).
tff(type_def_10,type,
'Num_bool_fun$': $tType ).
tff(type_def_11,type,
'Nat_nat_fun$': $tType ).
tff(type_def_12,type,
'Nat$': $tType ).
tff(type_def_13,type,
'Num$': $tType ).
tff(type_def_14,type,
'Bool_nat_fun$': $tType ).
tff(type_def_15,type,
tlbool: $tType ).
tff(type_def_16,type,
'Nat_num_fun$': $tType ).
tff(type_def_17,type,
'A_set_a_ltln_fun$': $tType ).
tff(type_def_18,type,
'A_ltln_bool_fun$': $tType ).
tff(type_def_19,type,
'A_set$': $tType ).
tff(type_def_20,type,
'A_ltln_set$': $tType ).
tff(type_def_21,type,
'A_set_list$': $tType ).
tff(type_def_22,type,
'A_ltln$': $tType ).
tff(type_def_23,type,
'Bool_bool_fun$': $tType ).
tff(type_def_24,type,
'Nat_a_set_fun$': $tType ).
tff(type_def_25,type,
'Nat_a_set_fun_set$': $tType ).
tff(type_def_26,type,
'Nat_bool_fun$': $tType ).
tff(type_def_27,type,
'A_ltln_a_set_a_ltln_fun_fun$': $tType ).
tff(type_def_28,type,
'Nat_int_fun$': $tType ).
tff(type_def_29,type,
'A_ltln_a_ltln_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'w$': 'Nat_a_set_fun$' ).
tff(func_def_1,type,
'uud$': 'Nat_nat_fun$' ).
tff(func_def_2,type,
'case_nat$a': ( tlbool * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_3,type,
'af_letter$': 'A_ltln_a_set_a_ltln_fun_fun$' ).
tff(func_def_4,type,
'plus$': ( 'Num$' * 'Num$' ) > 'Num$' ).
tff(func_def_5,type,
'f$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_6,type,
'g_F$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_7,type,
'mu_stable$': 'A_ltln$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_8,type,
'fun_app$h': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' ) > 'A_set_a_ltln_fun$' ).
tff(func_def_9,type,
'sgn$': $int > $int ).
tff(func_def_10,type,
'id$': 'A_ltln_a_ltln_fun$' ).
tff(func_def_11,type,
'dbl_dec$': $int > $int ).
tff(func_def_12,type,
'bit0$': 'Num$' > 'Num$' ).
tff(func_def_13,type,
'x$': 'A_ltln_set$' ).
tff(func_def_14,type,
'uua$': 'Nat_a_set_fun_set$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_15,type,
'fun_app$a': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_16,type,
'next_ltln$': 'A_ltln_a_ltln_fun$' ).
tff(func_def_17,type,
'unf$': 'A_ltln_a_ltln_fun$' ).
tff(func_def_18,type,
def_5: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_19,type,
'pred$': 'Nat_nat_fun$' ).
tff(func_def_20,type,
'suffix$': ( 'Nat$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_21,type,
'build$': ( 'A_set$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_22,type,
'uug$': ( 'Bool_nat_fun$' * 'Nat_bool_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_23,type,
'num_of_nat$': 'Nat_num_fun$' ).
tff(func_def_24,type,
'collect$': 'Nat_a_set_fun_bool_fun$' > 'Nat_a_set_fun_set$' ).
tff(func_def_25,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_26,type,
'conc$': ( 'A_set_list$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_27,type,
'fun_app$k': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_28,type,
'g$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_29,type,
def_10: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_30,type,
'gF_advice$': ( 'A_ltln$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_31,type,
'foldl$': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' * 'A_set_list$' ) > 'A_ltln$' ).
tff(func_def_32,type,
'dbl_inc$': $int > $int ).
tff(func_def_33,type,
def_1: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_34,type,
'subsequence$': ( 'Nat_a_set_fun$' * 'Nat$' * 'Nat$' ) > 'A_set_list$' ).
tff(func_def_35,type,
tltrue: tlbool ).
tff(func_def_36,type,
def_8: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_37,type,
'uui$': 'Nat_bool_fun$' ).
tff(func_def_38,type,
'uuf$': ( 'Nat_bool_fun$' * 'Nat_nat_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_39,type,
'fun_app$e': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_40,type,
'inc$': 'Num$' > 'Num$' ).
tff(func_def_41,type,
'uub$': $int > 'Int_bool_fun$' ).
tff(func_def_42,type,
'numeral$': 'Num$' > $int ).
tff(func_def_43,type,
def_9: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_44,type,
'fun_app$p': ( 'Nat_num_fun$' * 'Nat$' ) > 'Num$' ).
tff(func_def_45,type,
'sub$': ( 'Num$' * 'Num$' ) > $int ).
tff(func_def_46,type,
'bit1$': 'Num$' > 'Num$' ).
tff(func_def_47,type,
'nu_stable$': 'A_ltln$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_48,type,
'dbl$': $int > $int ).
tff(func_def_49,type,
'f_G$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_50,type,
'one$': 'Num$' ).
tff(func_def_51,type,
'fun_app$f': ( 'Bool_nat_fun$' * tlbool ) > 'Nat$' ).
tff(func_def_52,type,
'case_nat$': ( 'Nat$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_53,type,
'fun_app$i': ( 'A_ltln_a_ltln_fun$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_54,type,
'fun_app$n': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_55,type,
'fG_advice$': ( 'A_ltln$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_56,type,
def_4: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_57,type,
'uu$': 'A_ltln$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_58,type,
'language_ltln$': 'A_ltln$' > 'Nat_a_set_fun_set$' ).
tff(func_def_59,type,
'fun_app$g': ( 'A_set_a_ltln_fun$' * 'A_set$' ) > 'A_ltln$' ).
tff(func_def_60,type,
tlfalse: tlbool ).
tff(func_def_61,type,
'fun_app$j': ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set$' ).
tff(func_def_62,type,
'nat$': $int > 'Nat$' ).
tff(func_def_63,type,
'uuj$': 'Nat_bool_fun$' ).
tff(func_def_64,type,
'less$': 'Num$' > 'Num_bool_fun$' ).
tff(func_def_65,type,
def_2: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_66,type,
def_6: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).
tff(func_def_67,type,
'uue$': ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_68,type,
'uuc$': $int > 'Int_int_fun$' ).
tff(func_def_69,type,
'fun_app$m': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_70,type,
'uuh$': ( 'Bool_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_71,type,
def_3: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_72,type,
def_7: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_73,type,
'phi$': 'A_ltln$' ).
tff(func_def_81,type,
sK44: 'Nat$' > 'Nat$' ).
tff(func_def_82,type,
sK45: 'Nat$' > 'Nat$' ).
tff(func_def_83,type,
sK46: 'Num$' > 'Num$' ).
tff(func_def_84,type,
sK47: 'Num$' > 'Num$' ).
tff(func_def_85,type,
sK48: 'Nat$' > 'Nat$' ).
tff(func_def_86,type,
sK49: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_87,type,
sK50: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_88,type,
sK51: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$' ).
tff(func_def_89,type,
sK52: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_90,type,
sK53: 'Nat$' > 'Nat$' ).
tff(func_def_91,type,
sK54: 'A_ltln_a_ltln_fun$' > 'A_ltln$' ).
tff(func_def_92,type,
sK55: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_93,type,
sK56: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_94,type,
sK57: 'Num_bool_fun$' > 'Num$' ).
tff(func_def_95,type,
sK58: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_96,type,
sK59: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_97,type,
sK60: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_98,type,
sK61: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_99,type,
sK62: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_100,type,
sK63: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_101,type,
sK64: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_102,type,
sK65: 'A_ltln_a_ltln_fun$' > 'Nat_a_set_fun$' ).
tff(func_def_103,type,
sK66: 'A_ltln_a_ltln_fun$' > 'A_ltln$' ).
tff(func_def_104,type,
sK67: 'A_ltln_a_ltln_fun$' > 'A_ltln_set$' ).
tff(func_def_105,type,
sK68: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln$' ).
tff(func_def_106,type,
sK69: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln$' ).
tff(func_def_107,type,
sK70: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln_set$' ).
tff(func_def_108,type,
sK71: 'A_ltln_a_ltln_fun$' > 'Nat_a_set_fun$' ).
tff(func_def_109,type,
sK72: 'A_ltln_a_ltln_fun$' > 'A_ltln$' ).
tff(func_def_110,type,
sK73: 'A_ltln_a_ltln_fun$' > 'A_ltln_set$' ).
tff(func_def_111,type,
sK74: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln$' ).
tff(func_def_112,type,
sK75: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_113,type,
sK76: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_114,type,
sK77: ( 'Nat_a_set_fun_bool_fun$' * 'Nat_a_set_fun_bool_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_115,type,
sK78: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln_set$' ) > 'Nat$' ).
tff(func_def_116,type,
sK79: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_117,type,
sK80: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_118,type,
sK81: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_119,type,
sK82: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_120,type,
sK83: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_121,type,
sK84: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_122,type,
sK85: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_123,type,
sK86: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_124,type,
sK87: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_125,type,
sK88: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_126,type,
sK89: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_127,type,
sK90: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln_set$' ) > 'Nat$' ).
tff(func_def_128,type,
sK91: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_129,type,
sK92: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_130,type,
sK93: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_131,type,
sK94: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_132,type,
sK95: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_133,type,
sK96: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_134,type,
sK97: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_135,type,
sK98: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_136,type,
sK99: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_137,type,
sK100: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_138,type,
sK101: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_139,type,
sK102: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_140,type,
sK103: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_141,type,
sK104: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_142,type,
sK105: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_143,type,
sK106: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln_set$' * 'A_ltln$' ) > 'Nat$' ).
tff(pred_def_1,type,
'fun_app$b': ( 'Nat_a_set_fun_bool_fun$' * 'Nat_a_set_fun$' ) > $o ).
tff(pred_def_2,type,
'idx_sequence$': 'Nat_nat_fun$' > $o ).
tff(pred_def_3,type,
'fun_app$l': ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > $o ).
tff(pred_def_4,type,
'fun_app$c': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_5,type,
'member$': ( 'Nat_a_set_fun$' * 'Nat_a_set_fun_set$' ) > $o ).
tff(pred_def_6,type,
'fun_app$d': ( 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_7,type,
'fun_app$': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_8,type,
'gF_advice_congruent$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > $o ).
tff(pred_def_9,type,
'fun_app$o': ( 'Num_bool_fun$' * 'Num$' ) > $o ).
tff(pred_def_10,type,
'gF_advice_congruent_axioms$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > $o ).
tff(pred_def_11,type,
'semantics_ltln$': ( 'Nat_a_set_fun$' * 'A_ltln$' ) > $o ).
tff(pred_def_12,type,
'af_congruent_axioms$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_15,type,
sP0: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_16,type,
sP1: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_17,type,
sP2: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_18,type,
sP3: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_19,type,
sP4: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_20,type,
sP5: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_21,type,
sP6: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_22,type,
sP7: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_23,type,
sP8: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_24,type,
sP9: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_25,type,
sP10: 'A_ltln_a_ltln_fun$' > $o ).
tff(pred_def_26,type,
sP11: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_27,type,
sP12: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_28,type,
sP13: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_29,type,
sP14: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_30,type,
sP15: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_31,type,
sP16: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_32,type,
sP17: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_33,type,
sP18: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_34,type,
sP19: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_35,type,
sP20: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_36,type,
sP21: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_37,type,
sP22: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_38,type,
sP23: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_39,type,
sP24: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_40,type,
sP25: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_41,type,
sP26: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_42,type,
sP27: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_43,type,
sP28: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_44,type,
sP29: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_45,type,
sP30: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_46,type,
sP31: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_47,type,
sP32: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_48,type,
sP33: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_49,type,
sP34: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_50,type,
sP35: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_51,type,
sP36: 'Nat_nat_bool_fun_fun$' > $o ).
tff(pred_def_52,type,
sP37: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_53,type,
sP38: ( 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_54,type,
sP39: ( 'Nat_bool_fun$' * 'Nat$' * tlbool ) > $o ).
tff(pred_def_55,type,
sP40: ( 'Nat$' * 'Nat_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_56,type,
sP41: ( 'Nat$' * 'Nat_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_57,type,
sP42: ( 'Nat$' * 'Nat_nat_fun$' * 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_58,type,
sP43: ( 'Nat$' * 'Nat_nat_fun$' * 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(f5664,plain,
$false,
inference(avatar_sat_refutation,[],[f2779,f2784,f2788,f2792,f2796,f2801,f2806,f2811,f2816,f2821,f2825,f2829,f2834,f2839,f2844,f2849,f2854,f2860,f2864,f2868,f2873,f2877,f2881,f2885,f2889,f2893,f2897,f2901,f2906,f2910,f2914,f2918,f2922,f2926,f2930,f2934,f2938,f2942,f2946,f2950,f2954,f2959,f2963,f2967,f2971,f2975,f2997,f3001,f3005,f3009,f3013,f3017,f3021,f3025,f3029,f3033,f3037,f3041,f3045,f3049,f3053,f3057,f3061,f3065,f3069,f3073,f3077,f3081,f3085,f3089,f3093,f3097,f3101,f3105,f3109,f3113,f3117,f3121,f3126,f3130,f3134,f3138,f3142,f3146,f3150,f3154,f3158,f3162,f3166,f3170,f3174,f3178,f3213,f3278,f3298,f3302,f3306,f3310,f3314,f3318,f3322,f3326,f3330,f3334,f3338,f3342,f3346,f3350,f3354,f3358,f3362,f3366,f3370,f3374,f3378,f3382,f3386,f3390,f3394,f3399,f3403,f3407,f3411,f3415,f3419,f3423,f3427,f3431,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3491,f3526,f3621,f3768,f3829,f3833,f3837,f3842,f3848,f3852,f3856,f3860,f3864,f3868,f3872,f3876,f3880,f3884,f3888,f3892,f3896,f3900,f3904,f3908,f3912,f3916,f3920,f3924,f3928,f3932,f3936,f3940,f3944,f3948,f3952,f3956,f3960,f3964,f3968,f3972,f3976,f3980,f3984,f3988,f3992,f3996,f4000,f4004,f4030,f4288,f4292,f4296,f4300,f4304,f4308,f4312,f4316,f4320,f4324,f4328,f4332,f4336,f4340,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4372,f4376,f4380,f4384,f4388,f4392,f4396,f4400,f4404,f4408,f4412,f4416,f4420,f4424,f4428,f4432,f4436,f4440,f4444,f4448,f4452,f4456,f4460,f4464,f4470,f4474,f4478,f4482,f4486,f4579,f4708,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5069,f5073,f5077,f5081,f5085,f5089,f5093,f5097,f5101,f5105,f5109,f5113,f5117,f5121,f5125,f5129,f5133,f5137,f5141,f5145,f5149,f5153,f5157,f5161,f5165,f5169,f5173,f5177,f5181,f5185,f5189,f5193,f5197,f5201,f5205,f5209,f5213,f5217,f5221,f5225,f5229,f5233,f5237,f5243,f5247,f5251,f5255,f5259,f5263,f5663]) ).
tff(f5663,plain,
( ~ spl107_151
| spl107_18
| ~ spl107_249
| ~ spl107_262 ),
inference(avatar_split_clause,[],[f5483,f5111,f5058,f2857,f3845]) ).
tff(f3845,plain,
( spl107_151
<=> 'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('next_ltln$','phi$'),'x$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_151])]) ).
tff(f2857,plain,
( spl107_18
<=> 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('phi$','x$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_18])]) ).
tff(f5058,plain,
( spl107_249
<=> ! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'gF_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','gF_advice$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_249])]) ).
tff(f5111,plain,
( spl107_262
<=> ! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1)
| ~ 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_262])]) ).
tff(f5483,plain,
( ~ 'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('next_ltln$','phi$'),'x$'))
| spl107_18
| ~ spl107_249
| ~ spl107_262 ),
inference(forward_demodulation,[],[f5481,f5059]) ).
tff(f5059,plain,
( ! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'gF_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','gF_advice$'(X0,X1)) )
| ~ spl107_249 ),
inference(avatar_component_clause,[],[f5058]) ).
tff(f5481,plain,
( ~ 'semantics_ltln$'('w$','fun_app$i'('next_ltln$','gF_advice$'('phi$','x$')))
| spl107_18
| ~ spl107_262 ),
inference(resolution,[],[f5112,f2859]) ).
tff(f2859,plain,
( ~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('phi$','x$'))
| spl107_18 ),
inference(avatar_component_clause,[],[f2857]) ).
tff(f5112,plain,
( ! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1)
| ~ 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1)) )
| ~ spl107_262 ),
inference(avatar_component_clause,[],[f5111]) ).
tff(f5263,plain,
spl107_299,
inference(avatar_split_clause,[],[f2719,f5261]) ).
tff(f5261,plain,
( spl107_299
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,$sum(1,'fun_app$k'('of_nat$',X0)))
| ~ sP30(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_299])]) ).
tff(f2719,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,$sum(1,'fun_app$k'('of_nat$',X0)))
| ~ sP30(X0,X1,X2) ),
inference(forward_demodulation,[],[f2037,f611]) ).
tff(f611,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f2037,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,$sum('fun_app$k'('of_nat$',X0),1))
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f1211]) ).
tff(f1211,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less(0,$sum('fun_app$k'('of_nat$',X0),1))
& $less($sum('fun_app$k'('of_nat$',X2),1),'fun_app$k'('of_nat$',X1)) )
| ~ sP30(X0,X1,X2) ),
inference(rectify,[],[f1210]) ).
tff(f1210,plain,
! [X2: 'Nat$',X1: 'Nat$',X0: 'Nat$'] :
( ( ~ $less(0,$sum('fun_app$k'('of_nat$',X2),1))
& $less($sum('fun_app$k'('of_nat$',X0),1),'fun_app$k'('of_nat$',X1)) )
| ~ sP30(X2,X1,X0) ),
inference(nnf_transformation,[],[f933]) ).
tff(f933,plain,
! [X2: 'Nat$',X1: 'Nat$',X0: 'Nat$'] :
( ( ~ $less(0,$sum('fun_app$k'('of_nat$',X2),1))
& $less($sum('fun_app$k'('of_nat$',X0),1),'fun_app$k'('of_nat$',X1)) )
| ~ sP30(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
tff(f5259,plain,
spl107_298,
inference(avatar_split_clause,[],[f2482,f5257]) ).
tff(f5257,plain,
( spl107_298
<=> ! [X0: 'Nat$'] :
( ( 0 = $uminus('fun_app$k'('of_nat$',X0)) )
| $less(0,'fun_app$k'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_298])]) ).
tff(f2482,plain,
! [X0: 'Nat$'] :
( ( 0 = $uminus('fun_app$k'('of_nat$',X0)) )
| $less(0,'fun_app$k'('of_nat$',X0)) ),
inference(evaluation,[],[f1457]) ).
tff(f1457,plain,
! [X0: 'Nat$'] :
( ( 0 = $sum(0,$uminus('fun_app$k'('of_nat$',X0))) )
| $less(0,'fun_app$k'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f701]) ).
tff(f701,plain,
! [X0: 'Nat$'] :
( ( ( 0 = $sum(0,$uminus('fun_app$k'('of_nat$',X0))) )
| $less(0,'fun_app$k'('of_nat$',X0)) )
& ( ( 0 = 0 )
| ~ $less(0,'fun_app$k'('of_nat$',X0)) ) ),
inference(ennf_transformation,[],[f539]) ).
tff(f539,plain,
! [X0: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X0))
=> ( 0 = $sum(0,$uminus('fun_app$k'('of_nat$',X0))) ) )
& ( $less(0,'fun_app$k'('of_nat$',X0))
=> ( 0 = 0 ) ) ),
inference(theory_normalization,[],[f213]) ).
tff(f213,axiom,
! [X0: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X0))
=> ( 0 = $difference(0,'fun_app$k'('of_nat$',X0)) ) )
& ( $less(0,'fun_app$k'('of_nat$',X0))
=> ( 0 = 0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom211) ).
tff(f5255,plain,
spl107_297,
inference(avatar_split_clause,[],[f2307,f5253]) ).
tff(f5253,plain,
( spl107_297
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'dbl_dec$'('sub$'(X0,X1)) = 'sub$'('bit0$'(X0),'inc$'('bit0$'(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_297])]) ).
tff(f2307,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'dbl_dec$'('sub$'(X0,X1)) = 'sub$'('bit0$'(X0),'inc$'('bit0$'(X1))) ),
inference(definition_unfolding,[],[f1601,f1391]) ).
tff(f1391,plain,
! [X0: 'Num$'] : ( 'bit1$'(X0) = 'inc$'('bit0$'(X0)) ),
inference(cnf_transformation,[],[f421]) ).
tff(f421,axiom,
! [X0: 'Num$'] : ( 'bit1$'(X0) = 'inc$'('bit0$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).
tff(f1601,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'sub$'('bit0$'(X0),'bit1$'(X1)) = 'dbl_dec$'('sub$'(X0,X1)) ),
inference(cnf_transformation,[],[f383]) ).
tff(f383,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'sub$'('bit0$'(X0),'bit1$'(X1)) = 'dbl_dec$'('sub$'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom381) ).
tff(f5251,plain,
spl107_296,
inference(avatar_split_clause,[],[f2306,f5249]) ).
tff(f5249,plain,
( spl107_296
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'dbl_inc$'('sub$'(X0,X1)) = 'sub$'('inc$'('bit0$'(X0)),'bit0$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_296])]) ).
tff(f2306,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'dbl_inc$'('sub$'(X0,X1)) = 'sub$'('inc$'('bit0$'(X0)),'bit0$'(X1)) ),
inference(definition_unfolding,[],[f1600,f1391]) ).
tff(f1600,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'sub$'('bit1$'(X0),'bit0$'(X1)) = 'dbl_inc$'('sub$'(X0,X1)) ),
inference(cnf_transformation,[],[f384]) ).
tff(f384,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'sub$'('bit1$'(X0),'bit0$'(X1)) = 'dbl_inc$'('sub$'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).
tff(f5247,plain,
spl107_295,
inference(avatar_split_clause,[],[f2263,f5245]) ).
tff(f5245,plain,
( spl107_295
<=> ! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum($uminus('sub$'('inc$'(X0),'one$')),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_295])]) ).
tff(f2263,plain,
! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum($uminus('sub$'('inc$'(X0),'one$')),1) ),
inference(definition_unfolding,[],[f1422,f1403]) ).
tff(f1403,plain,
! [X0: 'Num$'] : ( 'numeral$'(X0) = 'sub$'('inc$'(X0),'one$') ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,axiom,
! [X0: 'Num$'] : ( 'numeral$'(X0) = 'sub$'('inc$'(X0),'one$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).
tff(f1422,plain,
! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum($uminus('numeral$'(X0)),1) ),
inference(cnf_transformation,[],[f398]) ).
tff(f398,axiom,
! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum($uminus('numeral$'(X0)),1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).
tff(f5243,plain,
spl107_294,
inference(avatar_split_clause,[],[f2255,f5241]) ).
tff(f5241,plain,
( spl107_294
<=> ! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum(1,$uminus('sub$'('inc$'(X0),'one$'))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_294])]) ).
tff(f2255,plain,
! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum(1,$uminus('sub$'('inc$'(X0),'one$'))) ),
inference(definition_unfolding,[],[f1413,f1403]) ).
tff(f1413,plain,
! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum(1,$uminus('numeral$'(X0))) ),
inference(cnf_transformation,[],[f530]) ).
tff(f530,plain,
! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $sum(1,$uminus('numeral$'(X0))) ),
inference(theory_normalization,[],[f312]) ).
tff(f312,axiom,
! [X0: 'Num$'] : ( 'sub$'('one$',X0) = $difference(1,'numeral$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).
tff(f5237,plain,
spl107_293,
inference(avatar_split_clause,[],[f2208,f5235]) ).
tff(f5235,plain,
( spl107_293
<=> ! [X0: 'Bool_bool_fun$',X3: 'Nat$',X2: 'Nat_bool_fun$',X1: tlbool] :
( 'fun_app$d'(X0,def_7(X1,X2,X3))
| ~ sP41(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_293])]) ).
tff(f2208,plain,
! [X2: 'Nat_bool_fun$',X3: 'Nat$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$d'(X0,def_7(X1,X2,X3))
| ~ sP41(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1291]) ).
tff(f1291,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( 'fun_app$d'(X0,def_7(X1,X2,X3))
| ~ sP41(X3,X2,X0,X1) )
& ( sP41(X3,X2,X0,X1)
| ~ 'fun_app$d'(X0,def_7(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f950]) ).
tff(f950,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$d'(X0,def_7(X1,X2,X3))
<=> sP41(X3,X2,X0,X1) ),
inference(definition_folding,[],[f887,f949]) ).
tff(f949,plain,
! [X3: 'Nat$',X2: 'Nat_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP41(X3,X2,X0,X1)
<=> ( ( 'fun_app$d'(X0,def_8(X2,X3))
| ( 'fun_app$k'('of_nat$',X3) != $sum('fun_app$k'('of_nat$','fun_app$e'('pred$',X3)),1) ) )
& ( 'fun_app$d'(X0,X1)
| ( 0 != 'fun_app$k'('of_nat$',X3) ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
tff(f887,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$d'(X0,def_7(X1,X2,X3))
<=> ( ( 'fun_app$d'(X0,def_8(X2,X3))
| ( 'fun_app$k'('of_nat$',X3) != $sum('fun_app$k'('of_nat$','fun_app$e'('pred$',X3)),1) ) )
& ( 'fun_app$d'(X0,X1)
| ( 0 != 'fun_app$k'('of_nat$',X3) ) ) ) ),
inference(ennf_transformation,[],[f299]) ).
tff(f299,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$d'(X0,def_7(X1,X2,X3))
<=> ~ ( ( ~ 'fun_app$d'(X0,def_8(X2,X3))
& ( 'fun_app$k'('of_nat$',X3) = $sum('fun_app$k'('of_nat$','fun_app$e'('pred$',X3)),1) ) )
| ( ~ 'fun_app$d'(X0,X1)
& ( 0 = 'fun_app$k'('of_nat$',X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom297) ).
tff(f5233,plain,
spl107_292,
inference(avatar_split_clause,[],[f2207,f5231]) ).
tff(f5231,plain,
( spl107_292
<=> ! [X0: 'Bool_bool_fun$',X3: 'Nat$',X2: 'Nat_bool_fun$',X1: tlbool] :
( sP41(X3,X2,X0,X1)
| ~ 'fun_app$d'(X0,def_7(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_292])]) ).
tff(f2207,plain,
! [X2: 'Nat_bool_fun$',X3: 'Nat$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP41(X3,X2,X0,X1)
| ~ 'fun_app$d'(X0,def_7(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1291]) ).
tff(f5229,plain,
spl107_291,
inference(avatar_split_clause,[],[f2200,f5227]) ).
tff(f5227,plain,
( spl107_291
<=> ! [X0: 'Bool_bool_fun$',X3: 'Nat$',X2: 'Nat_bool_fun$',X1: tlbool] :
( 'fun_app$d'(X0,def_9(X1,X2,X3))
| ~ sP40(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_291])]) ).
tff(f2200,plain,
! [X2: 'Nat_bool_fun$',X3: 'Nat$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$d'(X0,def_9(X1,X2,X3))
| ~ sP40(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1287]) ).
tff(f1287,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( 'fun_app$d'(X0,def_9(X1,X2,X3))
| ~ sP40(X3,X2,X0,X1) )
& ( sP40(X3,X2,X0,X1)
| ~ 'fun_app$d'(X0,def_9(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f948]) ).
tff(f948,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$d'(X0,def_9(X1,X2,X3))
<=> sP40(X3,X2,X0,X1) ),
inference(definition_folding,[],[f886,f947]) ).
tff(f947,plain,
! [X3: 'Nat$',X2: 'Nat_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP40(X3,X2,X0,X1)
<=> ( ( 'fun_app$d'(X0,def_10(X2,X3))
| ( 'fun_app$k'('of_nat$',X3) != $sum('fun_app$k'('of_nat$','fun_app$e'('pred$',X3)),1) ) )
& ( 'fun_app$d'(X0,X1)
| ( 0 != 'fun_app$k'('of_nat$',X3) ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
tff(f886,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$d'(X0,def_9(X1,X2,X3))
<=> ( ( 'fun_app$d'(X0,def_10(X2,X3))
| ( 'fun_app$k'('of_nat$',X3) != $sum('fun_app$k'('of_nat$','fun_app$e'('pred$',X3)),1) ) )
& ( 'fun_app$d'(X0,X1)
| ( 0 != 'fun_app$k'('of_nat$',X3) ) ) ) ),
inference(ennf_transformation,[],[f301]) ).
tff(f301,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$d'(X0,def_9(X1,X2,X3))
<=> ( ( ( 'fun_app$k'('of_nat$',X3) = $sum('fun_app$k'('of_nat$','fun_app$e'('pred$',X3)),1) )
=> 'fun_app$d'(X0,def_10(X2,X3)) )
& ( ( 0 = 'fun_app$k'('of_nat$',X3) )
=> 'fun_app$d'(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom299) ).
tff(f5225,plain,
spl107_290,
inference(avatar_split_clause,[],[f2199,f5223]) ).
tff(f5223,plain,
( spl107_290
<=> ! [X0: 'Bool_bool_fun$',X3: 'Nat$',X2: 'Nat_bool_fun$',X1: tlbool] :
( sP40(X3,X2,X0,X1)
| ~ 'fun_app$d'(X0,def_9(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_290])]) ).
tff(f2199,plain,
! [X2: 'Nat_bool_fun$',X3: 'Nat$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP40(X3,X2,X0,X1)
| ~ 'fun_app$d'(X0,def_9(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1287]) ).
tff(f5221,plain,
spl107_289,
inference(avatar_split_clause,[],[f2145,f5219]) ).
tff(f5219,plain,
( spl107_289
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_5(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_289])]) ).
tff(f2145,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_5(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1268]) ).
tff(f1268,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( ( tltrue = def_5(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) )
& ( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_5(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f687]) ).
tff(f687,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( tltrue = def_5(X0,X1,X2) )
<=> 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(rectify,[],[f510]) ).
tff(f510,axiom,
! [X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( def_5(X1,X2,X3) = tltrue )
<=> 'fun_app$c'('case_nat$a'(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_509) ).
tff(f5217,plain,
spl107_288,
inference(avatar_split_clause,[],[f2144,f5215]) ).
tff(f5215,plain,
( spl107_288
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_5(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_288])]) ).
tff(f2144,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_5(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1268]) ).
tff(f5213,plain,
spl107_287,
inference(avatar_split_clause,[],[f2143,f5211]) ).
tff(f5211,plain,
( spl107_287
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_4(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_287])]) ).
tff(f2143,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_4(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1267]) ).
tff(f1267,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( ( tltrue = def_4(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) )
& ( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_4(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f686]) ).
tff(f686,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( tltrue = def_4(X0,X1,X2) )
<=> 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(rectify,[],[f509]) ).
tff(f509,axiom,
! [X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( def_4(X1,X2,X3) = tltrue )
<=> 'fun_app$c'('case_nat$a'(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_508) ).
tff(f5209,plain,
spl107_286,
inference(avatar_split_clause,[],[f2142,f5207]) ).
tff(f5207,plain,
( spl107_286
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_4(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_286])]) ).
tff(f2142,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_4(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1267]) ).
tff(f5205,plain,
spl107_285,
inference(avatar_split_clause,[],[f2141,f5203]) ).
tff(f5203,plain,
( spl107_285
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_9(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_285])]) ).
tff(f2141,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_9(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1266]) ).
tff(f1266,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( ( tltrue = def_9(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) )
& ( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_9(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f685]) ).
tff(f685,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( tltrue = def_9(X0,X1,X2) )
<=> 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(rectify,[],[f514]) ).
tff(f514,axiom,
! [X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( tltrue = def_9(X1,X2,X3) )
<=> 'fun_app$c'('case_nat$a'(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_513) ).
tff(f5201,plain,
spl107_284,
inference(avatar_split_clause,[],[f2140,f5199]) ).
tff(f5199,plain,
( spl107_284
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_9(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_284])]) ).
tff(f2140,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_9(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1266]) ).
tff(f5197,plain,
( spl107_283
| ~ spl107_4
| ~ spl107_225 ),
inference(avatar_split_clause,[],[f4879,f4418,f2790,f5195]) ).
tff(f5195,plain,
( spl107_283
<=> ! [X0: 'Nat_nat_fun$',X1: 'Nat$'] : 'fun_app$c'('uuf$'('uuj$',X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_283])]) ).
tff(f2790,plain,
( spl107_4
<=> ! [X0: 'Nat$'] : 'fun_app$c'('uuj$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_4])]) ).
tff(f4418,plain,
( spl107_225
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat_nat_fun$'] :
( 'fun_app$c'('uuf$'(X0,X1),X2)
| ~ 'fun_app$c'(X0,'fun_app$e'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_225])]) ).
tff(f4879,plain,
( ! [X0: 'Nat_nat_fun$',X1: 'Nat$'] : 'fun_app$c'('uuf$'('uuj$',X0),X1)
| ~ spl107_4
| ~ spl107_225 ),
inference(resolution,[],[f4419,f2791]) ).
tff(f2791,plain,
( ! [X0: 'Nat$'] : 'fun_app$c'('uuj$',X0)
| ~ spl107_4 ),
inference(avatar_component_clause,[],[f2790]) ).
tff(f4419,plain,
( ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat_nat_fun$'] :
( ~ 'fun_app$c'(X0,'fun_app$e'(X1,X2))
| 'fun_app$c'('uuf$'(X0,X1),X2) )
| ~ spl107_225 ),
inference(avatar_component_clause,[],[f4418]) ).
tff(f5193,plain,
spl107_282,
inference(avatar_split_clause,[],[f2139,f5191]) ).
tff(f5191,plain,
( spl107_282
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_7(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_282])]) ).
tff(f2139,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = def_7(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1265]) ).
tff(f1265,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( ( tltrue = def_7(X0,X1,X2) )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) )
& ( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_7(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f684]) ).
tff(f684,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( tltrue = def_7(X0,X1,X2) )
<=> 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(rectify,[],[f512]) ).
tff(f512,axiom,
! [X1: tlbool,X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( tltrue = def_7(X1,X2,X3) )
<=> 'fun_app$c'('case_nat$a'(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_511) ).
tff(f5189,plain,
spl107_281,
inference(avatar_split_clause,[],[f2138,f5187]) ).
tff(f5187,plain,
( spl107_281
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_7(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_281])]) ).
tff(f2138,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ( tltrue != def_7(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1265]) ).
tff(f5185,plain,
spl107_280,
inference(avatar_split_clause,[],[f2137,f5183]) ).
tff(f5183,plain,
( spl107_280
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,$uminus(X1)),X2)
| ~ $less(X0,$sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_280])]) ).
tff(f2137,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,$uminus(X1)),X2)
| ~ $less(X0,$sum(X2,X1)) ),
inference(cnf_transformation,[],[f1264]) ).
tff(f1264,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less($sum(X0,$uminus(X1)),X2)
| ~ $less(X0,$sum(X2,X1)) )
& ( $less(X0,$sum(X2,X1))
| ~ $less($sum(X0,$uminus(X1)),X2) ) ),
inference(nnf_transformation,[],[f605]) ).
tff(f605,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less($sum(X0,$uminus(X1)),X2)
<=> $less(X0,$sum(X2,X1)) ),
inference(theory_normalization,[],[f483]) ).
tff(f483,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less($difference(X0,X1),X2)
<=> $less(X0,$sum(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).
tff(f5181,plain,
spl107_279,
inference(avatar_split_clause,[],[f2136,f5179]) ).
tff(f5179,plain,
( spl107_279
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X2,X1))
| ~ $less($sum(X0,$uminus(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_279])]) ).
tff(f2136,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X2,X1))
| ~ $less($sum(X0,$uminus(X1)),X2) ),
inference(cnf_transformation,[],[f1264]) ).
tff(f5177,plain,
spl107_278,
inference(avatar_split_clause,[],[f2135,f5175]) ).
tff(f5175,plain,
( spl107_278
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,$uminus(X2)))
| ~ $less($sum(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_278])]) ).
tff(f2135,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,$uminus(X2)))
| ~ $less($sum(X0,X2),X1) ),
inference(cnf_transformation,[],[f1263]) ).
tff(f1263,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less(X0,$sum(X1,$uminus(X2)))
| ~ $less($sum(X0,X2),X1) )
& ( $less($sum(X0,X2),X1)
| ~ $less(X0,$sum(X1,$uminus(X2))) ) ),
inference(nnf_transformation,[],[f604]) ).
tff(f604,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,$sum(X1,$uminus(X2)))
<=> $less($sum(X0,X2),X1) ),
inference(theory_normalization,[],[f482]) ).
tff(f482,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,$difference(X1,X2))
<=> $less($sum(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).
tff(f5173,plain,
spl107_277,
inference(avatar_split_clause,[],[f2134,f5171]) ).
tff(f5171,plain,
( spl107_277
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),X1)
| ~ $less(X0,$sum(X1,$uminus(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_277])]) ).
tff(f2134,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),X1)
| ~ $less(X0,$sum(X1,$uminus(X2))) ),
inference(cnf_transformation,[],[f1263]) ).
tff(f5169,plain,
spl107_276,
inference(avatar_split_clause,[],[f2113,f5167]) ).
tff(f5167,plain,
( spl107_276
<=> ! [X2: 'A_ltln$',X0: 'A_set_list$',X1: 'Nat_a_set_fun$'] :
( 'semantics_ltln$'('conc$'(X0,X1),X2)
| ~ 'semantics_ltln$'(X1,'foldl$'('af_letter$',X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_276])]) ).
tff(f2113,plain,
! [X2: 'A_ltln$',X0: 'A_set_list$',X1: 'Nat_a_set_fun$'] :
( 'semantics_ltln$'('conc$'(X0,X1),X2)
| ~ 'semantics_ltln$'(X1,'foldl$'('af_letter$',X2,X0)) ),
inference(cnf_transformation,[],[f1252]) ).
tff(f1252,plain,
! [X0: 'A_set_list$',X1: 'Nat_a_set_fun$',X2: 'A_ltln$'] :
( ( 'semantics_ltln$'('conc$'(X0,X1),X2)
| ~ 'semantics_ltln$'(X1,'foldl$'('af_letter$',X2,X0)) )
& ( 'semantics_ltln$'(X1,'foldl$'('af_letter$',X2,X0))
| ~ 'semantics_ltln$'('conc$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f293]) ).
tff(f293,axiom,
! [X0: 'A_set_list$',X1: 'Nat_a_set_fun$',X2: 'A_ltln$'] :
( 'semantics_ltln$'('conc$'(X0,X1),X2)
<=> 'semantics_ltln$'(X1,'foldl$'('af_letter$',X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).
tff(f5165,plain,
spl107_275,
inference(avatar_split_clause,[],[f2112,f5163]) ).
tff(f5163,plain,
( spl107_275
<=> ! [X2: 'A_ltln$',X0: 'A_set_list$',X1: 'Nat_a_set_fun$'] :
( 'semantics_ltln$'(X1,'foldl$'('af_letter$',X2,X0))
| ~ 'semantics_ltln$'('conc$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_275])]) ).
tff(f2112,plain,
! [X2: 'A_ltln$',X0: 'A_set_list$',X1: 'Nat_a_set_fun$'] :
( 'semantics_ltln$'(X1,'foldl$'('af_letter$',X2,X0))
| ~ 'semantics_ltln$'('conc$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1252]) ).
tff(f5161,plain,
spl107_274,
inference(avatar_split_clause,[],[f2090,f5159]) ).
tff(f5159,plain,
( spl107_274
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$k'('of_nat$',sK93(X0)),'fun_app$k'('of_nat$',sK94(X0)))
| ~ sP36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_274])]) ).
tff(f2090,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$k'('of_nat$',sK93(X0)),'fun_app$k'('of_nat$',sK94(X0)))
| ~ sP36(X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f1225,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ( ~ 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK94(X0))
& 'fun_app$c'('fun_app$n'(X0,sK93(X0)),sK94(X0))
& 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK93(X0))
& $less('fun_app$k'('of_nat$',sK93(X0)),'fun_app$k'('of_nat$',sK94(X0)))
& $less('fun_app$k'('of_nat$',sK92(X0)),'fun_app$k'('of_nat$',sK93(X0))) )
| ~ sP36(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92,sK93,sK94])],[f1223,f1224]) ).
tff(f1224,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ? [X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ~ 'fun_app$c'('fun_app$n'(X0,X1),X3)
& 'fun_app$c'('fun_app$n'(X0,X2),X3)
& 'fun_app$c'('fun_app$n'(X0,X1),X2)
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X3))
& $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X2)) )
=> ( ~ 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK94(X0))
& 'fun_app$c'('fun_app$n'(X0,sK93(X0)),sK94(X0))
& 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK93(X0))
& $less('fun_app$k'('of_nat$',sK93(X0)),'fun_app$k'('of_nat$',sK94(X0)))
& $less('fun_app$k'('of_nat$',sK92(X0)),'fun_app$k'('of_nat$',sK93(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1223,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ? [X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ~ 'fun_app$c'('fun_app$n'(X0,X1),X3)
& 'fun_app$c'('fun_app$n'(X0,X2),X3)
& 'fun_app$c'('fun_app$n'(X0,X1),X2)
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X3))
& $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X2)) )
| ~ sP36(X0) ),
inference(rectify,[],[f1222]) ).
tff(f1222,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ~ 'fun_app$c'('fun_app$n'(X2,X3),X5)
& 'fun_app$c'('fun_app$n'(X2,X4),X5)
& 'fun_app$c'('fun_app$n'(X2,X3),X4)
& $less('fun_app$k'('of_nat$',X4),'fun_app$k'('of_nat$',X5))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X4)) )
| ~ sP36(X2) ),
inference(nnf_transformation,[],[f940]) ).
tff(f940,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ~ 'fun_app$c'('fun_app$n'(X2,X3),X5)
& 'fun_app$c'('fun_app$n'(X2,X4),X5)
& 'fun_app$c'('fun_app$n'(X2,X3),X4)
& $less('fun_app$k'('of_nat$',X4),'fun_app$k'('of_nat$',X5))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X4)) )
| ~ sP36(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
tff(f5157,plain,
spl107_273,
inference(avatar_split_clause,[],[f2089,f5155]) ).
tff(f5155,plain,
( spl107_273
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$k'('of_nat$',sK92(X0)),'fun_app$k'('of_nat$',sK93(X0)))
| ~ sP36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_273])]) ).
tff(f2089,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$k'('of_nat$',sK92(X0)),'fun_app$k'('of_nat$',sK93(X0)))
| ~ sP36(X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f5153,plain,
( spl107_272
| ~ spl107_4
| ~ spl107_210 ),
inference(avatar_split_clause,[],[f4718,f4358,f2790,f5151]) ).
tff(f5151,plain,
( spl107_272
<=> ! [X0: 'Nat$'] : ( tltrue = def_8('uuj$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_272])]) ).
tff(f4358,plain,
( spl107_210
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_8(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_210])]) ).
tff(f4718,plain,
( ! [X0: 'Nat$'] : ( tltrue = def_8('uuj$',X0) )
| ~ spl107_4
| ~ spl107_210 ),
inference(resolution,[],[f4359,f2791]) ).
tff(f4359,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue = def_8(X0,X1) ) )
| ~ spl107_210 ),
inference(avatar_component_clause,[],[f4358]) ).
tff(f5149,plain,
spl107_271,
inference(avatar_split_clause,[],[f2075,f5147]) ).
tff(f5147,plain,
( spl107_271
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X0,X2))
| ~ $less(X1,X2)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_271])]) ).
tff(f2075,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X0,X2))
| ~ $less(X1,X2)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f832]) ).
tff(f832,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X1,$sum(X0,X2))
| ~ $less(X1,X2)
| ~ $less(0,X0) ),
inference(flattening,[],[f831]) ).
tff(f831,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X1,$sum(X0,X2))
| ~ $less(X1,X2)
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f478]) ).
tff(f478,axiom,
! [X0: $int,X1: $int,X2: $int] :
( ( $less(X1,X2)
& $less(0,X0) )
=> $less(X1,$sum(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).
tff(f5145,plain,
spl107_270,
inference(avatar_split_clause,[],[f2000,f5143]) ).
tff(f5143,plain,
( spl107_270
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1))
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_270])]) ).
tff(f2000,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1))
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1196]) ).
tff(f1196,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X0))
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1)) )
| ~ sP22(X0,X1,X2) ),
inference(rectify,[],[f1195]) ).
tff(f1195,plain,
! [X2: 'Nat$',X1: 'Nat$',X0: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X2))
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP22(X2,X1,X0) ),
inference(nnf_transformation,[],[f924]) ).
tff(f924,plain,
! [X2: 'Nat$',X1: 'Nat$',X0: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X2))
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP22(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
tff(f5141,plain,
spl107_269,
inference(avatar_split_clause,[],[f1972,f5139]) ).
tff(f5139,plain,
( spl107_269
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1))
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_269])]) ).
tff(f1972,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1))
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f1184]) ).
tff(f1184,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X0))
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1)) )
| ~ sP18(X0,X1,X2) ),
inference(rectify,[],[f1183]) ).
tff(f1183,plain,
! [X2: 'Nat$',X1: 'Nat$',X0: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X2))
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP18(X2,X1,X0) ),
inference(nnf_transformation,[],[f919]) ).
tff(f919,plain,
! [X2: 'Nat$',X1: 'Nat$',X0: 'Nat$'] :
( ( ~ $less(0,'fun_app$k'('of_nat$',X2))
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP18(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
tff(f5137,plain,
spl107_268,
inference(avatar_split_clause,[],[f1939,f5135]) ).
tff(f5135,plain,
( spl107_268
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_268])]) ).
tff(f1939,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) ),
inference(cnf_transformation,[],[f453]) ).
tff(f453,axiom,
! [X0: $int,X1: $int,X2: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).
tff(f5133,plain,
spl107_267,
inference(avatar_split_clause,[],[f1933,f5131]) ).
tff(f5131,plain,
( spl107_267
<=> ! [X2: 'Nat$',X0: 'Nat_nat_fun$',X1: 'Nat_nat_fun$'] : ( 'fun_app$e'('uue$'(X0,X1),X2) = 'fun_app$e'(X0,'fun_app$e'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_267])]) ).
tff(f1933,plain,
! [X2: 'Nat$',X0: 'Nat_nat_fun$',X1: 'Nat_nat_fun$'] : ( 'fun_app$e'('uue$'(X0,X1),X2) = 'fun_app$e'(X0,'fun_app$e'(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: 'Nat_nat_fun$',X1: 'Nat_nat_fun$',X2: 'Nat$'] : ( 'fun_app$e'('uue$'(X0,X1),X2) = 'fun_app$e'(X0,'fun_app$e'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
tff(f5129,plain,
spl107_266,
inference(avatar_split_clause,[],[f1932,f5127]) ).
tff(f5127,plain,
( spl107_266
<=> ! [X2: 'Nat$',X0: 'Bool_nat_fun$',X1: 'Nat_bool_fun$'] : ( 'fun_app$e'('uug$'(X0,X1),X2) = 'fun_app$f'(X0,def_2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_266])]) ).
tff(f1932,plain,
! [X2: 'Nat$',X0: 'Bool_nat_fun$',X1: 'Nat_bool_fun$'] : ( 'fun_app$e'('uug$'(X0,X1),X2) = 'fun_app$f'(X0,def_2(X1,X2)) ),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
! [X0: 'Bool_nat_fun$',X1: 'Nat_bool_fun$',X2: 'Nat$'] : ( 'fun_app$e'('uug$'(X0,X1),X2) = 'fun_app$f'(X0,def_2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
tff(f5125,plain,
spl107_265,
inference(avatar_split_clause,[],[f1918,f5123]) ).
tff(f5123,plain,
( spl107_265
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'(X1,sK87(X0,X1))
| 'fun_app$c'(X1,X0)
| ~ sP16(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_265])]) ).
tff(f1918,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'(X1,sK87(X0,X1))
| 'fun_app$c'(X1,X0)
| ~ sP16(X1,X0) ),
inference(cnf_transformation,[],[f1171]) ).
tff(f1171,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP16(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,X0) ) )
& ( ( 'fun_app$c'(X1,sK87(X0,X1))
& $less('fun_app$k'('of_nat$',sK87(X0,X1)),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,X0)
| ~ sP16(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f1169,f1170]) ).
tff(f1170,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
=> ( 'fun_app$c'(X1,sK87(X0,X1))
& $less('fun_app$k'('of_nat$',sK87(X0,X1)),'fun_app$k'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1169,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP16(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,X0) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,X0)
| ~ sP16(X1,X0) ) ),
inference(rectify,[],[f1168]) ).
tff(f1168,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP16(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,X0) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,X0)
| ~ sP16(X1,X0) ) ),
inference(flattening,[],[f1167]) ).
tff(f1167,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP16(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,X0) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,X0)
| ~ sP16(X1,X0) ) ),
inference(nnf_transformation,[],[f916]) ).
tff(f916,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP16(X1,X0)
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,X0) ) ),
inference(definition_folding,[],[f679,f915]) ).
tff(f915,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP16(X1,X0)
<=> ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
tff(f679,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,X0) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
<=> ( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).
tff(f5121,plain,
spl107_264,
inference(avatar_split_clause,[],[f1906,f5119]) ).
tff(f5119,plain,
( spl107_264
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP14(X1,X0)
| ~ 'fun_app$c'(X1,sK83(X0,X1))
| ~ 'fun_app$c'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_264])]) ).
tff(f1906,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP14(X1,X0)
| ~ 'fun_app$c'(X1,sK83(X0,X1))
| ~ 'fun_app$c'(X1,X0) ),
inference(cnf_transformation,[],[f1153]) ).
tff(f1153,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP14(X1,X0)
| ( ~ 'fun_app$c'(X1,sK83(X0,X1))
& $less('fun_app$k'('of_nat$',sK83(X0,X1)),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,X0) )
| ~ sP14(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f1151,f1152]) ).
tff(f1152,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
=> ( ~ 'fun_app$c'(X1,sK83(X0,X1))
& $less('fun_app$k'('of_nat$',sK83(X0,X1)),'fun_app$k'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1151,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP14(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,X0) )
| ~ sP14(X1,X0) ) ),
inference(rectify,[],[f1150]) ).
tff(f1150,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP14(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,X0) )
| ~ sP14(X1,X0) ) ),
inference(flattening,[],[f1149]) ).
tff(f1149,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP14(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,X0) )
| ~ sP14(X1,X0) ) ),
inference(nnf_transformation,[],[f912]) ).
tff(f912,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP14(X1,X0)
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,X0) ) ),
inference(definition_folding,[],[f796,f911]) ).
tff(f911,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP14(X1,X0)
<=> ! [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
tff(f796,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,X0) ) ),
inference(ennf_transformation,[],[f677]) ).
tff(f677,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1))
=> 'fun_app$c'(X1,X2) )
<=> ( ! [X3: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0))
=> 'fun_app$c'(X1,X3) )
& 'fun_app$c'(X1,X0) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1))
=> 'fun_app$c'(X1,X2) )
<=> ( ! [X2: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0))
=> 'fun_app$c'(X1,X2) )
& 'fun_app$c'(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).
tff(f5117,plain,
spl107_263,
inference(avatar_split_clause,[],[f1820,f5115]) ).
tff(f5115,plain,
( spl107_263
<=> ! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1))
| ~ 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_263])]) ).
tff(f1820,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1))
| ~ 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1) ),
inference(cnf_transformation,[],[f1094]) ).
tff(f1094,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( ( 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1))
| ~ 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1) )
& ( 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1)
| ~ 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1)) ) ),
inference(nnf_transformation,[],[f17]) ).
tff(f17,axiom,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1))
<=> 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
tff(f5113,plain,
spl107_262,
inference(avatar_split_clause,[],[f1819,f5111]) ).
tff(f1819,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1)
| ~ 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1)) ),
inference(cnf_transformation,[],[f1094]) ).
tff(f5109,plain,
( spl107_261
| ~ spl107_4
| ~ spl107_208 ),
inference(avatar_split_clause,[],[f4713,f4350,f2790,f5107]) ).
tff(f5107,plain,
( spl107_261
<=> ! [X0: 'Nat$'] : ( tltrue = def_10('uuj$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_261])]) ).
tff(f4350,plain,
( spl107_208
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_10(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_208])]) ).
tff(f4713,plain,
( ! [X0: 'Nat$'] : ( tltrue = def_10('uuj$',X0) )
| ~ spl107_4
| ~ spl107_208 ),
inference(resolution,[],[f4351,f2791]) ).
tff(f4351,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue = def_10(X0,X1) ) )
| ~ spl107_208 ),
inference(avatar_component_clause,[],[f4350]) ).
tff(f5105,plain,
spl107_260,
inference(avatar_split_clause,[],[f1780,f5103]) ).
tff(f5103,plain,
( spl107_260
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('nu_stable$'(X0),X1)
| ( 'g$'(X0,X1) != 'f_G$'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_260])]) ).
tff(f1780,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('nu_stable$'(X0),X1)
| ( 'g$'(X0,X1) != 'f_G$'(X0,X1) ) ),
inference(cnf_transformation,[],[f1074]) ).
tff(f1074,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ( 'fun_app$b'('nu_stable$'(X0),X1)
| ( 'g$'(X0,X1) != 'f_G$'(X0,X1) ) )
& ( ( 'g$'(X0,X1) = 'f_G$'(X0,X1) )
| ~ 'fun_app$b'('nu_stable$'(X0),X1) ) ),
inference(nnf_transformation,[],[f200]) ).
tff(f200,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('nu_stable$'(X0),X1)
<=> ( 'g$'(X0,X1) = 'f_G$'(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom198) ).
tff(f5101,plain,
spl107_259,
inference(avatar_split_clause,[],[f1779,f5099]) ).
tff(f5099,plain,
( spl107_259
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ( 'g$'(X0,X1) = 'f_G$'(X0,X1) )
| ~ 'fun_app$b'('nu_stable$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_259])]) ).
tff(f1779,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ( 'g$'(X0,X1) = 'f_G$'(X0,X1) )
| ~ 'fun_app$b'('nu_stable$'(X0),X1) ),
inference(cnf_transformation,[],[f1074]) ).
tff(f5097,plain,
spl107_258,
inference(avatar_split_clause,[],[f1778,f5095]) ).
tff(f5095,plain,
( spl107_258
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('mu_stable$'(X0),X1)
| ( 'f$'(X0,X1) != 'g_F$'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_258])]) ).
tff(f1778,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('mu_stable$'(X0),X1)
| ( 'f$'(X0,X1) != 'g_F$'(X0,X1) ) ),
inference(cnf_transformation,[],[f1073]) ).
tff(f1073,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ( 'fun_app$b'('mu_stable$'(X0),X1)
| ( 'f$'(X0,X1) != 'g_F$'(X0,X1) ) )
& ( ( 'f$'(X0,X1) = 'g_F$'(X0,X1) )
| ~ 'fun_app$b'('mu_stable$'(X0),X1) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('mu_stable$'(X0),X1)
<=> ( 'f$'(X0,X1) = 'g_F$'(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).
tff(f5093,plain,
spl107_257,
inference(avatar_split_clause,[],[f1777,f5091]) ).
tff(f5091,plain,
( spl107_257
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ( 'f$'(X0,X1) = 'g_F$'(X0,X1) )
| ~ 'fun_app$b'('mu_stable$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_257])]) ).
tff(f1777,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ( 'f$'(X0,X1) = 'g_F$'(X0,X1) )
| ~ 'fun_app$b'('mu_stable$'(X0),X1) ),
inference(cnf_transformation,[],[f1073]) ).
tff(f5089,plain,
spl107_256,
inference(avatar_split_clause,[],[f1715,f5087]) ).
tff(f5087,plain,
( spl107_256
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ~ 'fun_app$c'(X0,sK60(X0))
| ~ 'fun_app$c'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_256])]) ).
tff(f1715,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ~ 'fun_app$c'(X0,sK60(X0))
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1032]) ).
tff(f1032,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',sK60(X0))) )
& ~ 'fun_app$c'(X0,sK60(X0))
& $less(0,'fun_app$k'('of_nat$',sK60(X0))) )
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f769,f1031]) ).
tff(f1031,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) )
& ~ 'fun_app$c'(X0,X2)
& $less(0,'fun_app$k'('of_nat$',X2)) )
=> ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',sK60(X0))) )
& ~ 'fun_app$c'(X0,sK60(X0))
& $less(0,'fun_app$k'('of_nat$',sK60(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f769,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) )
& ~ 'fun_app$c'(X0,X2)
& $less(0,'fun_app$k'('of_nat$',X2)) )
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(flattening,[],[f768]) ).
tff(f768,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) )
& ~ 'fun_app$c'(X0,X2)
& $less(0,'fun_app$k'('of_nat$',X2)) )
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( ( ~ 'fun_app$c'(X0,X2)
& $less(0,'fun_app$k'('of_nat$',X2)) )
=> ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X0,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) ) )
& 'fun_app$c'(X0,'nat$'(0)) )
=> 'fun_app$c'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).
tff(f5085,plain,
spl107_255,
inference(avatar_split_clause,[],[f1712,f5083]) ).
tff(f5083,plain,
( spl107_255
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| 'fun_app$c'(X0,sK59(X0))
| ~ 'fun_app$c'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_255])]) ).
tff(f1712,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| 'fun_app$c'(X0,sK59(X0))
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1030]) ).
tff(f1030,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( ~ 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',sK59(X0)),1)))
& 'fun_app$c'(X0,sK59(X0)) )
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f767,f1029]) ).
tff(f1029,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& 'fun_app$c'(X0,X2) )
=> ( ~ 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',sK59(X0)),1)))
& 'fun_app$c'(X0,sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f767,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& 'fun_app$c'(X0,X2) )
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(flattening,[],[f766]) ).
tff(f766,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& 'fun_app$c'(X0,X2) )
| ~ 'fun_app$c'(X0,'nat$'(0)) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( 'fun_app$c'(X0,X2)
=> 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1))) )
& 'fun_app$c'(X0,'nat$'(0)) )
=> 'fun_app$c'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
tff(f5081,plain,
spl107_254,
inference(avatar_split_clause,[],[f1711,f5079]) ).
tff(f5079,plain,
( spl107_254
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'nat$'(0))
| ~ 'fun_app$c'(X0,sK58(X0))
| ~ 'fun_app$c'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_254])]) ).
tff(f1711,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'nat$'(0))
| ~ 'fun_app$c'(X0,sK58(X0))
| ~ 'fun_app$c'(X0,X1) ),
inference(cnf_transformation,[],[f1028]) ).
tff(f1028,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'nat$'(0))
| ( ~ 'fun_app$c'(X0,sK58(X0))
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',sK58(X0)),1))) )
| ~ 'fun_app$c'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f765,f1027]) ).
tff(f1027,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1))) )
=> ( ~ 'fun_app$c'(X0,sK58(X0))
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',sK58(X0)),1))) ) ),
introduced(choice_axiom,[]) ).
tff(f765,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'nat$'(0))
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1))) )
| ~ 'fun_app$c'(X0,X1) ),
inference(flattening,[],[f764]) ).
tff(f764,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'nat$'(0))
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1))) )
| ~ 'fun_app$c'(X0,X1) ),
inference(ennf_transformation,[],[f134]) ).
tff(f134,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
=> 'fun_app$c'(X0,X2) )
& 'fun_app$c'(X0,X1) )
=> 'fun_app$c'(X0,'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).
tff(f5077,plain,
spl107_253,
inference(avatar_split_clause,[],[f1708,f5075]) ).
tff(f5075,plain,
( spl107_253
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_253])]) ).
tff(f1708,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f761]) ).
tff(f761,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(X0,0) ),
inference(flattening,[],[f760]) ).
tff(f760,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(X0,0) ),
inference(ennf_transformation,[],[f476]) ).
tff(f476,axiom,
! [X0: $int,X1: $int] :
( ( $less(X1,0)
& $less(X0,0) )
=> $less($sum(X0,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).
tff(f5073,plain,
spl107_252,
inference(avatar_split_clause,[],[f1707,f5071]) ).
tff(f5071,plain,
( spl107_252
<=> ! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( 'fun_app$o'(X0,X1)
| ~ 'fun_app$o'(X0,'inc$'(sK57(X0)))
| ~ 'fun_app$o'(X0,'one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_252])]) ).
tff(f1707,plain,
! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( 'fun_app$o'(X0,X1)
| ~ 'fun_app$o'(X0,'inc$'(sK57(X0)))
| ~ 'fun_app$o'(X0,'one$') ),
inference(cnf_transformation,[],[f1026]) ).
tff(f1026,plain,
! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( 'fun_app$o'(X0,X1)
| ( ~ 'fun_app$o'(X0,'inc$'(sK57(X0)))
& 'fun_app$o'(X0,sK57(X0)) )
| ~ 'fun_app$o'(X0,'one$') ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f759,f1025]) ).
tff(f1025,plain,
! [X0: 'Num_bool_fun$'] :
( ? [X2: 'Num$'] :
( ~ 'fun_app$o'(X0,'inc$'(X2))
& 'fun_app$o'(X0,X2) )
=> ( ~ 'fun_app$o'(X0,'inc$'(sK57(X0)))
& 'fun_app$o'(X0,sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f759,plain,
! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( 'fun_app$o'(X0,X1)
| ? [X2: 'Num$'] :
( ~ 'fun_app$o'(X0,'inc$'(X2))
& 'fun_app$o'(X0,X2) )
| ~ 'fun_app$o'(X0,'one$') ),
inference(flattening,[],[f758]) ).
tff(f758,plain,
! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( 'fun_app$o'(X0,X1)
| ? [X2: 'Num$'] :
( ~ 'fun_app$o'(X0,'inc$'(X2))
& 'fun_app$o'(X0,X2) )
| ~ 'fun_app$o'(X0,'one$') ),
inference(ennf_transformation,[],[f280]) ).
tff(f280,axiom,
! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( ( ! [X2: 'Num$'] :
( 'fun_app$o'(X0,X2)
=> 'fun_app$o'(X0,'inc$'(X2)) )
& 'fun_app$o'(X0,'one$') )
=> 'fun_app$o'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
tff(f5069,plain,
spl107_251,
inference(avatar_split_clause,[],[f1683,f5067]) ).
tff(f5067,plain,
( spl107_251
<=> ! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(X0,0)
| ~ $less($sum(X0,X1),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_251])]) ).
tff(f1683,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(X0,0)
| ~ $less($sum(X0,X1),0) ),
inference(cnf_transformation,[],[f741]) ).
tff(f741,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(X0,0)
| ~ $less($sum(X0,X1),0) ),
inference(flattening,[],[f740]) ).
tff(f740,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(X0,0)
| ~ $less($sum(X0,X1),0) ),
inference(ennf_transformation,[],[f475]) ).
tff(f475,axiom,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),0)
=> ( $less(X1,0)
| $less(X0,0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).
tff(f5064,plain,
spl107_250,
inference(avatar_split_clause,[],[f1609,f5062]) ).
tff(f5062,plain,
( spl107_250
<=> ! [X0: 'Nat_a_set_fun$',X1: 'Nat$'] : ( 'conc$'('subsequence$'(X0,'nat$'(0),X1),'suffix$'(X1,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_250])]) ).
tff(f1609,plain,
! [X0: 'Nat_a_set_fun$',X1: 'Nat$'] : ( 'conc$'('subsequence$'(X0,'nat$'(0),X1),'suffix$'(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,axiom,
! [X0: 'Nat_a_set_fun$',X1: 'Nat$'] : ( 'conc$'('subsequence$'(X0,'nat$'(0),X1),'suffix$'(X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
tff(f5060,plain,
spl107_249,
inference(avatar_split_clause,[],[f1607,f5058]) ).
tff(f1607,plain,
! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'gF_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','gF_advice$'(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'gF_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','gF_advice$'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
tff(f5056,plain,
spl107_248,
inference(avatar_split_clause,[],[f1606,f5054]) ).
tff(f5054,plain,
( spl107_248
<=> ! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'fG_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','fG_advice$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_248])]) ).
tff(f1606,plain,
! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'fG_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','fG_advice$'(X0,X1)) ),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'fG_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','fG_advice$'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom123) ).
tff(f5052,plain,
spl107_247,
inference(avatar_split_clause,[],[f1604,f5050]) ).
tff(f5050,plain,
( spl107_247
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ~ $less($sum('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)),'fun_app$k'('of_nat$',X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_247])]) ).
tff(f1604,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ~ $less($sum('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)),'fun_app$k'('of_nat$',X1)),
inference(cnf_transformation,[],[f416]) ).
tff(f416,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ~ $less($sum('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)),'fun_app$k'('of_nat$',X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
tff(f5048,plain,
spl107_246,
inference(avatar_split_clause,[],[f1603,f5046]) ).
tff(f5046,plain,
( spl107_246
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ~ $less($sum('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)),'fun_app$k'('of_nat$',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_246])]) ).
tff(f1603,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ~ $less($sum('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)),'fun_app$k'('of_nat$',X0)),
inference(cnf_transformation,[],[f417]) ).
tff(f417,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ~ $less($sum('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)),'fun_app$k'('of_nat$',X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).
tff(f5044,plain,
spl107_245,
inference(avatar_split_clause,[],[f1445,f5042]) ).
tff(f5042,plain,
( spl107_245
<=> ! [X0: 'Nat_a_set_fun$'] : ( 'build$'('fun_app$j'(X0,'nat$'(0)),'suffix$'('nat$'(1),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_245])]) ).
tff(f1445,plain,
! [X0: 'Nat_a_set_fun$'] : ( 'build$'('fun_app$j'(X0,'nat$'(0)),'suffix$'('nat$'(1),X0)) = X0 ),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
! [X0: 'Nat_a_set_fun$'] : ( 'build$'('fun_app$j'(X0,'nat$'(0)),'suffix$'('nat$'(1),X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).
tff(f5040,plain,
spl107_244,
inference(avatar_split_clause,[],[f612,f5038]) ).
tff(f5038,plain,
( spl107_244
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(X0,X1),X2) = $sum(X0,$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_244])]) ).
tff(f612,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(X0,X1),X2) = $sum(X0,$sum(X1,X2)) ),
introduced(theory_axiom_136,[]) ).
tff(f4708,plain,
( spl107_243
| ~ spl107_43
| ~ spl107_186 ),
inference(avatar_split_clause,[],[f4264,f3986,f2961,f4706]) ).
tff(f4706,plain,
( spl107_243
<=> ! [X0: 'Nat_bool_fun$'] : sP39(X0,'nat$'(0),tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_243])]) ).
tff(f2961,plain,
( spl107_43
<=> ! [X1: 'Nat_bool_fun$'] : 'fun_app$c'('case_nat$a'(tltrue,X1),'nat$'(0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_43])]) ).
tff(f3986,plain,
( spl107_186
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( sP39(X1,X2,X0)
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_186])]) ).
tff(f4264,plain,
( ! [X0: 'Nat_bool_fun$'] : sP39(X0,'nat$'(0),tltrue)
| ~ spl107_43
| ~ spl107_186 ),
inference(resolution,[],[f3987,f2962]) ).
tff(f2962,plain,
( ! [X1: 'Nat_bool_fun$'] : 'fun_app$c'('case_nat$a'(tltrue,X1),'nat$'(0))
| ~ spl107_43 ),
inference(avatar_component_clause,[],[f2961]) ).
tff(f3987,plain,
( ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$c'('case_nat$a'(X0,X1),X2)
| sP39(X1,X2,X0) )
| ~ spl107_186 ),
inference(avatar_component_clause,[],[f3986]) ).
tff(f4579,plain,
( spl107_242
| ~ spl107_40
| ~ spl107_171 ),
inference(avatar_split_clause,[],[f4202,f3926,f2948,f4577]) ).
tff(f4577,plain,
( spl107_242
<=> ! [X0: 'Num$'] : 'fun_app$o'('less$'('one$'),'inc$'(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_242])]) ).
tff(f2948,plain,
( spl107_40
<=> ! [X0: 'Num$'] : $less(0,'sub$'('inc$'(X0),'one$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_40])]) ).
tff(f3926,plain,
( spl107_171
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$o'('less$'(X1),X0)
| ~ $less(0,'sub$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_171])]) ).
tff(f4202,plain,
( ! [X0: 'Num$'] : 'fun_app$o'('less$'('one$'),'inc$'(X0))
| ~ spl107_40
| ~ spl107_171 ),
inference(resolution,[],[f3927,f2949]) ).
tff(f2949,plain,
( ! [X0: 'Num$'] : $less(0,'sub$'('inc$'(X0),'one$'))
| ~ spl107_40 ),
inference(avatar_component_clause,[],[f2948]) ).
tff(f3927,plain,
( ! [X0: 'Num$',X1: 'Num$'] :
( ~ $less(0,'sub$'(X0,X1))
| 'fun_app$o'('less$'(X1),X0) )
| ~ spl107_171 ),
inference(avatar_component_clause,[],[f3926]) ).
tff(f4486,plain,
spl107_241,
inference(avatar_split_clause,[],[f2497,f4484]) ).
tff(f4484,plain,
( spl107_241
<=> ! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum('sub$'('inc$'(X0),'one$'),-1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_241])]) ).
tff(f2497,plain,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum('sub$'('inc$'(X0),'one$'),-1) ),
inference(evaluation,[],[f2254]) ).
tff(f2254,plain,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum('sub$'('inc$'(X0),'one$'),$uminus(1)) ),
inference(definition_unfolding,[],[f1412,f1403]) ).
tff(f1412,plain,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum('numeral$'(X0),$uminus(1)) ),
inference(cnf_transformation,[],[f529]) ).
tff(f529,plain,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum('numeral$'(X0),$uminus(1)) ),
inference(theory_normalization,[],[f313]) ).
tff(f313,axiom,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $difference('numeral$'(X0),1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom311) ).
tff(f4482,plain,
spl107_240,
inference(avatar_split_clause,[],[f2495,f4480]) ).
tff(f4480,plain,
( spl107_240
<=> ! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum(-1,'sub$'('inc$'(X0),'one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_240])]) ).
tff(f2495,plain,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum(-1,'sub$'('inc$'(X0),'one$')) ),
inference(evaluation,[],[f2260]) ).
tff(f2260,plain,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum($uminus(1),'sub$'('inc$'(X0),'one$')) ),
inference(definition_unfolding,[],[f1419,f1403]) ).
tff(f1419,plain,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum($uminus(1),'numeral$'(X0)) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,axiom,
! [X0: 'Num$'] : ( 'sub$'(X0,'one$') = $sum($uminus(1),'numeral$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
tff(f4478,plain,
spl107_239,
inference(avatar_split_clause,[],[f2483,f4476]) ).
tff(f4476,plain,
( spl107_239
<=> ! [X0: $int] :
( ( 'sgn$'(X0) = -1 )
| $less(0,X0)
| ( 0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_239])]) ).
tff(f2483,plain,
! [X0: $int] :
( ( 'sgn$'(X0) = -1 )
| $less(0,X0)
| ( 0 = X0 ) ),
inference(evaluation,[],[f1453]) ).
tff(f1453,plain,
! [X0: $int] :
( ( $uminus(1) = 'sgn$'(X0) )
| $less(0,X0)
| ( 0 = X0 ) ),
inference(cnf_transformation,[],[f699]) ).
tff(f699,plain,
! [X0: $int] :
( ( ( ( ( $uminus(1) = 'sgn$'(X0) )
| $less(0,X0) )
& ( ( 1 = 'sgn$'(X0) )
| ~ $less(0,X0) ) )
| ( 0 = X0 ) )
& ( ( 0 = 'sgn$'(X0) )
| ( 0 != X0 ) ) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,axiom,
! [X0: $int] :
( ( ( 0 != X0 )
=> ( ( ~ $less(0,X0)
=> ( $uminus(1) = 'sgn$'(X0) ) )
& ( $less(0,X0)
=> ( 1 = 'sgn$'(X0) ) ) ) )
& ( ( 0 = X0 )
=> ( 0 = 'sgn$'(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).
tff(f4474,plain,
spl107_238,
inference(avatar_split_clause,[],[f2474,f4472]) ).
tff(f4472,plain,
( spl107_238
<=> ! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ( $uminus('sub$'('inc$'(X0),'one$')) != -1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_238])]) ).
tff(f2474,plain,
! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ( $uminus('sub$'('inc$'(X0),'one$')) != -1 ) ),
inference(evaluation,[],[f2291]) ).
tff(f2291,plain,
! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ( $uminus(1) != $uminus('sub$'('inc$'(X0),'one$')) ) ),
inference(definition_unfolding,[],[f1554,f1403]) ).
tff(f1554,plain,
! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ( $uminus(1) != $uminus('numeral$'(X0)) ) ),
inference(cnf_transformation,[],[f1000]) ).
tff(f1000,plain,
! [X0: 'Num$'] :
( ( ( $uminus(1) = $uminus('numeral$'(X0)) )
| ( 'one$' != X0 ) )
& ( ( 'one$' = X0 )
| ( $uminus(1) != $uminus('numeral$'(X0)) ) ) ),
inference(nnf_transformation,[],[f277]) ).
tff(f277,axiom,
! [X0: 'Num$'] :
( ( $uminus(1) = $uminus('numeral$'(X0)) )
<=> ( 'one$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).
tff(f4470,plain,
spl107_237,
inference(avatar_split_clause,[],[f2471,f4468]) ).
tff(f4468,plain,
( spl107_237
<=> ! [X0: 'Num$'] :
( $less($uminus('sub$'('inc$'(X0),'one$')),-1)
| ( 'one$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_237])]) ).
tff(f2471,plain,
! [X0: 'Num$'] :
( $less($uminus('sub$'('inc$'(X0),'one$')),-1)
| ( 'one$' = X0 ) ),
inference(evaluation,[],[f2294]) ).
tff(f2294,plain,
! [X0: 'Num$'] :
( $less($uminus('sub$'('inc$'(X0),'one$')),$uminus(1))
| ( 'one$' = X0 ) ),
inference(definition_unfolding,[],[f1559,f1403]) ).
tff(f1559,plain,
! [X0: 'Num$'] :
( $less($uminus('numeral$'(X0)),$uminus(1))
| ( 'one$' = X0 ) ),
inference(cnf_transformation,[],[f1002]) ).
tff(f1002,plain,
! [X0: 'Num$'] :
( ( $less($uminus('numeral$'(X0)),$uminus(1))
| ( 'one$' = X0 ) )
& ( ( 'one$' != X0 )
| ~ $less($uminus('numeral$'(X0)),$uminus(1)) ) ),
inference(nnf_transformation,[],[f271]) ).
tff(f271,axiom,
! [X0: 'Num$'] :
( $less($uminus('numeral$'(X0)),$uminus(1))
<=> ( 'one$' != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269) ).
tff(f4464,plain,
spl107_236,
inference(avatar_split_clause,[],[f2425,f4462]) ).
tff(f4462,plain,
( spl107_236
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_236])]) ).
tff(f2425,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP13(X0,X1) ),
inference(evaluation,[],[f1892]) ).
tff(f1892,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,0)
| ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f1143]) ).
tff(f1143,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP13(X0,X1)
| ( ~ $less(0,$sum('fun_app$k'('of_nat$',X1),$uminus('fun_app$k'('of_nat$',X0))))
& ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) )
| ( ~ $less(0,0)
& $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ) )
& ( ( ( $less(0,$sum('fun_app$k'('of_nat$',X1),$uminus('fun_app$k'('of_nat$',X0))))
| $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) )
& ( $less(0,0)
| ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ) )
| ~ sP13(X0,X1) ) ),
inference(rectify,[],[f1142]) ).
tff(f1142,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( sP13(X1,X0)
| ( ~ $less(0,$sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))))
& ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ( ~ $less(0,0)
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) ) )
& ( ( ( $less(0,$sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))))
| $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
& ( $less(0,0)
| ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) ) )
| ~ sP13(X1,X0) ) ),
inference(flattening,[],[f1141]) ).
tff(f1141,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( sP13(X1,X0)
| ( ~ $less(0,$sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))))
& ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ( ~ $less(0,0)
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) ) )
& ( ( ( $less(0,$sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))))
| $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
& ( $less(0,0)
| ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) ) )
| ~ sP13(X1,X0) ) ),
inference(nnf_transformation,[],[f909]) ).
tff(f909,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( sP13(X1,X0)
<=> ( ( $less(0,$sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))))
| $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
& ( $less(0,0)
| ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
tff(f4460,plain,
spl107_235,
inference(avatar_split_clause,[],[f2315,f4458]) ).
tff(f4458,plain,
( spl107_235
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'inc$'('bit0$'(X0)) != 'inc$'('bit0$'(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_235])]) ).
tff(f2315,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'inc$'('bit0$'(X0)) != 'inc$'('bit0$'(X1)) ) ),
inference(definition_unfolding,[],[f1791,f1391,f1391]) ).
tff(f1791,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'bit1$'(X0) != 'bit1$'(X1) ) ),
inference(cnf_transformation,[],[f1080]) ).
tff(f1080,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ( 'bit1$'(X0) = 'bit1$'(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'bit1$'(X0) != 'bit1$'(X1) ) ) ),
inference(nnf_transformation,[],[f331]) ).
tff(f331,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'bit1$'(X0) = 'bit1$'(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).
tff(f4456,plain,
spl107_234,
inference(avatar_split_clause,[],[f2300,f4454]) ).
tff(f4454,plain,
( spl107_234
<=> ! [X0: 'Num$',X1: 'Num$'] : $less($uminus('sub$'('inc$'(X0),'one$')),'sub$'('inc$'(X1),'one$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_234])]) ).
tff(f2300,plain,
! [X0: 'Num$',X1: 'Num$'] : $less($uminus('sub$'('inc$'(X0),'one$')),'sub$'('inc$'(X1),'one$')),
inference(definition_unfolding,[],[f1568,f1403,f1403]) ).
tff(f1568,plain,
! [X0: 'Num$',X1: 'Num$'] : $less($uminus('numeral$'(X0)),'numeral$'(X1)),
inference(cnf_transformation,[],[f249]) ).
tff(f249,axiom,
! [X0: 'Num$',X1: 'Num$'] : $less($uminus('numeral$'(X0)),'numeral$'(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom247) ).
tff(f4452,plain,
spl107_233,
inference(avatar_split_clause,[],[f2299,f4450]) ).
tff(f4450,plain,
( spl107_233
<=> ! [X0: 'Num$',X1: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),$uminus('sub$'('inc$'(X1),'one$'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_233])]) ).
tff(f2299,plain,
! [X0: 'Num$',X1: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),$uminus('sub$'('inc$'(X1),'one$'))),
inference(definition_unfolding,[],[f1567,f1403,f1403]) ).
tff(f1567,plain,
! [X0: 'Num$',X1: 'Num$'] : ~ $less('numeral$'(X0),$uminus('numeral$'(X1))),
inference(cnf_transformation,[],[f248]) ).
tff(f248,axiom,
! [X0: 'Num$',X1: 'Num$'] : ~ $less('numeral$'(X0),$uminus('numeral$'(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom246) ).
tff(f4448,plain,
spl107_232,
inference(avatar_split_clause,[],[f2297,f4446]) ).
tff(f4446,plain,
( spl107_232
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'sub$'('inc$'(X0),'one$') != $uminus('sub$'('inc$'(X1),'one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_232])]) ).
tff(f2297,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'sub$'('inc$'(X0),'one$') != $uminus('sub$'('inc$'(X1),'one$')) ),
inference(definition_unfolding,[],[f1565,f1403,f1403]) ).
tff(f1565,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'numeral$'(X0) != $uminus('numeral$'(X1)) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'numeral$'(X0) != $uminus('numeral$'(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).
tff(f4444,plain,
spl107_231,
inference(avatar_split_clause,[],[f2289,f4442]) ).
tff(f4442,plain,
( spl107_231
<=> ! [X0: 'Num$'] :
( 'fun_app$o'('less$'('one$'),X0)
| ~ $less(1,'sub$'('inc$'(X0),'one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_231])]) ).
tff(f2289,plain,
! [X0: 'Num$'] :
( 'fun_app$o'('less$'('one$'),X0)
| ~ $less(1,'sub$'('inc$'(X0),'one$')) ),
inference(definition_unfolding,[],[f1518,f1403]) ).
tff(f1518,plain,
! [X0: 'Num$'] :
( 'fun_app$o'('less$'('one$'),X0)
| ~ $less(1,'numeral$'(X0)) ),
inference(cnf_transformation,[],[f980]) ).
tff(f980,plain,
! [X0: 'Num$'] :
( ( $less(1,'numeral$'(X0))
| ~ 'fun_app$o'('less$'('one$'),X0) )
& ( 'fun_app$o'('less$'('one$'),X0)
| ~ $less(1,'numeral$'(X0)) ) ),
inference(nnf_transformation,[],[f279]) ).
tff(f279,axiom,
! [X0: 'Num$'] :
( $less(1,'numeral$'(X0))
<=> 'fun_app$o'('less$'('one$'),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).
tff(f4440,plain,
spl107_230,
inference(avatar_split_clause,[],[f2288,f4438]) ).
tff(f4438,plain,
( spl107_230
<=> ! [X0: 'Num$'] :
( $less(1,'sub$'('inc$'(X0),'one$'))
| ~ 'fun_app$o'('less$'('one$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_230])]) ).
tff(f2288,plain,
! [X0: 'Num$'] :
( $less(1,'sub$'('inc$'(X0),'one$'))
| ~ 'fun_app$o'('less$'('one$'),X0) ),
inference(definition_unfolding,[],[f1519,f1403]) ).
tff(f1519,plain,
! [X0: 'Num$'] :
( $less(1,'numeral$'(X0))
| ~ 'fun_app$o'('less$'('one$'),X0) ),
inference(cnf_transformation,[],[f980]) ).
tff(f4436,plain,
spl107_229,
inference(avatar_split_clause,[],[f2210,f4434]) ).
tff(f4434,plain,
( spl107_229
<=> ! [X2: 'A_set$',X0: 'A_set$',X1: 'Nat_a_set_fun$',X3: 'Nat_a_set_fun$'] :
( ( X1 = X3 )
| ( 'build$'(X0,X1) != 'build$'(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_229])]) ).
tff(f2210,plain,
! [X2: 'A_set$',X3: 'Nat_a_set_fun$',X0: 'A_set$',X1: 'Nat_a_set_fun$'] :
( ( X1 = X3 )
| ( 'build$'(X0,X1) != 'build$'(X2,X3) ) ),
inference(cnf_transformation,[],[f1293]) ).
tff(f1293,plain,
! [X0: 'A_set$',X1: 'Nat_a_set_fun$',X2: 'A_set$',X3: 'Nat_a_set_fun$'] :
( ( ( 'build$'(X0,X1) = 'build$'(X2,X3) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X1 = X3 )
& ( X0 = X2 ) )
| ( 'build$'(X0,X1) != 'build$'(X2,X3) ) ) ),
inference(flattening,[],[f1292]) ).
tff(f1292,plain,
! [X0: 'A_set$',X1: 'Nat_a_set_fun$',X2: 'A_set$',X3: 'Nat_a_set_fun$'] :
( ( ( 'build$'(X0,X1) = 'build$'(X2,X3) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X1 = X3 )
& ( X0 = X2 ) )
| ( 'build$'(X0,X1) != 'build$'(X2,X3) ) ) ),
inference(nnf_transformation,[],[f38]) ).
tff(f38,axiom,
! [X0: 'A_set$',X1: 'Nat_a_set_fun$',X2: 'A_set$',X3: 'Nat_a_set_fun$'] :
( ( 'build$'(X0,X1) = 'build$'(X2,X3) )
<=> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).
tff(f4432,plain,
spl107_228,
inference(avatar_split_clause,[],[f2209,f4430]) ).
tff(f4430,plain,
( spl107_228
<=> ! [X0: 'A_set$',X3: 'Nat_a_set_fun$',X2: 'A_set$',X1: 'Nat_a_set_fun$'] :
( ( X0 = X2 )
| ( 'build$'(X0,X1) != 'build$'(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_228])]) ).
tff(f2209,plain,
! [X2: 'A_set$',X3: 'Nat_a_set_fun$',X0: 'A_set$',X1: 'Nat_a_set_fun$'] :
( ( X0 = X2 )
| ( 'build$'(X0,X1) != 'build$'(X2,X3) ) ),
inference(cnf_transformation,[],[f1293]) ).
tff(f4428,plain,
spl107_227,
inference(avatar_split_clause,[],[f2146,f4426]) ).
tff(f4426,plain,
( spl107_227
<=> ! [X2: 'Nat_a_set_fun$',X0: 'A_set_list$',X1: 'Nat_a_set_fun$'] :
( ( X1 = X2 )
| ( 'conc$'(X0,X1) != 'conc$'(X0,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_227])]) ).
tff(f2146,plain,
! [X2: 'Nat_a_set_fun$',X0: 'A_set_list$',X1: 'Nat_a_set_fun$'] :
( ( X1 = X2 )
| ( 'conc$'(X0,X1) != 'conc$'(X0,X2) ) ),
inference(cnf_transformation,[],[f1269]) ).
tff(f1269,plain,
! [X0: 'A_set_list$',X1: 'Nat_a_set_fun$',X2: 'Nat_a_set_fun$'] :
( ( ( 'conc$'(X0,X1) = 'conc$'(X0,X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( 'conc$'(X0,X1) != 'conc$'(X0,X2) ) ) ),
inference(nnf_transformation,[],[f274]) ).
tff(f274,axiom,
! [X0: 'A_set_list$',X1: 'Nat_a_set_fun$',X2: 'Nat_a_set_fun$'] :
( ( 'conc$'(X0,X1) = 'conc$'(X0,X2) )
<=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
tff(f4424,plain,
( spl107_226
| ~ spl107_4
| ~ spl107_122 ),
inference(avatar_split_clause,[],[f3637,f3405,f2790,f4422]) ).
tff(f4422,plain,
( spl107_226
<=> ! [X0: 'Nat$'] : ( tltrue = def_1('uuj$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_226])]) ).
tff(f3405,plain,
( spl107_122
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_1(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_122])]) ).
tff(f3637,plain,
( ! [X0: 'Nat$'] : ( tltrue = def_1('uuj$',X0) )
| ~ spl107_4
| ~ spl107_122 ),
inference(resolution,[],[f3406,f2791]) ).
tff(f3406,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,X1)
| ( tltrue = def_1(X0,X1) ) )
| ~ spl107_122 ),
inference(avatar_component_clause,[],[f3405]) ).
tff(f4420,plain,
spl107_225,
inference(avatar_split_clause,[],[f2119,f4418]) ).
tff(f2119,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat_nat_fun$'] :
( 'fun_app$c'('uuf$'(X0,X1),X2)
| ~ 'fun_app$c'(X0,'fun_app$e'(X1,X2)) ),
inference(cnf_transformation,[],[f1255]) ).
tff(f1255,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat_nat_fun$',X2: 'Nat$'] :
( ( 'fun_app$c'('uuf$'(X0,X1),X2)
| ~ 'fun_app$c'(X0,'fun_app$e'(X1,X2)) )
& ( 'fun_app$c'(X0,'fun_app$e'(X1,X2))
| ~ 'fun_app$c'('uuf$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f7,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat_nat_fun$',X2: 'Nat$'] :
( 'fun_app$c'('uuf$'(X0,X1),X2)
<=> 'fun_app$c'(X0,'fun_app$e'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
tff(f4416,plain,
spl107_224,
inference(avatar_split_clause,[],[f2118,f4414]) ).
tff(f4414,plain,
( spl107_224
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat_nat_fun$'] :
( 'fun_app$c'(X0,'fun_app$e'(X1,X2))
| ~ 'fun_app$c'('uuf$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_224])]) ).
tff(f2118,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat_nat_fun$'] :
( 'fun_app$c'(X0,'fun_app$e'(X1,X2))
| ~ 'fun_app$c'('uuf$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1255]) ).
tff(f4412,plain,
spl107_223,
inference(avatar_split_clause,[],[f2117,f4410]) ).
tff(f4410,plain,
( spl107_223
<=> ! [X2: 'Nat$',X0: 'Bool_bool_fun$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('uuh$'(X0,X1),X2)
| ~ 'fun_app$d'(X0,def_1(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_223])]) ).
tff(f2117,plain,
! [X2: 'Nat$',X0: 'Bool_bool_fun$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('uuh$'(X0,X1),X2)
| ~ 'fun_app$d'(X0,def_1(X1,X2)) ),
inference(cnf_transformation,[],[f1254]) ).
tff(f1254,plain,
! [X0: 'Bool_bool_fun$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( 'fun_app$c'('uuh$'(X0,X1),X2)
| ~ 'fun_app$d'(X0,def_1(X1,X2)) )
& ( 'fun_app$d'(X0,def_1(X1,X2))
| ~ 'fun_app$c'('uuh$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f5,axiom,
! [X0: 'Bool_bool_fun$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( 'fun_app$c'('uuh$'(X0,X1),X2)
<=> 'fun_app$d'(X0,def_1(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
tff(f4408,plain,
spl107_222,
inference(avatar_split_clause,[],[f2116,f4406]) ).
tff(f4406,plain,
( spl107_222
<=> ! [X2: 'Nat$',X0: 'Bool_bool_fun$',X1: 'Nat_bool_fun$'] :
( 'fun_app$d'(X0,def_1(X1,X2))
| ~ 'fun_app$c'('uuh$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_222])]) ).
tff(f2116,plain,
! [X2: 'Nat$',X0: 'Bool_bool_fun$',X1: 'Nat_bool_fun$'] :
( 'fun_app$d'(X0,def_1(X1,X2))
| ~ 'fun_app$c'('uuh$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1254]) ).
tff(f4404,plain,
spl107_221,
inference(avatar_split_clause,[],[f2071,f4402]) ).
tff(f4402,plain,
( spl107_221
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X2)
| ~ $less($sum(X0,X1),$sum(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_221])]) ).
tff(f2071,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X2)
| ~ $less($sum(X0,X1),$sum(X0,X2)) ),
inference(cnf_transformation,[],[f826]) ).
tff(f826,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X1,X2)
| ~ $less($sum(X0,X1),$sum(X0,X2)) ),
inference(ennf_transformation,[],[f428]) ).
tff(f428,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less($sum(X0,X1),$sum(X0,X2))
=> $less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
tff(f4400,plain,
spl107_220,
inference(avatar_split_clause,[],[f2070,f4398]) ).
tff(f4398,plain,
( spl107_220
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less($sum(X0,X1),$sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_220])]) ).
tff(f2070,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less($sum(X0,X1),$sum(X2,X1)) ),
inference(cnf_transformation,[],[f825]) ).
tff(f825,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,X2)
| ~ $less($sum(X0,X1),$sum(X2,X1)) ),
inference(ennf_transformation,[],[f427]) ).
tff(f427,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less($sum(X0,X1),$sum(X2,X1))
=> $less(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).
tff(f4396,plain,
spl107_219,
inference(avatar_split_clause,[],[f2063,f4394]) ).
tff(f4394,plain,
( spl107_219
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( X1 = X2 )
| ( $sum(X0,X1) != $sum(X0,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_219])]) ).
tff(f2063,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( X1 = X2 )
| ( $sum(X0,X1) != $sum(X0,X2) ) ),
inference(cnf_transformation,[],[f819]) ).
tff(f819,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( X1 = X2 )
| ( $sum(X0,X1) != $sum(X0,X2) ) ),
inference(ennf_transformation,[],[f452]) ).
tff(f452,axiom,
! [X0: $int,X1: $int,X2: $int] :
( ( $sum(X0,X1) = $sum(X0,X2) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).
tff(f4392,plain,
spl107_218,
inference(avatar_split_clause,[],[f2062,f4390]) ).
tff(f4390,plain,
( spl107_218
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( X0 = X2 )
| ( $sum(X0,X1) != $sum(X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_218])]) ).
tff(f2062,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( X0 = X2 )
| ( $sum(X0,X1) != $sum(X2,X1) ) ),
inference(cnf_transformation,[],[f818]) ).
tff(f818,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( X0 = X2 )
| ( $sum(X0,X1) != $sum(X2,X1) ) ),
inference(ennf_transformation,[],[f451]) ).
tff(f451,axiom,
! [X0: $int,X1: $int,X2: $int] :
( ( $sum(X0,X1) = $sum(X2,X1) )
=> ( X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
tff(f4388,plain,
spl107_217,
inference(avatar_split_clause,[],[f2057,f4386]) ).
tff(f4386,plain,
( spl107_217
<=> ! [X2: 'Nat$',X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('mu_stable$'(X0),'suffix$'(X2,X1))
| ~ 'fun_app$b'('mu_stable$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_217])]) ).
tff(f2057,plain,
! [X2: 'Nat$',X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('mu_stable$'(X0),'suffix$'(X2,X1))
| ~ 'fun_app$b'('mu_stable$'(X0),X1) ),
inference(cnf_transformation,[],[f813]) ).
tff(f813,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X2: 'Nat$'] :
( 'fun_app$b'('mu_stable$'(X0),'suffix$'(X2,X1))
| ~ 'fun_app$b'('mu_stable$'(X0),X1) ),
inference(ennf_transformation,[],[f257]) ).
tff(f257,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X2: 'Nat$'] :
( 'fun_app$b'('mu_stable$'(X0),X1)
=> 'fun_app$b'('mu_stable$'(X0),'suffix$'(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom255) ).
tff(f4384,plain,
spl107_216,
inference(avatar_split_clause,[],[f2056,f4382]) ).
tff(f4382,plain,
( spl107_216
<=> ! [X2: 'Nat$',X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('nu_stable$'(X0),'suffix$'(X2,X1))
| ~ 'fun_app$b'('nu_stable$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_216])]) ).
tff(f2056,plain,
! [X2: 'Nat$',X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('nu_stable$'(X0),'suffix$'(X2,X1))
| ~ 'fun_app$b'('nu_stable$'(X0),X1) ),
inference(cnf_transformation,[],[f812]) ).
tff(f812,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X2: 'Nat$'] :
( 'fun_app$b'('nu_stable$'(X0),'suffix$'(X2,X1))
| ~ 'fun_app$b'('nu_stable$'(X0),X1) ),
inference(ennf_transformation,[],[f256]) ).
tff(f256,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X2: 'Nat$'] :
( 'fun_app$b'('nu_stable$'(X0),X1)
=> 'fun_app$b'('nu_stable$'(X0),'suffix$'(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).
tff(f4380,plain,
( spl107_215
| ~ spl107_4
| ~ spl107_120 ),
inference(avatar_split_clause,[],[f3633,f3397,f2790,f4378]) ).
tff(f4378,plain,
( spl107_215
<=> ! [X0: 'Nat$'] : ( tltrue = def_3('uuj$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_215])]) ).
tff(f3397,plain,
( spl107_120
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( def_3(X0,X1) = tltrue )
| ~ 'fun_app$c'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_120])]) ).
tff(f3633,plain,
( ! [X0: 'Nat$'] : ( tltrue = def_3('uuj$',X0) )
| ~ spl107_4
| ~ spl107_120 ),
inference(resolution,[],[f3398,f2791]) ).
tff(f3398,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,X1)
| ( def_3(X0,X1) = tltrue ) )
| ~ spl107_120 ),
inference(avatar_component_clause,[],[f3397]) ).
tff(f4376,plain,
spl107_214,
inference(avatar_split_clause,[],[f2055,f4374]) ).
tff(f4374,plain,
( spl107_214
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X0),$sum(X2,X1))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_214])]) ).
tff(f2055,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X0),$sum(X2,X1))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f811]) ).
tff(f811,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less($sum(X2,X0),$sum(X2,X1))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f430]) ).
tff(f430,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,X1)
=> $less($sum(X2,X0),$sum(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).
tff(f4372,plain,
spl107_213,
inference(avatar_split_clause,[],[f1899,f4370]) ).
tff(f4370,plain,
( spl107_213
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( sP13(X1,X0)
| ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_213])]) ).
tff(f1899,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP13(X1,X0)
| ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1144]) ).
tff(f1144,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP13(X1,X0)
| ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) )
& ( $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP13(X1,X0) ) ),
inference(nnf_transformation,[],[f910]) ).
tff(f910,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP13(X1,X0)
<=> $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ),
inference(definition_folding,[],[f795,f909]) ).
tff(f795,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( $less(0,$sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))))
| $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
& ( $less(0,0)
| ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) ) )
<=> $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f579]) ).
tff(f579,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1))
=> $less(0,$sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1)))) )
& ( $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1))
=> $less(0,0) ) )
<=> $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ),
inference(theory_normalization,[],[f221]) ).
tff(f221,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1))
=> $less(0,$difference('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1))) )
& ( $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1))
=> $less(0,0) ) )
<=> $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).
tff(f4368,plain,
spl107_212,
inference(avatar_split_clause,[],[f1898,f4366]) ).
tff(f4366,plain,
( spl107_212
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP13(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_212])]) ).
tff(f1898,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP13(X1,X0) ),
inference(cnf_transformation,[],[f1144]) ).
tff(f4364,plain,
spl107_211,
inference(avatar_split_clause,[],[f1848,f4362]) ).
tff(f4362,plain,
( spl107_211
<=> ! [X0: 'A_ltln$',X1: 'A_ltln$'] :
( ( X0 = X1 )
| ( 'fun_app$i'('next_ltln$',X1) != 'fun_app$i'('next_ltln$',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_211])]) ).
tff(f1848,plain,
! [X0: 'A_ltln$',X1: 'A_ltln$'] :
( ( X0 = X1 )
| ( 'fun_app$i'('next_ltln$',X1) != 'fun_app$i'('next_ltln$',X0) ) ),
inference(cnf_transformation,[],[f1109]) ).
tff(f1109,plain,
! [X0: 'A_ltln$',X1: 'A_ltln$'] :
( ( ( 'fun_app$i'('next_ltln$',X1) = 'fun_app$i'('next_ltln$',X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$i'('next_ltln$',X1) != 'fun_app$i'('next_ltln$',X0) ) ) ),
inference(nnf_transformation,[],[f19]) ).
tff(f19,axiom,
! [X0: 'A_ltln$',X1: 'A_ltln$'] :
( ( 'fun_app$i'('next_ltln$',X1) = 'fun_app$i'('next_ltln$',X0) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
tff(f4360,plain,
spl107_210,
inference(avatar_split_clause,[],[f1788,f4358]) ).
tff(f1788,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_8(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) ),
inference(cnf_transformation,[],[f1078]) ).
tff(f1078,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ( tltrue = def_8(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) )
& ( 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue != def_8(X0,X1) ) ) ),
inference(nnf_transformation,[],[f674]) ).
tff(f674,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_8(X0,X1) )
<=> 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) ),
inference(rectify,[],[f513]) ).
tff(f513,axiom,
! [X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( tltrue = def_8(X2,X3) )
<=> 'fun_app$c'(X2,'fun_app$e'('pred$',X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_512) ).
tff(f4356,plain,
spl107_209,
inference(avatar_split_clause,[],[f1787,f4354]) ).
tff(f4354,plain,
( spl107_209
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue != def_8(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_209])]) ).
tff(f1787,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue != def_8(X0,X1) ) ),
inference(cnf_transformation,[],[f1078]) ).
tff(f4352,plain,
spl107_208,
inference(avatar_split_clause,[],[f1786,f4350]) ).
tff(f1786,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_10(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) ),
inference(cnf_transformation,[],[f1077]) ).
tff(f1077,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ( tltrue = def_10(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) )
& ( 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue != def_10(X0,X1) ) ) ),
inference(nnf_transformation,[],[f673]) ).
tff(f673,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_10(X0,X1) )
<=> 'fun_app$c'(X0,'fun_app$e'('pred$',X1)) ),
inference(rectify,[],[f515]) ).
tff(f515,axiom,
! [X2: 'Nat_bool_fun$',X3: 'Nat$'] :
( ( tltrue = def_10(X2,X3) )
<=> 'fun_app$c'(X2,'fun_app$e'('pred$',X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_514) ).
tff(f4348,plain,
spl107_207,
inference(avatar_split_clause,[],[f1785,f4346]) ).
tff(f4346,plain,
( spl107_207
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue != def_10(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_207])]) ).
tff(f1785,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,'fun_app$e'('pred$',X1))
| ( tltrue != def_10(X0,X1) ) ),
inference(cnf_transformation,[],[f1077]) ).
tff(f4344,plain,
spl107_206,
inference(avatar_split_clause,[],[f1755,f4342]) ).
tff(f4342,plain,
( spl107_206
<=> ! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X12: 'A_ltln$',X1: 'A_ltln_a_ltln_fun$'] :
( 'fun_app$l'('fun_app$m'(X0,X12),'fun_app$i'(X1,X12))
| ~ 'gF_advice_congruent_axioms$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_206])]) ).
tff(f1755,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln_a_ltln_fun$',X12: 'A_ltln$'] :
( 'fun_app$l'('fun_app$m'(X0,X12),'fun_app$i'(X1,X12))
| ~ 'gF_advice_congruent_axioms$'(X0,X1) ),
inference(cnf_transformation,[],[f1063]) ).
tff(f1063,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln_a_ltln_fun$'] :
( ( ! [X2: 'A_ltln$',X3: 'A_ltln$',X4: 'A_ltln_set$'] :
( 'fun_app$l'('fun_app$m'(X0,'gF_advice$'('fun_app$i'(X1,X2),X4)),'gF_advice$'('fun_app$i'(X1,X3),X4))
| ~ 'fun_app$l'('fun_app$m'(X0,X2),X3) )
& ! [X5: 'Nat_a_set_fun$',X6: 'A_ltln$',X7: 'A_ltln_set$'] :
( 'semantics_ltln$'('suffix$'(sK78(X5,X6,X7),X5),'gF_advice$'('foldl$'('af_letter$',X6,'subsequence$'(X5,'nat$'(0),sK78(X5,X6,X7))),X7))
| ~ 'semantics_ltln$'(X5,'gF_advice$'('fun_app$i'(X1,X6),X7)) )
& ! [X9: 'Nat_a_set_fun$',X10: 'A_ltln$',X11: 'A_ltln_set$'] :
( 'semantics_ltln$'(X9,'gF_advice$'('fun_app$i'(X1,X10),X11))
| ~ 'semantics_ltln$'(X9,'gF_advice$'(X10,X11)) )
& ! [X12: 'A_ltln$'] : 'fun_app$l'('fun_app$m'(X0,X12),'fun_app$i'(X1,X12)) )
| ~ 'gF_advice_congruent_axioms$'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f794,f1062]) ).
tff(f1062,plain,
! [X5: 'Nat_a_set_fun$',X6: 'A_ltln$',X7: 'A_ltln_set$'] :
( ? [X8: 'Nat$'] : 'semantics_ltln$'('suffix$'(X8,X5),'gF_advice$'('foldl$'('af_letter$',X6,'subsequence$'(X5,'nat$'(0),X8)),X7))
=> 'semantics_ltln$'('suffix$'(sK78(X5,X6,X7),X5),'gF_advice$'('foldl$'('af_letter$',X6,'subsequence$'(X5,'nat$'(0),sK78(X5,X6,X7))),X7)) ),
introduced(choice_axiom,[]) ).
tff(f794,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln_a_ltln_fun$'] :
( ( ! [X2: 'A_ltln$',X3: 'A_ltln$',X4: 'A_ltln_set$'] :
( 'fun_app$l'('fun_app$m'(X0,'gF_advice$'('fun_app$i'(X1,X2),X4)),'gF_advice$'('fun_app$i'(X1,X3),X4))
| ~ 'fun_app$l'('fun_app$m'(X0,X2),X3) )
& ! [X5: 'Nat_a_set_fun$',X6: 'A_ltln$',X7: 'A_ltln_set$'] :
( ? [X8: 'Nat$'] : 'semantics_ltln$'('suffix$'(X8,X5),'gF_advice$'('foldl$'('af_letter$',X6,'subsequence$'(X5,'nat$'(0),X8)),X7))
| ~ 'semantics_ltln$'(X5,'gF_advice$'('fun_app$i'(X1,X6),X7)) )
& ! [X9: 'Nat_a_set_fun$',X10: 'A_ltln$',X11: 'A_ltln_set$'] :
( 'semantics_ltln$'(X9,'gF_advice$'('fun_app$i'(X1,X10),X11))
| ~ 'semantics_ltln$'(X9,'gF_advice$'(X10,X11)) )
& ! [X12: 'A_ltln$'] : 'fun_app$l'('fun_app$m'(X0,X12),'fun_app$i'(X1,X12)) )
| ~ 'gF_advice_congruent_axioms$'(X0,X1) ),
inference(ennf_transformation,[],[f690]) ).
tff(f690,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln_a_ltln_fun$'] :
( 'gF_advice_congruent_axioms$'(X0,X1)
=> ( ! [X2: 'A_ltln$',X3: 'A_ltln$',X4: 'A_ltln_set$'] :
( 'fun_app$l'('fun_app$m'(X0,X2),X3)
=> 'fun_app$l'('fun_app$m'(X0,'gF_advice$'('fun_app$i'(X1,X2),X4)),'gF_advice$'('fun_app$i'(X1,X3),X4)) )
& ! [X5: 'Nat_a_set_fun$',X6: 'A_ltln$',X7: 'A_ltln_set$'] :
( 'semantics_ltln$'(X5,'gF_advice$'('fun_app$i'(X1,X6),X7))
=> ? [X8: 'Nat$'] : 'semantics_ltln$'('suffix$'(X8,X5),'gF_advice$'('foldl$'('af_letter$',X6,'subsequence$'(X5,'nat$'(0),X8)),X7)) )
& ! [X9: 'Nat_a_set_fun$',X10: 'A_ltln$',X11: 'A_ltln_set$'] :
( 'semantics_ltln$'(X9,'gF_advice$'(X10,X11))
=> 'semantics_ltln$'(X9,'gF_advice$'('fun_app$i'(X1,X10),X11)) )
& ! [X12: 'A_ltln$'] : 'fun_app$l'('fun_app$m'(X0,X12),'fun_app$i'(X1,X12)) ) ),
inference(unused_predicate_definition_removal,[],[f672]) ).
tff(f672,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln_a_ltln_fun$'] :
( 'gF_advice_congruent_axioms$'(X0,X1)
<=> ( ! [X2: 'A_ltln$',X3: 'A_ltln$',X4: 'A_ltln_set$'] :
( 'fun_app$l'('fun_app$m'(X0,X2),X3)
=> 'fun_app$l'('fun_app$m'(X0,'gF_advice$'('fun_app$i'(X1,X2),X4)),'gF_advice$'('fun_app$i'(X1,X3),X4)) )
& ! [X5: 'Nat_a_set_fun$',X6: 'A_ltln$',X7: 'A_ltln_set$'] :
( 'semantics_ltln$'(X5,'gF_advice$'('fun_app$i'(X1,X6),X7))
=> ? [X8: 'Nat$'] : 'semantics_ltln$'('suffix$'(X8,X5),'gF_advice$'('foldl$'('af_letter$',X6,'subsequence$'(X5,'nat$'(0),X8)),X7)) )
& ! [X9: 'Nat_a_set_fun$',X10: 'A_ltln$',X11: 'A_ltln_set$'] :
( 'semantics_ltln$'(X9,'gF_advice$'(X10,X11))
=> 'semantics_ltln$'(X9,'gF_advice$'('fun_app$i'(X1,X10),X11)) )
& ! [X12: 'A_ltln$'] : 'fun_app$l'('fun_app$m'(X0,X12),'fun_app$i'(X1,X12)) ) ),
inference(rectify,[],[f150]) ).
tff(f150,axiom,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln_a_ltln_fun$'] :
( 'gF_advice_congruent_axioms$'(X0,X1)
<=> ( ! [X2: 'A_ltln$',X3: 'A_ltln$',X4: 'A_ltln_set$'] :
( 'fun_app$l'('fun_app$m'(X0,X2),X3)
=> 'fun_app$l'('fun_app$m'(X0,'gF_advice$'('fun_app$i'(X1,X2),X4)),'gF_advice$'('fun_app$i'(X1,X3),X4)) )
& ! [X2: 'Nat_a_set_fun$',X3: 'A_ltln$',X4: 'A_ltln_set$'] :
( 'semantics_ltln$'(X2,'gF_advice$'('fun_app$i'(X1,X3),X4))
=> ? [X5: 'Nat$'] : 'semantics_ltln$'('suffix$'(X5,X2),'gF_advice$'('foldl$'('af_letter$',X3,'subsequence$'(X2,'nat$'(0),X5)),X4)) )
& ! [X2: 'Nat_a_set_fun$',X3: 'A_ltln$',X4: 'A_ltln_set$'] :
( 'semantics_ltln$'(X2,'gF_advice$'(X3,X4))
=> 'semantics_ltln$'(X2,'gF_advice$'('fun_app$i'(X1,X3),X4)) )
& ! [X2: 'A_ltln$'] : 'fun_app$l'('fun_app$m'(X0,X2),'fun_app$i'(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).
tff(f4340,plain,
spl107_205,
inference(avatar_split_clause,[],[f1741,f4338]) ).
tff(f4338,plain,
( spl107_205
<=> ! [X0: 'A_ltln_a_ltln_fun$'] :
( 'semantics_ltln$'(sK65(X0),'gF_advice$'(sK66(X0),sK67(X0)))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_205])]) ).
tff(f1741,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( 'semantics_ltln$'(sK65(X0),'gF_advice$'(sK66(X0),sK67(X0)))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f1048]) ).
tff(f1048,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ( ~ 'semantics_ltln$'(sK65(X0),'gF_advice$'('fun_app$i'(X0,sK66(X0)),sK67(X0)))
& 'semantics_ltln$'(sK65(X0),'gF_advice$'(sK66(X0),sK67(X0))) )
| ~ sP10(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65,sK66,sK67])],[f1046,f1047]) ).
tff(f1047,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ? [X1: 'Nat_a_set_fun$',X2: 'A_ltln$',X3: 'A_ltln_set$'] :
( ~ 'semantics_ltln$'(X1,'gF_advice$'('fun_app$i'(X0,X2),X3))
& 'semantics_ltln$'(X1,'gF_advice$'(X2,X3)) )
=> ( ~ 'semantics_ltln$'(sK65(X0),'gF_advice$'('fun_app$i'(X0,sK66(X0)),sK67(X0)))
& 'semantics_ltln$'(sK65(X0),'gF_advice$'(sK66(X0),sK67(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1046,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ? [X1: 'Nat_a_set_fun$',X2: 'A_ltln$',X3: 'A_ltln_set$'] :
( ~ 'semantics_ltln$'(X1,'gF_advice$'('fun_app$i'(X0,X2),X3))
& 'semantics_ltln$'(X1,'gF_advice$'(X2,X3)) )
| ~ sP10(X0) ),
inference(rectify,[],[f1045]) ).
tff(f1045,plain,
! [X1: 'A_ltln_a_ltln_fun$'] :
( ? [X9: 'Nat_a_set_fun$',X10: 'A_ltln$',X11: 'A_ltln_set$'] :
( ~ 'semantics_ltln$'(X9,'gF_advice$'('fun_app$i'(X1,X10),X11))
& 'semantics_ltln$'(X9,'gF_advice$'(X10,X11)) )
| ~ sP10(X1) ),
inference(nnf_transformation,[],[f903]) ).
tff(f903,plain,
! [X1: 'A_ltln_a_ltln_fun$'] :
( ? [X9: 'Nat_a_set_fun$',X10: 'A_ltln$',X11: 'A_ltln_set$'] :
( ~ 'semantics_ltln$'(X9,'gF_advice$'('fun_app$i'(X1,X10),X11))
& 'semantics_ltln$'(X9,'gF_advice$'(X10,X11)) )
| ~ sP10(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
tff(f4336,plain,
spl107_204,
inference(avatar_split_clause,[],[f1733,f4334]) ).
tff(f4334,plain,
( spl107_204
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_204])]) ).
tff(f1733,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1042]) ).
tff(f1042,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 0 != $sum('fun_app$k'('of_nat$',X1),$uminus('fun_app$k'('of_nat$',X0))) )
& ~ $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) )
| ~ sP9(X0,X1) ),
inference(rectify,[],[f1041]) ).
tff(f1041,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( ( 0 != $sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))) )
& ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP9(X1,X0) ),
inference(nnf_transformation,[],[f901]) ).
tff(f901,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( ( 0 != $sum('fun_app$k'('of_nat$',X0),$uminus('fun_app$k'('of_nat$',X1))) )
& ~ $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP9(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
tff(f4332,plain,
spl107_203,
inference(avatar_split_clause,[],[f1706,f4330]) ).
tff(f4330,plain,
( spl107_203
<=> ! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( 'fun_app$o'(X0,X1)
| 'fun_app$o'(X0,sK57(X0))
| ~ 'fun_app$o'(X0,'one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_203])]) ).
tff(f1706,plain,
! [X0: 'Num_bool_fun$',X1: 'Num$'] :
( 'fun_app$o'(X0,X1)
| 'fun_app$o'(X0,sK57(X0))
| ~ 'fun_app$o'(X0,'one$') ),
inference(cnf_transformation,[],[f1026]) ).
tff(f4328,plain,
spl107_202,
inference(avatar_split_clause,[],[f1598,f4326]) ).
tff(f4326,plain,
( spl107_202
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X0),$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_202])]) ).
tff(f1598,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X0),$uminus(X1)) ),
inference(cnf_transformation,[],[f354]) ).
tff(f354,axiom,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X0),$uminus(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom352) ).
tff(f4324,plain,
spl107_201,
inference(avatar_split_clause,[],[f1578,f4322]) ).
tff(f4322,plain,
( spl107_201
<=> ! [X0: $int,X1: $int] : ( $sum(X1,$uminus(X0)) = $uminus($sum(X0,$uminus(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_201])]) ).
tff(f1578,plain,
! [X0: $int,X1: $int] : ( $sum(X1,$uminus(X0)) = $uminus($sum(X0,$uminus(X1))) ),
inference(cnf_transformation,[],[f554]) ).
tff(f554,plain,
! [X0: $int,X1: $int] : ( $sum(X1,$uminus(X0)) = $uminus($sum(X0,$uminus(X1))) ),
inference(theory_normalization,[],[f211]) ).
tff(f211,axiom,
! [X0: $int,X1: $int] : ( $uminus($difference(X0,X1)) = $difference(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).
tff(f4320,plain,
spl107_200,
inference(avatar_split_clause,[],[f1562,f4318]) ).
tff(f4318,plain,
( spl107_200
<=> ! [X0: 'A_ltln_a_ltln_fun$'] :
( ( 'id$' = X0 )
| ( sK54(X0) != 'fun_app$i'(X0,sK54(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_200])]) ).
tff(f1562,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ( 'id$' = X0 )
| ( sK54(X0) != 'fun_app$i'(X0,sK54(X0)) ) ),
inference(cnf_transformation,[],[f1007]) ).
tff(f1007,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ( ! [X1: 'A_ltln$'] : ( 'fun_app$i'(X0,X1) = X1 )
| ( 'id$' != X0 ) )
& ( ( 'id$' = X0 )
| ( sK54(X0) != 'fun_app$i'(X0,sK54(X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f1005,f1006]) ).
tff(f1006,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ? [X2: 'A_ltln$'] : ( 'fun_app$i'(X0,X2) != X2 )
=> ( sK54(X0) != 'fun_app$i'(X0,sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1005,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ( ! [X1: 'A_ltln$'] : ( 'fun_app$i'(X0,X1) = X1 )
| ( 'id$' != X0 ) )
& ( ( 'id$' = X0 )
| ? [X2: 'A_ltln$'] : ( 'fun_app$i'(X0,X2) != X2 ) ) ),
inference(rectify,[],[f1004]) ).
tff(f1004,plain,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ( ! [X1: 'A_ltln$'] : ( 'fun_app$i'(X0,X1) = X1 )
| ( 'id$' != X0 ) )
& ( ( 'id$' = X0 )
| ? [X1: 'A_ltln$'] : ( 'fun_app$i'(X0,X1) != X1 ) ) ),
inference(nnf_transformation,[],[f188]) ).
tff(f188,axiom,
! [X0: 'A_ltln_a_ltln_fun$'] :
( ! [X1: 'A_ltln$'] : ( 'fun_app$i'(X0,X1) = X1 )
<=> ( 'id$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).
tff(f4316,plain,
spl107_199,
inference(avatar_split_clause,[],[f1549,f4314]) ).
tff(f4314,plain,
( spl107_199
<=> ! [X0: 'Nat$'] :
( ( 0 = 'fun_app$k'('of_nat$',X0) )
| ~ $less('fun_app$k'('of_nat$',X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_199])]) ).
tff(f1549,plain,
! [X0: 'Nat$'] :
( ( 0 = 'fun_app$k'('of_nat$',X0) )
| ~ $less('fun_app$k'('of_nat$',X0),1) ),
inference(cnf_transformation,[],[f998]) ).
tff(f998,plain,
! [X0: 'Nat$'] :
( ( $less('fun_app$k'('of_nat$',X0),1)
| ( 0 != 'fun_app$k'('of_nat$',X0) ) )
& ( ( 0 = 'fun_app$k'('of_nat$',X0) )
| ~ $less('fun_app$k'('of_nat$',X0),1) ) ),
inference(nnf_transformation,[],[f52]) ).
tff(f52,axiom,
! [X0: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X0),1)
<=> ( 0 = 'fun_app$k'('of_nat$',X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
tff(f4312,plain,
spl107_198,
inference(avatar_split_clause,[],[f1540,f4310]) ).
tff(f4310,plain,
( spl107_198
<=> ! [X0: 'Nat$'] :
( ( 0 = 'fun_app$k'('of_nat$',X0) )
| ~ 'fun_app$c'('case_nat$a'(tltrue,'uui$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_198])]) ).
tff(f1540,plain,
! [X0: 'Nat$'] :
( ( 0 = 'fun_app$k'('of_nat$',X0) )
| ~ 'fun_app$c'('case_nat$a'(tltrue,'uui$'),X0) ),
inference(cnf_transformation,[],[f990]) ).
tff(f990,plain,
! [X0: 'Nat$'] :
( ( ( 0 = 'fun_app$k'('of_nat$',X0) )
| ~ 'fun_app$c'('case_nat$a'(tltrue,'uui$'),X0) )
& ( 'fun_app$c'('case_nat$a'(tltrue,'uui$'),X0)
| ( 0 != 'fun_app$k'('of_nat$',X0) ) ) ),
inference(nnf_transformation,[],[f303]) ).
tff(f303,axiom,
! [X0: 'Nat$'] :
( ( 0 = 'fun_app$k'('of_nat$',X0) )
<=> 'fun_app$c'('case_nat$a'(tltrue,'uui$'),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom301) ).
tff(f4308,plain,
spl107_197,
inference(avatar_split_clause,[],[f1539,f4306]) ).
tff(f4306,plain,
( spl107_197
<=> ! [X0: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(tltrue,'uui$'),X0)
| ( 0 != 'fun_app$k'('of_nat$',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_197])]) ).
tff(f1539,plain,
! [X0: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(tltrue,'uui$'),X0)
| ( 0 != 'fun_app$k'('of_nat$',X0) ) ),
inference(cnf_transformation,[],[f990]) ).
tff(f4304,plain,
spl107_196,
inference(avatar_split_clause,[],[f1532,f4302]) ).
tff(f4302,plain,
( spl107_196
<=> ! [X0: 'Nat$'] :
( ( 0 != 'fun_app$k'('of_nat$',X0) )
| ~ 'fun_app$c'('case_nat$a'(tlfalse,'uuj$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_196])]) ).
tff(f1532,plain,
! [X0: 'Nat$'] :
( ( 0 != 'fun_app$k'('of_nat$',X0) )
| ~ 'fun_app$c'('case_nat$a'(tlfalse,'uuj$'),X0) ),
inference(cnf_transformation,[],[f986]) ).
tff(f986,plain,
! [X0: 'Nat$'] :
( ( ( 0 != 'fun_app$k'('of_nat$',X0) )
| ~ 'fun_app$c'('case_nat$a'(tlfalse,'uuj$'),X0) )
& ( 'fun_app$c'('case_nat$a'(tlfalse,'uuj$'),X0)
| ( 0 = 'fun_app$k'('of_nat$',X0) ) ) ),
inference(nnf_transformation,[],[f304]) ).
tff(f304,axiom,
! [X0: 'Nat$'] :
( ( 0 != 'fun_app$k'('of_nat$',X0) )
<=> 'fun_app$c'('case_nat$a'(tlfalse,'uuj$'),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
tff(f4300,plain,
spl107_195,
inference(avatar_split_clause,[],[f1531,f4298]) ).
tff(f4298,plain,
( spl107_195
<=> ! [X0: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(tlfalse,'uuj$'),X0)
| ( 0 = 'fun_app$k'('of_nat$',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_195])]) ).
tff(f1531,plain,
! [X0: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(tlfalse,'uuj$'),X0)
| ( 0 = 'fun_app$k'('of_nat$',X0) ) ),
inference(cnf_transformation,[],[f986]) ).
tff(f4296,plain,
spl107_194,
inference(avatar_split_clause,[],[f1486,f4294]) ).
tff(f4294,plain,
( spl107_194
<=> ! [X0: 'Nat$'] :
( $less(0,'fun_app$k'('of_nat$',X0))
| ( 0 = 'fun_app$k'('of_nat$',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_194])]) ).
tff(f1486,plain,
! [X0: 'Nat$'] :
( $less(0,'fun_app$k'('of_nat$',X0))
| ( 0 = 'fun_app$k'('of_nat$',X0) ) ),
inference(cnf_transformation,[],[f718]) ).
tff(f718,plain,
! [X0: 'Nat$'] :
( $less(0,'fun_app$k'('of_nat$',X0))
| ( 0 = 'fun_app$k'('of_nat$',X0) ) ),
inference(ennf_transformation,[],[f650]) ).
tff(f650,plain,
! [X0: 'Nat$'] :
( ( 0 != 'fun_app$k'('of_nat$',X0) )
=> $less(0,'fun_app$k'('of_nat$',X0)) ),
inference(flattening,[],[f649]) ).
tff(f649,plain,
! [X0: 'Nat$'] :
( ( ~ 0 = 'fun_app$k'('of_nat$',X0) )
=> $less(0,'fun_app$k'('of_nat$',X0)) ),
inference(true_and_false_elimination,[],[f147]) ).
tff(f147,axiom,
! [X0: 'Nat$'] :
( ( ( 0 = 'fun_app$k'('of_nat$',X0) )
=> $false )
=> $less(0,'fun_app$k'('of_nat$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).
tff(f4292,plain,
spl107_193,
inference(avatar_split_clause,[],[f619,f4290]) ).
tff(f4290,plain,
( spl107_193
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_193])]) ).
tff(f619,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f4288,plain,
spl107_192,
inference(avatar_split_clause,[],[f614,f4286]) ).
tff(f4286,plain,
( spl107_192
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_192])]) ).
tff(f614,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f4030,plain,
( spl107_191
| ~ spl107_4
| ~ spl107_142 ),
inference(avatar_split_clause,[],[f3811,f3485,f2790,f4028]) ).
tff(f4028,plain,
( spl107_191
<=> ! [X0: 'Nat$'] : ~ sP37('uuj$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_191])]) ).
tff(f3485,plain,
( spl107_142
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,sK96(X0,X1))
| ~ sP37(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_142])]) ).
tff(f3811,plain,
( ! [X0: 'Nat$'] : ~ sP37('uuj$',X0)
| ~ spl107_4
| ~ spl107_142 ),
inference(resolution,[],[f3486,f2791]) ).
tff(f3486,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,sK96(X0,X1))
| ~ sP37(X0,X1) )
| ~ spl107_142 ),
inference(avatar_component_clause,[],[f3485]) ).
tff(f4004,plain,
spl107_190,
inference(avatar_split_clause,[],[f2374,f4002]) ).
tff(f4002,plain,
( spl107_190
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP39(X0,X1,tltrue)
| ( 0 != 'fun_app$k'('of_nat$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_190])]) ).
tff(f2374,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP39(X0,X1,tltrue)
| ( 0 != 'fun_app$k'('of_nat$',X1) ) ),
inference(equality_resolution,[],[f2123]) ).
tff(f2123,plain,
! [X2: tlbool,X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP39(X0,X1,X2)
| ( 0 != 'fun_app$k'('of_nat$',X1) )
| ( tltrue != X2 ) ),
inference(cnf_transformation,[],[f1258]) ).
tff(f1258,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: tlbool] :
( ( sP39(X0,X1,X2)
| ( ~ sP38(X1,X0)
& ( 0 != 'fun_app$k'('of_nat$',X1) ) )
| ( ( tltrue != X2 )
& ( 0 = 'fun_app$k'('of_nat$',X1) ) ) )
& ( ( ( sP38(X1,X0)
| ( 0 = 'fun_app$k'('of_nat$',X1) ) )
& ( ( tltrue = X2 )
| ( 0 != 'fun_app$k'('of_nat$',X1) ) ) )
| ~ sP39(X0,X1,X2) ) ),
inference(rectify,[],[f1257]) ).
tff(f1257,plain,
! [X1: 'Nat_bool_fun$',X2: 'Nat$',X0: tlbool] :
( ( sP39(X1,X2,X0)
| ( ~ sP38(X2,X1)
& ( 0 != 'fun_app$k'('of_nat$',X2) ) )
| ( ( tltrue != X0 )
& ( 0 = 'fun_app$k'('of_nat$',X2) ) ) )
& ( ( ( sP38(X2,X1)
| ( 0 = 'fun_app$k'('of_nat$',X2) ) )
& ( ( tltrue = X0 )
| ( 0 != 'fun_app$k'('of_nat$',X2) ) ) )
| ~ sP39(X1,X2,X0) ) ),
inference(flattening,[],[f1256]) ).
tff(f1256,plain,
! [X1: 'Nat_bool_fun$',X2: 'Nat$',X0: tlbool] :
( ( sP39(X1,X2,X0)
| ( ~ sP38(X2,X1)
& ( 0 != 'fun_app$k'('of_nat$',X2) ) )
| ( ( tltrue != X0 )
& ( 0 = 'fun_app$k'('of_nat$',X2) ) ) )
& ( ( ( sP38(X2,X1)
| ( 0 = 'fun_app$k'('of_nat$',X2) ) )
& ( ( tltrue = X0 )
| ( 0 != 'fun_app$k'('of_nat$',X2) ) ) )
| ~ sP39(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f945]) ).
tff(f945,plain,
! [X1: 'Nat_bool_fun$',X2: 'Nat$',X0: tlbool] :
( sP39(X1,X2,X0)
<=> ( ( sP38(X2,X1)
| ( 0 = 'fun_app$k'('of_nat$',X2) ) )
& ( ( tltrue = X0 )
| ( 0 != 'fun_app$k'('of_nat$',X2) ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
tff(f4000,plain,
spl107_189,
inference(avatar_split_clause,[],[f2285,f3998]) ).
tff(f3998,plain,
( spl107_189
<=> ! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ( 1 != 'sub$'('inc$'(X0),'one$') ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_189])]) ).
tff(f2285,plain,
! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ( 1 != 'sub$'('inc$'(X0),'one$') ) ),
inference(definition_unfolding,[],[f1500,f1403]) ).
tff(f1500,plain,
! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ( 1 != 'numeral$'(X0) ) ),
inference(cnf_transformation,[],[f971]) ).
tff(f971,plain,
! [X0: 'Num$'] :
( ( ( 1 = 'numeral$'(X0) )
| ( 'one$' != X0 ) )
& ( ( 'one$' = X0 )
| ( 1 != 'numeral$'(X0) ) ) ),
inference(nnf_transformation,[],[f275]) ).
tff(f275,axiom,
! [X0: 'Num$'] :
( ( 1 = 'numeral$'(X0) )
<=> ( 'one$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).
tff(f3996,plain,
spl107_188,
inference(avatar_split_clause,[],[f2252,f3994]) ).
tff(f3994,plain,
( spl107_188
<=> ! [X0: 'Num$'] : ( 'fun_app$p'('num_of_nat$','nat$'('sub$'('inc$'(X0),'one$'))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_188])]) ).
tff(f2252,plain,
! [X0: 'Num$'] : ( 'fun_app$p'('num_of_nat$','nat$'('sub$'('inc$'(X0),'one$'))) = X0 ),
inference(definition_unfolding,[],[f1409,f1403]) ).
tff(f1409,plain,
! [X0: 'Num$'] : ( 'fun_app$p'('num_of_nat$','nat$'('numeral$'(X0))) = X0 ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,axiom,
! [X0: 'Num$'] : ( 'fun_app$p'('num_of_nat$','nat$'('numeral$'(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).
tff(f3992,plain,
spl107_187,
inference(avatar_split_clause,[],[f2133,f3990]) ).
tff(f3990,plain,
( spl107_187
<=> ! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ~ sP39(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_187])]) ).
tff(f2133,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ~ sP39(X1,X2,X0) ),
inference(cnf_transformation,[],[f1262]) ).
tff(f1262,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( 'fun_app$c'('case_nat$a'(X0,X1),X2)
| ~ sP39(X1,X2,X0) )
& ( sP39(X1,X2,X0)
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f946]) ).
tff(f946,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
<=> sP39(X1,X2,X0) ),
inference(definition_folding,[],[f855,f945,f944]) ).
tff(f944,plain,
! [X2: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP38(X2,X1)
<=> ( ( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),$uminus(1))))
| $less('fun_app$k'('of_nat$',X2),1) )
& ( 'fun_app$c'(X1,'nat$'(0))
| ~ $less('fun_app$k'('of_nat$',X2),1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
tff(f855,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
<=> ( ( ( ( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),$uminus(1))))
| $less('fun_app$k'('of_nat$',X2),1) )
& ( 'fun_app$c'(X1,'nat$'(0))
| ~ $less('fun_app$k'('of_nat$',X2),1) ) )
| ( 0 = 'fun_app$k'('of_nat$',X2) ) )
& ( ( tltrue = X0 )
| ( 0 != 'fun_app$k'('of_nat$',X2) ) ) ) ),
inference(ennf_transformation,[],[f603]) ).
tff(f603,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
<=> ( ( ( 0 != 'fun_app$k'('of_nat$',X2) )
=> ( ( ~ $less('fun_app$k'('of_nat$',X2),1)
=> 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),$uminus(1)))) )
& ( $less('fun_app$k'('of_nat$',X2),1)
=> 'fun_app$c'(X1,'nat$'(0)) ) ) )
& ( ( 0 = 'fun_app$k'('of_nat$',X2) )
=> ( tltrue = X0 ) ) ) ),
inference(theory_normalization,[],[f297]) ).
tff(f297,axiom,
! [X0: tlbool,X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),X2)
<=> ( ( ( 0 != 'fun_app$k'('of_nat$',X2) )
=> ( ( ~ $less('fun_app$k'('of_nat$',X2),1)
=> 'fun_app$c'(X1,'nat$'($difference('fun_app$k'('of_nat$',X2),1))) )
& ( $less('fun_app$k'('of_nat$',X2),1)
=> 'fun_app$c'(X1,'nat$'(0)) ) ) )
& ( ( 0 = 'fun_app$k'('of_nat$',X2) )
=> ( tltrue = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).
tff(f3988,plain,
spl107_186,
inference(avatar_split_clause,[],[f2132,f3986]) ).
tff(f2132,plain,
! [X2: 'Nat$',X0: tlbool,X1: 'Nat_bool_fun$'] :
( sP39(X1,X2,X0)
| ~ 'fun_app$c'('case_nat$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1262]) ).
tff(f3984,plain,
spl107_185,
inference(avatar_split_clause,[],[f2093,f3982]) ).
tff(f3982,plain,
( spl107_185
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( ~ 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK94(X0))
| ~ sP36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_185])]) ).
tff(f2093,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ~ 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK94(X0))
| ~ sP36(X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f3980,plain,
spl107_184,
inference(avatar_split_clause,[],[f2092,f3978]) ).
tff(f3978,plain,
( spl107_184
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$c'('fun_app$n'(X0,sK93(X0)),sK94(X0))
| ~ sP36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_184])]) ).
tff(f2092,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$c'('fun_app$n'(X0,sK93(X0)),sK94(X0))
| ~ sP36(X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f3976,plain,
spl107_183,
inference(avatar_split_clause,[],[f2091,f3974]) ).
tff(f3974,plain,
( spl107_183
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK93(X0))
| ~ sP36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_183])]) ).
tff(f2091,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$c'('fun_app$n'(X0,sK92(X0)),sK93(X0))
| ~ sP36(X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f3972,plain,
spl107_182,
inference(avatar_split_clause,[],[f2001,f3970]) ).
tff(f3970,plain,
( spl107_182
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,'fun_app$k'('of_nat$',X0))
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_182])]) ).
tff(f2001,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,'fun_app$k'('of_nat$',X0))
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1196]) ).
tff(f3968,plain,
( spl107_181
| ~ spl107_3
| ~ spl107_140 ),
inference(avatar_split_clause,[],[f3806,f3477,f2786,f3966]) ).
tff(f3966,plain,
( spl107_181
<=> ! [X0: 'Nat$'] : ~ sP17('uui$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_181])]) ).
tff(f2786,plain,
( spl107_3
<=> ! [X0: 'Nat$'] : ~ 'fun_app$c'('uui$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_3])]) ).
tff(f3477,plain,
( spl107_140
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,sK88(X0,X1))
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_140])]) ).
tff(f3806,plain,
( ! [X0: 'Nat$'] : ~ sP17('uui$',X0)
| ~ spl107_3
| ~ spl107_140 ),
inference(resolution,[],[f3478,f2787]) ).
tff(f2787,plain,
( ! [X0: 'Nat$'] : ~ 'fun_app$c'('uui$',X0)
| ~ spl107_3 ),
inference(avatar_component_clause,[],[f2786]) ).
tff(f3478,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,sK88(X0,X1))
| ~ sP17(X0,X1) )
| ~ spl107_140 ),
inference(avatar_component_clause,[],[f3477]) ).
tff(f3964,plain,
spl107_180,
inference(avatar_split_clause,[],[f1973,f3962]) ).
tff(f3962,plain,
( spl107_180
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,'fun_app$k'('of_nat$',X0))
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_180])]) ).
tff(f1973,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,'fun_app$k'('of_nat$',X0))
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f1184]) ).
tff(f3960,plain,
spl107_179,
inference(avatar_split_clause,[],[f1929,f3958]) ).
tff(f3958,plain,
( spl107_179
<=> ! [X2: 'Nat_a_set_fun$',X0: 'A_ltln$',X1: 'Nat$'] : ( 'f_G$'(X0,'suffix$'(X1,X2)) = 'f_G$'(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_179])]) ).
tff(f1929,plain,
! [X2: 'Nat_a_set_fun$',X0: 'A_ltln$',X1: 'Nat$'] : ( 'f_G$'(X0,'suffix$'(X1,X2)) = 'f_G$'(X0,X2) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,axiom,
! [X0: 'A_ltln$',X1: 'Nat$',X2: 'Nat_a_set_fun$'] : ( 'f_G$'(X0,'suffix$'(X1,X2)) = 'f_G$'(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).
tff(f3956,plain,
spl107_178,
inference(avatar_split_clause,[],[f1928,f3954]) ).
tff(f3954,plain,
( spl107_178
<=> ! [X2: 'Nat_a_set_fun$',X0: 'A_ltln$',X1: 'Nat$'] : ( 'g_F$'(X0,'suffix$'(X1,X2)) = 'g_F$'(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_178])]) ).
tff(f1928,plain,
! [X2: 'Nat_a_set_fun$',X0: 'A_ltln$',X1: 'Nat$'] : ( 'g_F$'(X0,'suffix$'(X1,X2)) = 'g_F$'(X0,X2) ),
inference(cnf_transformation,[],[f196]) ).
tff(f196,axiom,
! [X0: 'A_ltln$',X1: 'Nat$',X2: 'Nat_a_set_fun$'] : ( 'g_F$'(X0,'suffix$'(X1,X2)) = 'g_F$'(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).
tff(f3952,plain,
spl107_177,
inference(avatar_split_clause,[],[f1839,f3950]) ).
tff(f3950,plain,
( spl107_177
<=> ! [X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = X0 )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_177])]) ).
tff(f1839,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( tltrue = X0 )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),'nat$'(0)) ),
inference(cnf_transformation,[],[f1104]) ).
tff(f1104,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$'] :
( ( 'fun_app$c'('case_nat$a'(X0,X1),'nat$'(0))
| ( tltrue != X0 ) )
& ( ( tltrue = X0 )
| ~ 'fun_app$c'('case_nat$a'(X0,X1),'nat$'(0)) ) ),
inference(nnf_transformation,[],[f287]) ).
tff(f287,axiom,
! [X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),'nat$'(0))
<=> ( tltrue = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).
tff(f3948,plain,
spl107_176,
inference(avatar_split_clause,[],[f1834,f3946]) ).
tff(f3946,plain,
( spl107_176
<=> ! [X0: 'Num$',X1: 'Num$'] :
( $less('sub$'(X0,X1),0)
| ~ 'fun_app$o'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_176])]) ).
tff(f1834,plain,
! [X0: 'Num$',X1: 'Num$'] :
( $less('sub$'(X0,X1),0)
| ~ 'fun_app$o'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f1101]) ).
tff(f1101,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( $less('sub$'(X0,X1),0)
| ~ 'fun_app$o'('less$'(X0),X1) )
& ( 'fun_app$o'('less$'(X0),X1)
| ~ $less('sub$'(X0,X1),0) ) ),
inference(nnf_transformation,[],[f318]) ).
tff(f318,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( $less('sub$'(X0,X1),0)
<=> 'fun_app$o'('less$'(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).
tff(f3944,plain,
spl107_175,
inference(avatar_split_clause,[],[f1833,f3942]) ).
tff(f3942,plain,
( spl107_175
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$o'('less$'(X0),X1)
| ~ $less('sub$'(X0,X1),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_175])]) ).
tff(f1833,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$o'('less$'(X0),X1)
| ~ $less('sub$'(X0,X1),0) ),
inference(cnf_transformation,[],[f1101]) ).
tff(f3940,plain,
spl107_174,
inference(avatar_split_clause,[],[f1828,f3938]) ).
tff(f3938,plain,
( spl107_174
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X0,$uminus(X1)))
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_174])]) ).
tff(f1828,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(X0,$uminus(X1)))
| ~ $less(X1,X0) ),
inference(cnf_transformation,[],[f1098]) ).
tff(f1098,plain,
! [X0: $int,X1: $int] :
( ( $less(0,$sum(X0,$uminus(X1)))
| ~ $less(X1,X0) )
& ( $less(X1,X0)
| ~ $less(0,$sum(X0,$uminus(X1))) ) ),
inference(nnf_transformation,[],[f578]) ).
tff(f578,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(X0,$uminus(X1)))
<=> $less(X1,X0) ),
inference(theory_normalization,[],[f216]) ).
tff(f216,axiom,
! [X0: $int,X1: $int] :
( $less(0,$difference(X0,X1))
<=> $less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).
tff(f3936,plain,
spl107_173,
inference(avatar_split_clause,[],[f1827,f3934]) ).
tff(f3934,plain,
( spl107_173
<=> ! [X0: $int,X1: $int] :
( $less(X1,X0)
| ~ $less(0,$sum(X0,$uminus(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_173])]) ).
tff(f1827,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| ~ $less(0,$sum(X0,$uminus(X1))) ),
inference(cnf_transformation,[],[f1098]) ).
tff(f3932,plain,
spl107_172,
inference(avatar_split_clause,[],[f1826,f3930]) ).
tff(f3930,plain,
( spl107_172
<=> ! [X0: 'Num$',X1: 'Num$'] :
( $less(0,'sub$'(X0,X1))
| ~ 'fun_app$o'('less$'(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_172])]) ).
tff(f1826,plain,
! [X0: 'Num$',X1: 'Num$'] :
( $less(0,'sub$'(X0,X1))
| ~ 'fun_app$o'('less$'(X1),X0) ),
inference(cnf_transformation,[],[f1097]) ).
tff(f1097,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( $less(0,'sub$'(X0,X1))
| ~ 'fun_app$o'('less$'(X1),X0) )
& ( 'fun_app$o'('less$'(X1),X0)
| ~ $less(0,'sub$'(X0,X1)) ) ),
inference(nnf_transformation,[],[f317]) ).
tff(f317,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( $less(0,'sub$'(X0,X1))
<=> 'fun_app$o'('less$'(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).
tff(f3928,plain,
spl107_171,
inference(avatar_split_clause,[],[f1825,f3926]) ).
tff(f1825,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$o'('less$'(X1),X0)
| ~ $less(0,'sub$'(X0,X1)) ),
inference(cnf_transformation,[],[f1097]) ).
tff(f3924,plain,
( spl107_170
| ~ spl107_3
| ~ spl107_139 ),
inference(avatar_split_clause,[],[f3801,f3473,f2786,f3922]) ).
tff(f3922,plain,
( spl107_170
<=> ! [X0: 'Nat$'] : ~ sP16('uui$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_170])]) ).
tff(f3473,plain,
( spl107_139
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,sK86(X0,X1))
| ~ sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_139])]) ).
tff(f3801,plain,
( ! [X0: 'Nat$'] : ~ sP16('uui$',X0)
| ~ spl107_3
| ~ spl107_139 ),
inference(resolution,[],[f3474,f2787]) ).
tff(f3474,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,sK86(X0,X1))
| ~ sP16(X0,X1) )
| ~ spl107_139 ),
inference(avatar_component_clause,[],[f3473]) ).
tff(f3920,plain,
spl107_169,
inference(avatar_split_clause,[],[f1768,f3918]) ).
tff(f3918,plain,
( spl107_169
<=> ! [X0: $int,X1: $int] :
( ( $uminus(X1) = X0 )
| ( 0 != $sum(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_169])]) ).
tff(f1768,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X1) = X0 )
| ( 0 != $sum(X0,X1) ) ),
inference(cnf_transformation,[],[f1068]) ).
tff(f1068,plain,
! [X0: $int,X1: $int] :
( ( ( $uminus(X1) = X0 )
| ( 0 != $sum(X0,X1) ) )
& ( ( 0 = $sum(X0,X1) )
| ( $uminus(X1) != X0 ) ) ),
inference(nnf_transformation,[],[f487]) ).
tff(f487,axiom,
! [X0: $int,X1: $int] :
( ( $uminus(X1) = X0 )
<=> ( 0 = $sum(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).
tff(f3916,plain,
spl107_168,
inference(avatar_split_clause,[],[f1760,f3914]) ).
tff(f3914,plain,
( spl107_168
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less($sum(X0,$uminus(X1)),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_168])]) ).
tff(f1760,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less($sum(X0,$uminus(X1)),0) ),
inference(cnf_transformation,[],[f1064]) ).
tff(f1064,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,X1)
| ~ $less($sum(X0,$uminus(X1)),0) )
& ( $less($sum(X0,$uminus(X1)),0)
| ~ $less(X0,X1) ) ),
inference(nnf_transformation,[],[f577]) ).
tff(f577,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
<=> $less($sum(X0,$uminus(X1)),0) ),
inference(theory_normalization,[],[f243]) ).
tff(f243,axiom,
! [X0: $int,X1: $int] :
( $less(X0,X1)
<=> $less($difference(X0,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom241) ).
tff(f3912,plain,
spl107_167,
inference(avatar_split_clause,[],[f1759,f3910]) ).
tff(f3910,plain,
( spl107_167
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,$uminus(X1)),0)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_167])]) ).
tff(f1759,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,$uminus(X1)),0)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1064]) ).
tff(f3908,plain,
spl107_166,
inference(avatar_split_clause,[],[f1754,f3906]) ).
tff(f3906,plain,
( spl107_166
<=> ! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( 0 != $sum(X0,$uminus(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_166])]) ).
tff(f1754,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( 0 != $sum(X0,$uminus(X1)) ) ),
inference(cnf_transformation,[],[f1061]) ).
tff(f1061,plain,
! [X0: $int,X1: $int] :
( ( ( X0 = X1 )
| ( 0 != $sum(X0,$uminus(X1)) ) )
& ( ( 0 = $sum(X0,$uminus(X1)) )
| ( X0 != X1 ) ) ),
inference(nnf_transformation,[],[f576]) ).
tff(f576,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
<=> ( 0 = $sum(X0,$uminus(X1)) ) ),
inference(theory_normalization,[],[f226]) ).
tff(f226,axiom,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
<=> ( $difference(X0,X1) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).
tff(f3904,plain,
spl107_165,
inference(avatar_split_clause,[],[f1659,f3902]) ).
tff(f3902,plain,
( spl107_165
<=> ! [X0: $int,X1: $int] :
( ( $uminus(X0) = X1 )
| ( 0 != $sum(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_165])]) ).
tff(f1659,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X0) = X1 )
| ( 0 != $sum(X0,X1) ) ),
inference(cnf_transformation,[],[f735]) ).
tff(f735,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X0) = X1 )
| ( 0 != $sum(X0,X1) ) ),
inference(ennf_transformation,[],[f486]) ).
tff(f486,axiom,
! [X0: $int,X1: $int] :
( ( 0 = $sum(X0,X1) )
=> ( $uminus(X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).
tff(f3900,plain,
spl107_164,
inference(avatar_split_clause,[],[f1592,f3898]) ).
tff(f3898,plain,
( spl107_164
<=> ! [X0: 'A_ltln$',X1: 'A_set$'] : ( 'fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$',X0)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_164])]) ).
tff(f1592,plain,
! [X0: 'A_ltln$',X1: 'A_set$'] : ( 'fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$',X0)),X1) = X0 ),
inference(cnf_transformation,[],[f21]) ).
tff(f21,axiom,
! [X0: 'A_ltln$',X1: 'A_set$'] : ( 'fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$',X0)),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
tff(f3896,plain,
spl107_163,
inference(avatar_split_clause,[],[f1589,f3894]) ).
tff(f3894,plain,
( spl107_163
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'f_G$'('fun_app$i'('next_ltln$',X0),X1) = 'f_G$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_163])]) ).
tff(f1589,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'f_G$'('fun_app$i'('next_ltln$',X0),X1) = 'f_G$'(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'f_G$'('fun_app$i'('next_ltln$',X0),X1) = 'f_G$'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).
tff(f3892,plain,
spl107_162,
inference(avatar_split_clause,[],[f1588,f3890]) ).
tff(f3890,plain,
( spl107_162
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'g_F$'('fun_app$i'('next_ltln$',X0),X1) = 'g_F$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_162])]) ).
tff(f1588,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'g_F$'('fun_app$i'('next_ltln$',X0),X1) = 'g_F$'(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'g_F$'('fun_app$i'('next_ltln$',X0),X1) = 'g_F$'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).
tff(f3888,plain,
spl107_161,
inference(avatar_split_clause,[],[f1587,f3886]) ).
tff(f3886,plain,
( spl107_161
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'f$'('fun_app$i'('next_ltln$',X0),X1) = 'f$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_161])]) ).
tff(f1587,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'f$'('fun_app$i'('next_ltln$',X0),X1) = 'f$'(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'f$'('fun_app$i'('next_ltln$',X0),X1) = 'f$'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom190) ).
tff(f3884,plain,
spl107_160,
inference(avatar_split_clause,[],[f1586,f3882]) ).
tff(f3882,plain,
( spl107_160
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'g$'('fun_app$i'('next_ltln$',X0),X1) = 'g$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_160])]) ).
tff(f1586,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'g$'('fun_app$i'('next_ltln$',X0),X1) = 'g$'(X0,X1) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] : ( 'g$'('fun_app$i'('next_ltln$',X0),X1) = 'g$'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).
tff(f3880,plain,
( spl107_159
| ~ spl107_4
| ~ spl107_138 ),
inference(avatar_split_clause,[],[f3800,f3469,f2790,f3878]) ).
tff(f3878,plain,
( spl107_159
<=> ! [X0: 'Nat$'] : sP15('uuj$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_159])]) ).
tff(f3469,plain,
( spl107_138
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP15(X0,X1)
| ~ 'fun_app$c'(X0,sK84(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_138])]) ).
tff(f3800,plain,
( ! [X0: 'Nat$'] : sP15('uuj$',X0)
| ~ spl107_4
| ~ spl107_138 ),
inference(resolution,[],[f3470,f2791]) ).
tff(f3470,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,sK84(X0,X1))
| sP15(X0,X1) )
| ~ spl107_138 ),
inference(avatar_component_clause,[],[f3469]) ).
tff(f3876,plain,
spl107_158,
inference(avatar_split_clause,[],[f1584,f3874]) ).
tff(f3874,plain,
( spl107_158
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'plus$'(X0,'inc$'(X1)) = 'inc$'('plus$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_158])]) ).
tff(f1584,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'plus$'(X0,'inc$'(X1)) = 'inc$'('plus$'(X0,X1)) ),
inference(cnf_transformation,[],[f423]) ).
tff(f423,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'plus$'(X0,'inc$'(X1)) = 'inc$'('plus$'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).
tff(f3872,plain,
spl107_157,
inference(avatar_split_clause,[],[f1579,f3870]) ).
tff(f3870,plain,
( spl107_157
<=> ! [X0: $int,X1: $int] : ( 'fun_app$a'('uuc$'(X0),X1) = $sum(X0,$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_157])]) ).
tff(f1579,plain,
! [X0: $int,X1: $int] : ( 'fun_app$a'('uuc$'(X0),X1) = $sum(X0,$uminus(X1)) ),
inference(cnf_transformation,[],[f555]) ).
tff(f555,plain,
! [X0: $int,X1: $int] : ( 'fun_app$a'('uuc$'(X0),X1) = $sum(X0,$uminus(X1)) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,axiom,
! [X0: $int,X1: $int] : ( 'fun_app$a'('uuc$'(X0),X1) = $difference(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
tff(f3868,plain,
spl107_156,
inference(avatar_split_clause,[],[f1487,f3866]) ).
tff(f3866,plain,
( spl107_156
<=> ! [X0: 'A_ltln_a_ltln_bool_fun_fun$'] :
( 'af_congruent_axioms$'(X0)
| 'fun_app$l'('fun_app$m'(X0,sK49(X0)),sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_156])]) ).
tff(f1487,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$'] :
( 'af_congruent_axioms$'(X0)
| 'fun_app$l'('fun_app$m'(X0,sK49(X0)),sK50(X0)) ),
inference(cnf_transformation,[],[f965]) ).
tff(f965,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$'] :
( 'af_congruent_axioms$'(X0)
| ( ~ 'fun_app$l'('fun_app$m'(X0,'fun_app$g'('fun_app$h'('af_letter$',sK49(X0)),sK51(X0))),'fun_app$g'('fun_app$h'('af_letter$',sK50(X0)),sK51(X0)))
& 'fun_app$l'('fun_app$m'(X0,sK49(X0)),sK50(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51])],[f719,f964]) ).
tff(f964,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$'] :
( ? [X1: 'A_ltln$',X2: 'A_ltln$',X3: 'A_set$'] :
( ~ 'fun_app$l'('fun_app$m'(X0,'fun_app$g'('fun_app$h'('af_letter$',X1),X3)),'fun_app$g'('fun_app$h'('af_letter$',X2),X3))
& 'fun_app$l'('fun_app$m'(X0,X1),X2) )
=> ( ~ 'fun_app$l'('fun_app$m'(X0,'fun_app$g'('fun_app$h'('af_letter$',sK49(X0)),sK51(X0))),'fun_app$g'('fun_app$h'('af_letter$',sK50(X0)),sK51(X0)))
& 'fun_app$l'('fun_app$m'(X0,sK49(X0)),sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f719,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$'] :
( 'af_congruent_axioms$'(X0)
| ? [X1: 'A_ltln$',X2: 'A_ltln$',X3: 'A_set$'] :
( ~ 'fun_app$l'('fun_app$m'(X0,'fun_app$g'('fun_app$h'('af_letter$',X1),X3)),'fun_app$g'('fun_app$h'('af_letter$',X2),X3))
& 'fun_app$l'('fun_app$m'(X0,X1),X2) ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f36,axiom,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$'] :
( ! [X1: 'A_ltln$',X2: 'A_ltln$',X3: 'A_set$'] :
( 'fun_app$l'('fun_app$m'(X0,X1),X2)
=> 'fun_app$l'('fun_app$m'(X0,'fun_app$g'('fun_app$h'('af_letter$',X1),X3)),'fun_app$g'('fun_app$h'('af_letter$',X2),X3)) )
=> 'af_congruent_axioms$'(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).
tff(f3864,plain,
spl107_155,
inference(avatar_split_clause,[],[f1455,f3862]) ).
tff(f3862,plain,
( spl107_155
<=> ! [X0: $int] :
( ( 0 = 'fun_app$k'('of_nat$','nat$'(X0)) )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_155])]) ).
tff(f1455,plain,
! [X0: $int] :
( ( 0 = 'fun_app$k'('of_nat$','nat$'(X0)) )
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f700]) ).
tff(f700,plain,
! [X0: $int] :
( ( ( 0 = 'fun_app$k'('of_nat$','nat$'(X0)) )
| ~ $less(X0,0) )
& ( ( 'fun_app$k'('of_nat$','nat$'(X0)) = X0 )
| $less(X0,0) ) ),
inference(ennf_transformation,[],[f538]) ).
tff(f538,plain,
! [X0: $int] :
( ( $less(X0,0)
=> ( 0 = 'fun_app$k'('of_nat$','nat$'(X0)) ) )
& ( ~ $less(X0,0)
=> ( 'fun_app$k'('of_nat$','nat$'(X0)) = X0 ) ) ),
inference(theory_normalization,[],[f505]) ).
tff(f505,axiom,
! [X0: $int] :
( ( ~ $lesseq(0,X0)
=> ( 0 = 'fun_app$k'('of_nat$','nat$'(X0)) ) )
& ( $lesseq(0,X0)
=> ( 'fun_app$k'('of_nat$','nat$'(X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).
tff(f3860,plain,
spl107_154,
inference(avatar_split_clause,[],[f1454,f3858]) ).
tff(f3858,plain,
( spl107_154
<=> ! [X0: $int] :
( ( 'fun_app$k'('of_nat$','nat$'(X0)) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_154])]) ).
tff(f1454,plain,
! [X0: $int] :
( ( 'fun_app$k'('of_nat$','nat$'(X0)) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f700]) ).
tff(f3856,plain,
spl107_153,
inference(avatar_split_clause,[],[f1423,f3854]) ).
tff(f3854,plain,
( spl107_153
<=> ! [X0: 'A_ltln$'] : ( 'fun_app$i'('next_ltln$',X0) = 'fun_app$i'('unf$','fun_app$i'('next_ltln$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_153])]) ).
tff(f1423,plain,
! [X0: 'A_ltln$'] : ( 'fun_app$i'('next_ltln$',X0) = 'fun_app$i'('unf$','fun_app$i'('next_ltln$',X0)) ),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
! [X0: 'A_ltln$'] : ( 'fun_app$i'('next_ltln$',X0) = 'fun_app$i'('unf$','fun_app$i'('next_ltln$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
tff(f3852,plain,
spl107_152,
inference(avatar_split_clause,[],[f1414,f3850]) ).
tff(f3850,plain,
( spl107_152
<=> ! [X0: 'Nat$'] : ( 'fun_app$k'('of_nat$',X0) != $sum('fun_app$k'('of_nat$',X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_152])]) ).
tff(f1414,plain,
! [X0: 'Nat$'] : ( 'fun_app$k'('of_nat$',X0) != $sum('fun_app$k'('of_nat$',X0),1) ),
inference(cnf_transformation,[],[f96]) ).
tff(f96,axiom,
! [X0: 'Nat$'] : ( 'fun_app$k'('of_nat$',X0) != $sum('fun_app$k'('of_nat$',X0),1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
tff(f3848,plain,
( spl107_151
| ~ spl107_150 ),
inference(avatar_split_clause,[],[f3843,f3839,f3845]) ).
tff(f3839,plain,
( spl107_150
<=> 'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('unf$','fun_app$i'('next_ltln$','phi$')),'x$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_150])]) ).
tff(f3843,plain,
( 'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('next_ltln$','phi$'),'x$'))
| ~ spl107_150 ),
inference(forward_demodulation,[],[f3841,f1423]) ).
tff(f3841,plain,
( 'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('unf$','fun_app$i'('next_ltln$','phi$')),'x$'))
| ~ spl107_150 ),
inference(avatar_component_clause,[],[f3839]) ).
tff(f3842,plain,
spl107_150,
inference(avatar_split_clause,[],[f1349,f3839]) ).
tff(f1349,plain,
'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('unf$','fun_app$i'('next_ltln$','phi$')),'x$')),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('unf$','fun_app$i'('next_ltln$','phi$')),'x$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
tff(f3837,plain,
( spl107_149
| ~ spl107_4
| ~ spl107_137 ),
inference(avatar_split_clause,[],[f3799,f3465,f2790,f3835]) ).
tff(f3835,plain,
( spl107_149
<=> ! [X0: 'Nat$'] : sP14('uuj$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_149])]) ).
tff(f3465,plain,
( spl107_137
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP14(X0,X1)
| ~ 'fun_app$c'(X0,sK82(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_137])]) ).
tff(f3799,plain,
( ! [X0: 'Nat$'] : sP14('uuj$',X0)
| ~ spl107_4
| ~ spl107_137 ),
inference(resolution,[],[f3466,f2791]) ).
tff(f3466,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,sK82(X0,X1))
| sP14(X0,X1) )
| ~ spl107_137 ),
inference(avatar_component_clause,[],[f3465]) ).
tff(f3833,plain,
spl107_148,
inference(avatar_split_clause,[],[f618,f3831]) ).
tff(f3831,plain,
( spl107_148
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_148])]) ).
tff(f618,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f3829,plain,
spl107_147,
inference(avatar_split_clause,[],[f617,f3827]) ).
tff(f3827,plain,
( spl107_147
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_147])]) ).
tff(f617,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f3768,plain,
( spl107_146
| ~ spl107_4
| ~ spl107_118 ),
inference(avatar_split_clause,[],[f3629,f3388,f2790,f3766]) ).
tff(f3766,plain,
( spl107_146
<=> ! [X0: 'Nat$'] : ( tltrue = def_2('uuj$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_146])]) ).
tff(f3388,plain,
( spl107_118
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_2(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_118])]) ).
tff(f3629,plain,
( ! [X0: 'Nat$'] : ( tltrue = def_2('uuj$',X0) )
| ~ spl107_4
| ~ spl107_118 ),
inference(resolution,[],[f3389,f2791]) ).
tff(f3389,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,X1)
| ( tltrue = def_2(X0,X1) ) )
| ~ spl107_118 ),
inference(avatar_component_clause,[],[f3388]) ).
tff(f3621,plain,
( spl107_145
| ~ spl107_26
| ~ spl107_104 ),
inference(avatar_split_clause,[],[f3557,f3332,f2891,f3619]) ).
tff(f3619,plain,
( spl107_145
<=> ! [X0: $int] : $less($sum(X0,-1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_145])]) ).
tff(f2891,plain,
( spl107_26
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_26])]) ).
tff(f3332,plain,
( spl107_104
<=> ! [X0: $int,X1: $int] : ( $sum($sum(X0,$uminus(X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_104])]) ).
tff(f3557,plain,
( ! [X0: $int] : $less($sum(X0,-1),X0)
| ~ spl107_26
| ~ spl107_104 ),
inference(evaluation,[],[f3556]) ).
tff(f3556,plain,
( ! [X0: $int] : $less($sum(X0,$uminus(1)),X0)
| ~ spl107_26
| ~ spl107_104 ),
inference(superposition,[],[f2892,f3333]) ).
tff(f3333,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(X0,$uminus(X1)),X1) = X0 )
| ~ spl107_104 ),
inference(avatar_component_clause,[],[f3332]) ).
tff(f2892,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl107_26 ),
inference(avatar_component_clause,[],[f2891]) ).
tff(f3526,plain,
( spl107_144
| ~ spl107_30
| ~ spl107_95 ),
inference(avatar_split_clause,[],[f3498,f3296,f2908,f3524]) ).
tff(f3524,plain,
( spl107_144
<=> ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_144])]) ).
tff(f2908,plain,
( spl107_30
<=> ! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_30])]) ).
tff(f3296,plain,
( spl107_95
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_95])]) ).
tff(f3498,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl107_30
| ~ spl107_95 ),
inference(evaluation,[],[f3497]) ).
tff(f3497,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) )
| ~ spl107_30
| ~ spl107_95 ),
inference(superposition,[],[f3297,f2909]) ).
tff(f2909,plain,
( ! [X0: $int] : ( 0 = $sum($uminus(X0),X0) )
| ~ spl107_30 ),
inference(avatar_component_clause,[],[f2908]) ).
tff(f3297,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl107_95 ),
inference(avatar_component_clause,[],[f3296]) ).
tff(f3491,plain,
spl107_143,
inference(avatar_split_clause,[],[f2251,f3489]) ).
tff(f3489,plain,
( spl107_143
<=> ! [X0: 'Num$'] : ( 'bit0$'('inc$'(X0)) = 'inc$'('inc$'('bit0$'(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_143])]) ).
tff(f2251,plain,
! [X0: 'Num$'] : ( 'bit0$'('inc$'(X0)) = 'inc$'('inc$'('bit0$'(X0))) ),
inference(definition_unfolding,[],[f1406,f1391]) ).
tff(f1406,plain,
! [X0: 'Num$'] : ( 'inc$'('bit1$'(X0)) = 'bit0$'('inc$'(X0)) ),
inference(cnf_transformation,[],[f420]) ).
tff(f420,axiom,
! [X0: 'Num$'] : ( 'inc$'('bit1$'(X0)) = 'bit0$'('inc$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).
tff(f3487,plain,
spl107_142,
inference(avatar_split_clause,[],[f2097,f3485]) ).
tff(f2097,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$c'(X0,sK96(X0,X1))
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f1232]) ).
tff(f1232,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ~ 'fun_app$c'(X0,sK96(X0,X1))
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',sK96(X0,X1)),1)))
& $less('fun_app$k'('of_nat$',sK96(X0,X1)),'fun_app$k'('of_nat$',X1)) )
| ~ sP37(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96])],[f1230,f1231]) ).
tff(f1231,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1)) )
=> ( ~ 'fun_app$c'(X0,sK96(X0,X1))
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',sK96(X0,X1)),1)))
& $less('fun_app$k'('of_nat$',sK96(X0,X1)),'fun_app$k'('of_nat$',X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1230,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& 'fun_app$c'(X0,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X1)) )
| ~ sP37(X0,X1) ),
inference(rectify,[],[f1229]) ).
tff(f1229,plain,
! [X2: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X2,X3)
& 'fun_app$c'(X2,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X1)) )
| ~ sP37(X2,X1) ),
inference(nnf_transformation,[],[f942]) ).
tff(f942,plain,
! [X2: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X2,X3)
& 'fun_app$c'(X2,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X1)) )
| ~ sP37(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
tff(f3483,plain,
( spl107_141
| ~ spl107_40
| ~ spl107_52 ),
inference(avatar_split_clause,[],[f3197,f3015,f2948,f3481]) ).
tff(f3481,plain,
( spl107_141
<=> ! [X0: 'Num$'] : ( 1 = 'sgn$'('sub$'('inc$'(X0),'one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_141])]) ).
tff(f3015,plain,
( spl107_52
<=> ! [X0: $int] :
( ( 1 = 'sgn$'(X0) )
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_52])]) ).
tff(f3197,plain,
( ! [X0: 'Num$'] : ( 1 = 'sgn$'('sub$'('inc$'(X0),'one$')) )
| ~ spl107_40
| ~ spl107_52 ),
inference(resolution,[],[f3016,f2949]) ).
tff(f3016,plain,
( ! [X0: $int] :
( ~ $less(0,X0)
| ( 1 = 'sgn$'(X0) ) )
| ~ spl107_52 ),
inference(avatar_component_clause,[],[f3015]) ).
tff(f3479,plain,
spl107_140,
inference(avatar_split_clause,[],[f1922,f3477]) ).
tff(f1922,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,sK88(X0,X1))
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f1175]) ).
tff(f1175,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP17(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ( 'fun_app$c'(X0,sK88(X0,X1))
& $less('fun_app$k'('of_nat$',sK88(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP17(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f1173,f1174]) ).
tff(f1174,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
& $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
=> ( 'fun_app$c'(X0,sK88(X0,X1))
& $less('fun_app$k'('of_nat$',sK88(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1173,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP17(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
& $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP17(X0,X1) ) ),
inference(rectify,[],[f1172]) ).
tff(f1172,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP17(X1,X0)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) )
& ( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
| ~ sP17(X1,X0) ) ),
inference(nnf_transformation,[],[f917]) ).
tff(f917,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP17(X1,X0)
<=> ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
tff(f3475,plain,
spl107_139,
inference(avatar_split_clause,[],[f1915,f3473]) ).
tff(f1915,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,sK86(X0,X1))
| ~ sP16(X0,X1) ),
inference(cnf_transformation,[],[f1166]) ).
tff(f1166,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP16(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ( 'fun_app$c'(X0,sK86(X0,X1))
& $less('fun_app$k'('of_nat$',sK86(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP16(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f1164,f1165]) ).
tff(f1165,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
& $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
=> ( 'fun_app$c'(X0,sK86(X0,X1))
& $less('fun_app$k'('of_nat$',sK86(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1164,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP16(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
& $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP16(X0,X1) ) ),
inference(rectify,[],[f1163]) ).
tff(f1163,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP16(X1,X0)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) )
& ( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
| ~ sP16(X1,X0) ) ),
inference(nnf_transformation,[],[f915]) ).
tff(f3471,plain,
spl107_138,
inference(avatar_split_clause,[],[f1909,f3469]) ).
tff(f1909,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP15(X0,X1)
| ~ 'fun_app$c'(X0,sK84(X0,X1)) ),
inference(cnf_transformation,[],[f1157]) ).
tff(f1157,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP15(X0,X1)
| ( ~ 'fun_app$c'(X0,sK84(X0,X1))
& $less('fun_app$k'('of_nat$',sK84(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP15(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f1155,f1156]) ).
tff(f1156,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) )
=> ( ~ 'fun_app$c'(X0,sK84(X0,X1))
& $less('fun_app$k'('of_nat$',sK84(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1155,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP15(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP15(X0,X1) ) ),
inference(rectify,[],[f1154]) ).
tff(f1154,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP15(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) )
& ( ! [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
| ~ sP15(X1,X0) ) ),
inference(nnf_transformation,[],[f913]) ).
tff(f913,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP15(X1,X0)
<=> ! [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
tff(f3467,plain,
spl107_137,
inference(avatar_split_clause,[],[f1902,f3465]) ).
tff(f1902,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP14(X0,X1)
| ~ 'fun_app$c'(X0,sK82(X0,X1)) ),
inference(cnf_transformation,[],[f1148]) ).
tff(f1148,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP14(X0,X1)
| ( ~ 'fun_app$c'(X0,sK82(X0,X1))
& $less('fun_app$k'('of_nat$',sK82(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP14(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f1146,f1147]) ).
tff(f1147,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) )
=> ( ~ 'fun_app$c'(X0,sK82(X0,X1))
& $less('fun_app$k'('of_nat$',sK82(X0,X1)),$sum('fun_app$k'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1146,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP14(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),$sum('fun_app$k'('of_nat$',X1),1)) )
| ~ sP14(X0,X1) ) ),
inference(rectify,[],[f1145]) ).
tff(f1145,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP14(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) ) )
& ( ! [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
| ~ sP14(X1,X0) ) ),
inference(nnf_transformation,[],[f911]) ).
tff(f3463,plain,
spl107_136,
inference(avatar_split_clause,[],[f1838,f3461]) ).
tff(f3461,plain,
( spl107_136
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,X1),X1)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_136])]) ).
tff(f1838,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),X1)
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f1103]) ).
tff(f1103,plain,
! [X0: $int,X1: $int] :
( ( $less($sum(X0,X1),X1)
| ~ $less(X0,0) )
& ( $less(X0,0)
| ~ $less($sum(X0,X1),X1) ) ),
inference(nnf_transformation,[],[f358]) ).
tff(f358,axiom,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),X1)
<=> $less(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356) ).
tff(f3459,plain,
spl107_135,
inference(avatar_split_clause,[],[f1837,f3457]) ).
tff(f3457,plain,
( spl107_135
<=> ! [X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less($sum(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_135])]) ).
tff(f1837,plain,
! [X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less($sum(X0,X1),X1) ),
inference(cnf_transformation,[],[f1103]) ).
tff(f3455,plain,
spl107_134,
inference(avatar_split_clause,[],[f1836,f3453]) ).
tff(f3453,plain,
( spl107_134
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,X1),X0)
| ~ $less(X1,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_134])]) ).
tff(f1836,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),X0)
| ~ $less(X1,0) ),
inference(cnf_transformation,[],[f1102]) ).
tff(f1102,plain,
! [X0: $int,X1: $int] :
( ( $less($sum(X0,X1),X0)
| ~ $less(X1,0) )
& ( $less(X1,0)
| ~ $less($sum(X0,X1),X0) ) ),
inference(nnf_transformation,[],[f357]) ).
tff(f357,axiom,
! [X0: $int,X1: $int] :
( $less($sum(X0,X1),X0)
<=> $less(X1,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom355) ).
tff(f3451,plain,
spl107_133,
inference(avatar_split_clause,[],[f1835,f3449]) ).
tff(f3449,plain,
( spl107_133
<=> ! [X0: $int,X1: $int] :
( $less(X1,0)
| ~ $less($sum(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_133])]) ).
tff(f1835,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| ~ $less($sum(X0,X1),X0) ),
inference(cnf_transformation,[],[f1102]) ).
tff(f3447,plain,
spl107_132,
inference(avatar_split_clause,[],[f1831,f3445]) ).
tff(f3445,plain,
( spl107_132
<=> ! [X0: $int,X1: $int] :
( $less(X1,X0)
| ~ $less($uminus(X0),$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_132])]) ).
tff(f1831,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| ~ $less($uminus(X0),$uminus(X1)) ),
inference(cnf_transformation,[],[f1100]) ).
tff(f1100,plain,
! [X0: $int,X1: $int] :
( ( $less($uminus(X0),$uminus(X1))
| ~ $less(X1,X0) )
& ( $less(X1,X0)
| ~ $less($uminus(X0),$uminus(X1)) ) ),
inference(nnf_transformation,[],[f65]) ).
tff(f65,axiom,
! [X0: $int,X1: $int] :
( $less($uminus(X0),$uminus(X1))
<=> $less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
tff(f3443,plain,
spl107_131,
inference(avatar_split_clause,[],[f1824,f3441]) ).
tff(f3441,plain,
( spl107_131
<=> ! [X0: $int,X1: $int] :
( $less(X0,$sum(X0,X1))
| ~ $less(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_131])]) ).
tff(f1824,plain,
! [X0: $int,X1: $int] :
( $less(X0,$sum(X0,X1))
| ~ $less(0,X1) ),
inference(cnf_transformation,[],[f1096]) ).
tff(f1096,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,$sum(X0,X1))
| ~ $less(0,X1) )
& ( $less(0,X1)
| ~ $less(X0,$sum(X0,X1)) ) ),
inference(nnf_transformation,[],[f359]) ).
tff(f359,axiom,
! [X0: $int,X1: $int] :
( $less(X0,$sum(X0,X1))
<=> $less(0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom357) ).
tff(f3439,plain,
( spl107_130
| ~ spl107_48
| ~ spl107_49 ),
inference(avatar_split_clause,[],[f3185,f3003,f2999,f3437]) ).
tff(f3437,plain,
( spl107_130
<=> ! [X0: 'Nat$'] : ( 0 != $sum(1,'fun_app$k'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_130])]) ).
tff(f2999,plain,
( spl107_48
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_48])]) ).
tff(f3003,plain,
( spl107_49
<=> ! [X0: 'Nat$'] : ( 0 != $sum('fun_app$k'('of_nat$',X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_49])]) ).
tff(f3185,plain,
( ! [X0: 'Nat$'] : ( 0 != $sum(1,'fun_app$k'('of_nat$',X0)) )
| ~ spl107_48
| ~ spl107_49 ),
inference(superposition,[],[f3004,f3000]) ).
tff(f3000,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl107_48 ),
inference(avatar_component_clause,[],[f2999]) ).
tff(f3004,plain,
( ! [X0: 'Nat$'] : ( 0 != $sum('fun_app$k'('of_nat$',X0),1) )
| ~ spl107_49 ),
inference(avatar_component_clause,[],[f3003]) ).
tff(f3435,plain,
spl107_129,
inference(avatar_split_clause,[],[f1823,f3433]) ).
tff(f3433,plain,
( spl107_129
<=> ! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(X0,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_129])]) ).
tff(f1823,plain,
! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(X0,$sum(X0,X1)) ),
inference(cnf_transformation,[],[f1096]) ).
tff(f3431,plain,
spl107_128,
inference(avatar_split_clause,[],[f1822,f3429]) ).
tff(f3429,plain,
( spl107_128
<=> ! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,X0))
| ~ $less(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_128])]) ).
tff(f1822,plain,
! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,X0))
| ~ $less(0,X1) ),
inference(cnf_transformation,[],[f1095]) ).
tff(f1095,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,$sum(X1,X0))
| ~ $less(0,X1) )
& ( $less(0,X1)
| ~ $less(X0,$sum(X1,X0)) ) ),
inference(nnf_transformation,[],[f360]) ).
tff(f360,axiom,
! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,X0))
<=> $less(0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).
tff(f3427,plain,
spl107_127,
inference(avatar_split_clause,[],[f1821,f3425]) ).
tff(f3425,plain,
( spl107_127
<=> ! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(X0,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_127])]) ).
tff(f1821,plain,
! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(X0,$sum(X1,X0)) ),
inference(cnf_transformation,[],[f1095]) ).
tff(f3423,plain,
spl107_126,
inference(avatar_split_clause,[],[f1816,f3421]) ).
tff(f3421,plain,
( spl107_126
<=> ! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,'fun_app$i'('unf$',X1))
| ~ 'semantics_ltln$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_126])]) ).
tff(f1816,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,'fun_app$i'('unf$',X1))
| ~ 'semantics_ltln$'(X0,X1) ),
inference(cnf_transformation,[],[f1092]) ).
tff(f1092,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( ( 'semantics_ltln$'(X0,'fun_app$i'('unf$',X1))
| ~ 'semantics_ltln$'(X0,X1) )
& ( 'semantics_ltln$'(X0,X1)
| ~ 'semantics_ltln$'(X0,'fun_app$i'('unf$',X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,axiom,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,'fun_app$i'('unf$',X1))
<=> 'semantics_ltln$'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).
tff(f3419,plain,
spl107_125,
inference(avatar_split_clause,[],[f1815,f3417]) ).
tff(f3417,plain,
( spl107_125
<=> ! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,X1)
| ~ 'semantics_ltln$'(X0,'fun_app$i'('unf$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_125])]) ).
tff(f1815,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,X1)
| ~ 'semantics_ltln$'(X0,'fun_app$i'('unf$',X1)) ),
inference(cnf_transformation,[],[f1092]) ).
tff(f3415,plain,
spl107_124,
inference(avatar_split_clause,[],[f1809,f3413]) ).
tff(f3413,plain,
( spl107_124
<=> ! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( $sum(X1,X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_124])]) ).
tff(f1809,plain,
! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( $sum(X1,X0) != X0 ) ),
inference(cnf_transformation,[],[f1089]) ).
tff(f1089,plain,
! [X0: $int,X1: $int] :
( ( ( $sum(X1,X0) = X0 )
| ( 0 != X1 ) )
& ( ( 0 = X1 )
| ( $sum(X1,X0) != X0 ) ) ),
inference(nnf_transformation,[],[f339]) ).
tff(f339,axiom,
! [X0: $int,X1: $int] :
( ( $sum(X1,X0) = X0 )
<=> ( 0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom337) ).
tff(f3411,plain,
spl107_123,
inference(avatar_split_clause,[],[f1807,f3409]) ).
tff(f3409,plain,
( spl107_123
<=> ! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( $sum(X0,X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_123])]) ).
tff(f1807,plain,
! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( $sum(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f1088]) ).
tff(f1088,plain,
! [X0: $int,X1: $int] :
( ( ( $sum(X0,X1) = X0 )
| ( 0 != X1 ) )
& ( ( 0 = X1 )
| ( $sum(X0,X1) != X0 ) ) ),
inference(nnf_transformation,[],[f340]) ).
tff(f340,axiom,
! [X0: $int,X1: $int] :
( ( $sum(X0,X1) = X0 )
<=> ( 0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).
tff(f3407,plain,
spl107_122,
inference(avatar_split_clause,[],[f1806,f3405]) ).
tff(f1806,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_1(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ),
inference(cnf_transformation,[],[f1087]) ).
tff(f1087,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ( tltrue = def_1(X0,X1) )
| ~ 'fun_app$c'(X0,X1) )
& ( 'fun_app$c'(X0,X1)
| ( tltrue != def_1(X0,X1) ) ) ),
inference(nnf_transformation,[],[f676]) ).
tff(f676,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_1(X0,X1) )
<=> 'fun_app$c'(X0,X1) ),
inference(rectify,[],[f506]) ).
tff(f506,axiom,
! [X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( def_1(X1,X2) = tltrue )
<=> 'fun_app$c'(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_505) ).
tff(f3403,plain,
spl107_121,
inference(avatar_split_clause,[],[f1805,f3401]) ).
tff(f3401,plain,
( spl107_121
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_1(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_121])]) ).
tff(f1805,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_1(X0,X1) ) ),
inference(cnf_transformation,[],[f1087]) ).
tff(f3399,plain,
spl107_120,
inference(avatar_split_clause,[],[f1804,f3397]) ).
tff(f1804,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( def_3(X0,X1) = tltrue )
| ~ 'fun_app$c'(X0,X1) ),
inference(cnf_transformation,[],[f1086]) ).
tff(f1086,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ( def_3(X0,X1) = tltrue )
| ~ 'fun_app$c'(X0,X1) )
& ( 'fun_app$c'(X0,X1)
| ( def_3(X0,X1) != tltrue ) ) ),
inference(nnf_transformation,[],[f508]) ).
tff(f508,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( def_3(X0,X1) = tltrue )
<=> 'fun_app$c'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_507) ).
tff(f3394,plain,
spl107_119,
inference(avatar_split_clause,[],[f1803,f3392]) ).
tff(f3392,plain,
( spl107_119
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( def_3(X0,X1) != tltrue ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_119])]) ).
tff(f1803,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( def_3(X0,X1) != tltrue ) ),
inference(cnf_transformation,[],[f1086]) ).
tff(f3390,plain,
spl107_118,
inference(avatar_split_clause,[],[f1802,f3388]) ).
tff(f1802,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_2(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ),
inference(cnf_transformation,[],[f1085]) ).
tff(f1085,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ( tltrue = def_2(X0,X1) )
| ~ 'fun_app$c'(X0,X1) )
& ( 'fun_app$c'(X0,X1)
| ( tltrue != def_2(X0,X1) ) ) ),
inference(nnf_transformation,[],[f675]) ).
tff(f675,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( tltrue = def_2(X0,X1) )
<=> 'fun_app$c'(X0,X1) ),
inference(rectify,[],[f507]) ).
tff(f507,axiom,
! [X1: 'Nat_bool_fun$',X2: 'Nat$'] :
( ( def_2(X1,X2) = tltrue )
<=> 'fun_app$c'(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_506) ).
tff(f3386,plain,
spl107_117,
inference(avatar_split_clause,[],[f1801,f3384]) ).
tff(f3384,plain,
( spl107_117
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_2(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_117])]) ).
tff(f1801,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_2(X0,X1) ) ),
inference(cnf_transformation,[],[f1085]) ).
tff(f3382,plain,
spl107_116,
inference(avatar_split_clause,[],[f1800,f3380]) ).
tff(f3380,plain,
( spl107_116
<=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( def_6(X0,X1) = tltrue )
| ~ 'fun_app$d'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_116])]) ).
tff(f1800,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( def_6(X0,X1) = tltrue )
| ~ 'fun_app$d'(X0,X1) ),
inference(cnf_transformation,[],[f1084]) ).
tff(f1084,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( ( def_6(X0,X1) = tltrue )
| ~ 'fun_app$d'(X0,X1) )
& ( 'fun_app$d'(X0,X1)
| ( def_6(X0,X1) != tltrue ) ) ),
inference(nnf_transformation,[],[f511]) ).
tff(f511,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( def_6(X0,X1) = tltrue )
<=> 'fun_app$d'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_510) ).
tff(f3378,plain,
spl107_115,
inference(avatar_split_clause,[],[f1799,f3376]) ).
tff(f3376,plain,
( spl107_115
<=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$d'(X0,X1)
| ( def_6(X0,X1) != tltrue ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_115])]) ).
tff(f1799,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$d'(X0,X1)
| ( def_6(X0,X1) != tltrue ) ),
inference(cnf_transformation,[],[f1084]) ).
tff(f3374,plain,
spl107_114,
inference(avatar_split_clause,[],[f1797,f3372]) ).
tff(f3372,plain,
( spl107_114
<=> ! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( $uminus(X0) != $uminus(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_114])]) ).
tff(f1797,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( $uminus(X0) != $uminus(X1) ) ),
inference(cnf_transformation,[],[f1083]) ).
tff(f1083,plain,
! [X0: $int,X1: $int] :
( ( ( $uminus(X0) = $uminus(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( $uminus(X0) != $uminus(X1) ) ) ),
inference(nnf_transformation,[],[f58]) ).
tff(f58,axiom,
! [X0: $int,X1: $int] :
( ( $uminus(X0) = $uminus(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).
tff(f3370,plain,
spl107_113,
inference(avatar_split_clause,[],[f1793,f3368]) ).
tff(f3368,plain,
( spl107_113
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'bit0$'(X0) != 'bit0$'(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_113])]) ).
tff(f1793,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'bit0$'(X0) != 'bit0$'(X1) ) ),
inference(cnf_transformation,[],[f1081]) ).
tff(f1081,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ( 'bit0$'(X0) = 'bit0$'(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'bit0$'(X0) != 'bit0$'(X1) ) ) ),
inference(nnf_transformation,[],[f326]) ).
tff(f326,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'bit0$'(X0) = 'bit0$'(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).
tff(f3366,plain,
spl107_112,
inference(avatar_split_clause,[],[f1784,f3364]) ).
tff(f3364,plain,
( spl107_112
<=> ! [X0: $int,X1: $int] :
( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_112])]) ).
tff(f1784,plain,
! [X0: $int,X1: $int] :
( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) ),
inference(cnf_transformation,[],[f1076]) ).
tff(f1076,plain,
! [X0: $int,X1: $int] :
( ( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) )
& ( $less($uminus(X1),X0)
| ~ $less($uminus(X0),X1) ) ),
inference(nnf_transformation,[],[f111]) ).
tff(f111,axiom,
! [X0: $int,X1: $int] :
( $less($uminus(X0),X1)
<=> $less($uminus(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom109) ).
tff(f3362,plain,
spl107_111,
inference(avatar_split_clause,[],[f1782,f3360]) ).
tff(f3360,plain,
( spl107_111
<=> ! [X0: $int,X1: $int] :
( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_111])]) ).
tff(f1782,plain,
! [X0: $int,X1: $int] :
( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) ),
inference(cnf_transformation,[],[f1075]) ).
tff(f1075,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) )
& ( $less(X1,$uminus(X0))
| ~ $less(X0,$uminus(X1)) ) ),
inference(nnf_transformation,[],[f112]) ).
tff(f112,axiom,
! [X0: $int,X1: $int] :
( $less(X0,$uminus(X1))
<=> $less(X1,$uminus(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).
tff(f3358,plain,
spl107_110,
inference(avatar_split_clause,[],[f1657,f3356]) ).
tff(f3356,plain,
( spl107_110
<=> ! [X0: $int,X1: $int] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_110])]) ).
tff(f1657,plain,
! [X0: $int,X1: $int] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f733]) ).
tff(f733,plain,
! [X0: $int,X1: $int] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,axiom,
! [X0: $int,X1: $int] :
( $less(X0,X1)
=> $less($uminus(X1),$uminus(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).
tff(f3354,plain,
( spl107_109
| ~ spl107_43
| ~ spl107_81 ),
inference(avatar_split_clause,[],[f3268,f3132,f2961,f3352]) ).
tff(f3352,plain,
( spl107_109
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] : sP17('case_nat$a'(tltrue,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_109])]) ).
tff(f3132,plain,
( spl107_81
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP17(X1,X0)
| ~ 'fun_app$c'(X1,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_81])]) ).
tff(f3268,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] : sP17('case_nat$a'(tltrue,X0),X1)
| ~ spl107_43
| ~ spl107_81 ),
inference(resolution,[],[f3133,f2962]) ).
tff(f3133,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$c'(X1,'nat$'(0))
| sP17(X1,X0) )
| ~ spl107_81 ),
inference(avatar_component_clause,[],[f3132]) ).
tff(f3350,plain,
spl107_108,
inference(avatar_split_clause,[],[f1583,f3348]) ).
tff(f3348,plain,
( spl107_108
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_108])]) ).
tff(f1583,plain,
! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f353]) ).
tff(f353,axiom,
! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom351) ).
tff(f3346,plain,
spl107_107,
inference(avatar_split_clause,[],[f1582,f3344]) ).
tff(f3344,plain,
( spl107_107
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_107])]) ).
tff(f1582,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(cnf_transformation,[],[f352]) ).
tff(f352,axiom,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).
tff(f3342,plain,
spl107_106,
inference(avatar_split_clause,[],[f1581,f3340]) ).
tff(f3340,plain,
( spl107_106
<=> ! [X0: 'Nat$',X1: 'Nat_nat_fun$'] : ( 'fun_app$e'('case_nat$'(X0,X1),'nat$'(0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_106])]) ).
tff(f1581,plain,
! [X0: 'Nat$',X1: 'Nat_nat_fun$'] : ( 'fun_app$e'('case_nat$'(X0,X1),'nat$'(0)) = X0 ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,axiom,
! [X0: 'Nat$',X1: 'Nat_nat_fun$'] : ( 'fun_app$e'('case_nat$'(X0,X1),'nat$'(0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).
tff(f3338,plain,
spl107_105,
inference(avatar_split_clause,[],[f1580,f3336]) ).
tff(f3336,plain,
( spl107_105
<=> ! [X0: 'A_set$',X1: 'Nat_a_set_fun$'] : ( 'fun_app$j'('build$'(X0,X1),'nat$'(0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_105])]) ).
tff(f1580,plain,
! [X0: 'A_set$',X1: 'Nat_a_set_fun$'] : ( 'fun_app$j'('build$'(X0,X1),'nat$'(0)) = X0 ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
! [X0: 'A_set$',X1: 'Nat_a_set_fun$'] : ( 'fun_app$j'('build$'(X0,X1),'nat$'(0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).
tff(f3334,plain,
spl107_104,
inference(avatar_split_clause,[],[f1573,f3332]) ).
tff(f1573,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,$uminus(X1)),X1) = X0 ),
inference(cnf_transformation,[],[f549]) ).
tff(f549,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,$uminus(X1)),X1) = X0 ),
inference(theory_normalization,[],[f347]) ).
tff(f347,axiom,
! [X0: $int,X1: $int] : ( $sum($difference(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).
tff(f3330,plain,
spl107_103,
inference(avatar_split_clause,[],[f1571,f3328]) ).
tff(f3328,plain,
( spl107_103
<=> ! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_103])]) ).
tff(f1571,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X1)) = X0 ),
inference(cnf_transformation,[],[f547]) ).
tff(f547,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X1)) = X0 ),
inference(theory_normalization,[],[f351]) ).
tff(f351,axiom,
! [X0: $int,X1: $int] : ( $difference($sum(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom349) ).
tff(f3326,plain,
spl107_102,
inference(avatar_split_clause,[],[f1570,f3324]) ).
tff(f3324,plain,
( spl107_102
<=> ! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_102])]) ).
tff(f1570,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X0)) = X1 ),
inference(cnf_transformation,[],[f546]) ).
tff(f546,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X0)) = X1 ),
inference(theory_normalization,[],[f349]) ).
tff(f349,axiom,
! [X0: $int,X1: $int] : ( $difference($sum(X0,X1),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).
tff(f3322,plain,
spl107_101,
inference(avatar_split_clause,[],[f1553,f3320]) ).
tff(f3320,plain,
( spl107_101
<=> ! [X0: $int] :
( $less($sum(X0,X0),0)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_101])]) ).
tff(f1553,plain,
! [X0: $int] :
( $less($sum(X0,X0),0)
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f999]) ).
tff(f999,plain,
! [X0: $int] :
( ( $less($sum(X0,X0),0)
| ~ $less(X0,0) )
& ( $less(X0,0)
| ~ $less($sum(X0,X0),0) ) ),
inference(nnf_transformation,[],[f361]) ).
tff(f361,axiom,
! [X0: $int] :
( $less($sum(X0,X0),0)
<=> $less(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).
tff(f3318,plain,
spl107_100,
inference(avatar_split_clause,[],[f1552,f3316]) ).
tff(f3316,plain,
( spl107_100
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less($sum(X0,X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_100])]) ).
tff(f1552,plain,
! [X0: $int] :
( $less(X0,0)
| ~ $less($sum(X0,X0),0) ),
inference(cnf_transformation,[],[f999]) ).
tff(f3314,plain,
spl107_99,
inference(avatar_split_clause,[],[f1548,f3312]) ).
tff(f3312,plain,
( spl107_99
<=> ! [X0: $int] :
( $less(0,$sum(X0,X0))
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_99])]) ).
tff(f1548,plain,
! [X0: $int] :
( $less(0,$sum(X0,X0))
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f997]) ).
tff(f997,plain,
! [X0: $int] :
( ( $less(0,$sum(X0,X0))
| ~ $less(0,X0) )
& ( $less(0,X0)
| ~ $less(0,$sum(X0,X0)) ) ),
inference(nnf_transformation,[],[f362]) ).
tff(f362,axiom,
! [X0: $int] :
( $less(0,$sum(X0,X0))
<=> $less(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
tff(f3310,plain,
spl107_98,
inference(avatar_split_clause,[],[f1547,f3308]) ).
tff(f3308,plain,
( spl107_98
<=> ! [X0: $int] :
( $less(0,X0)
| ~ $less(0,$sum(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_98])]) ).
tff(f1547,plain,
! [X0: $int] :
( $less(0,X0)
| ~ $less(0,$sum(X0,X0)) ),
inference(cnf_transformation,[],[f997]) ).
tff(f3306,plain,
spl107_97,
inference(avatar_split_clause,[],[f1541,f3304]) ).
tff(f3304,plain,
( spl107_97
<=> ! [X0: $int] :
( ( 0 = X0 )
| ( 0 != $sum(X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_97])]) ).
tff(f1541,plain,
! [X0: $int] :
( ( 0 = X0 )
| ( 0 != $sum(X0,X0) ) ),
inference(cnf_transformation,[],[f991]) ).
tff(f991,plain,
! [X0: $int] :
( ( ( 0 = $sum(X0,X0) )
| ( 0 != X0 ) )
& ( ( 0 = X0 )
| ( 0 != $sum(X0,X0) ) ) ),
inference(nnf_transformation,[],[f336]) ).
tff(f336,axiom,
! [X0: $int] :
( ( 0 = $sum(X0,X0) )
<=> ( 0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
tff(f3302,plain,
spl107_96,
inference(avatar_split_clause,[],[f622,f3300]) ).
tff(f3300,plain,
( spl107_96
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_96])]) ).
tff(f622,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f3298,plain,
spl107_95,
inference(avatar_split_clause,[],[f620,f3296]) ).
tff(f620,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f3278,plain,
( spl107_94
| ~ spl107_4
| ~ spl107_81 ),
inference(avatar_split_clause,[],[f3267,f3132,f2790,f3276]) ).
tff(f3276,plain,
( spl107_94
<=> ! [X0: 'Nat$'] : sP17('uuj$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_94])]) ).
tff(f3267,plain,
( ! [X0: 'Nat$'] : sP17('uuj$',X0)
| ~ spl107_4
| ~ spl107_81 ),
inference(resolution,[],[f3133,f2791]) ).
tff(f3213,plain,
( spl107_93
| ~ spl107_26
| ~ spl107_48 ),
inference(avatar_split_clause,[],[f3181,f2999,f2891,f3211]) ).
tff(f3211,plain,
( spl107_93
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_93])]) ).
tff(f3181,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl107_26
| ~ spl107_48 ),
inference(superposition,[],[f2892,f3000]) ).
tff(f3178,plain,
spl107_92,
inference(avatar_split_clause,[],[f2506,f3176]) ).
tff(f3176,plain,
( spl107_92
<=> ! [X0: 'Nat$'] : $less(0,$sum(1,'fun_app$k'('of_nat$',X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_92])]) ).
tff(f2506,plain,
! [X0: 'Nat$'] : $less(0,$sum(1,'fun_app$k'('of_nat$',X0))),
inference(forward_demodulation,[],[f1410,f611]) ).
tff(f1410,plain,
! [X0: 'Nat$'] : $less(0,$sum('fun_app$k'('of_nat$',X0),1)),
inference(cnf_transformation,[],[f76]) ).
tff(f76,axiom,
! [X0: 'Nat$'] : $less(0,$sum('fun_app$k'('of_nat$',X0),1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).
tff(f3174,plain,
spl107_91,
inference(avatar_split_clause,[],[f2498,f3172]) ).
tff(f3172,plain,
( spl107_91
<=> ! [X0: 'Num$'] : ~ $less(-1,$uminus('sub$'('inc$'(X0),'one$'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_91])]) ).
tff(f2498,plain,
! [X0: 'Num$'] : ~ $less(-1,$uminus('sub$'('inc$'(X0),'one$'))),
inference(evaluation,[],[f2248]) ).
tff(f2248,plain,
! [X0: 'Num$'] : ~ $less($uminus(1),$uminus('sub$'('inc$'(X0),'one$'))),
inference(definition_unfolding,[],[f1386,f1403]) ).
tff(f1386,plain,
! [X0: 'Num$'] : ~ $less($uminus(1),$uminus('numeral$'(X0))),
inference(cnf_transformation,[],[f264]) ).
tff(f264,axiom,
! [X0: 'Num$'] : ~ $less($uminus(1),$uminus('numeral$'(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
tff(f3170,plain,
spl107_90,
inference(avatar_split_clause,[],[f2481,f3168]) ).
tff(f3168,plain,
( spl107_90
<=> ! [X0: $int] :
( ( 'sgn$'(X0) = -1 )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_90])]) ).
tff(f2481,plain,
! [X0: $int] :
( ( 'sgn$'(X0) = -1 )
| ~ $less(X0,0) ),
inference(evaluation,[],[f1467]) ).
tff(f1467,plain,
! [X0: $int] :
( ( $uminus(1) = 'sgn$'(X0) )
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f706]) ).
tff(f706,plain,
! [X0: $int] :
( ( $uminus(1) = 'sgn$'(X0) )
| ~ $less(X0,0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,axiom,
! [X0: $int] :
( $less(X0,0)
=> ( $uminus(1) = 'sgn$'(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).
tff(f3166,plain,
spl107_89,
inference(avatar_split_clause,[],[f2476,f3164]) ).
tff(f3164,plain,
( spl107_89
<=> ! [X0: $int] :
( $less(X0,0)
| ( 'sgn$'(X0) != -1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_89])]) ).
tff(f2476,plain,
! [X0: $int] :
( $less(X0,0)
| ( 'sgn$'(X0) != -1 ) ),
inference(evaluation,[],[f1543]) ).
tff(f1543,plain,
! [X0: $int] :
( $less(X0,0)
| ( $uminus(1) != 'sgn$'(X0) ) ),
inference(cnf_transformation,[],[f992]) ).
tff(f992,plain,
! [X0: $int] :
( ( ( $uminus(1) = 'sgn$'(X0) )
| ~ $less(X0,0) )
& ( $less(X0,0)
| ( $uminus(1) != 'sgn$'(X0) ) ) ),
inference(nnf_transformation,[],[f189]) ).
tff(f189,axiom,
! [X0: $int] :
( ( $uminus(1) = 'sgn$'(X0) )
<=> $less(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
tff(f3162,plain,
spl107_88,
inference(avatar_split_clause,[],[f2373,f3160]) ).
tff(f3160,plain,
( spl107_88
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP39(X0,X1,tltrue)
| ~ sP38(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_88])]) ).
tff(f2373,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP39(X0,X1,tltrue)
| ~ sP38(X1,X0) ),
inference(equality_resolution,[],[f2125]) ).
tff(f2125,plain,
! [X2: tlbool,X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP39(X0,X1,X2)
| ~ sP38(X1,X0)
| ( tltrue != X2 ) ),
inference(cnf_transformation,[],[f1258]) ).
tff(f3158,plain,
spl107_87,
inference(avatar_split_clause,[],[f2247,f3156]) ).
tff(f3156,plain,
( spl107_87
<=> ! [X0: 'Num$'] : $less($uminus('sub$'('inc$'(X0),'one$')),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_87])]) ).
tff(f2247,plain,
! [X0: 'Num$'] : $less($uminus('sub$'('inc$'(X0),'one$')),0),
inference(definition_unfolding,[],[f1385,f1403]) ).
tff(f1385,plain,
! [X0: 'Num$'] : $less($uminus('numeral$'(X0)),0),
inference(cnf_transformation,[],[f258]) ).
tff(f258,axiom,
! [X0: 'Num$'] : $less($uminus('numeral$'(X0)),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).
tff(f3154,plain,
spl107_86,
inference(avatar_split_clause,[],[f2246,f3152]) ).
tff(f3152,plain,
( spl107_86
<=> ! [X0: 'Num$'] : $less($uminus('sub$'('inc$'(X0),'one$')),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_86])]) ).
tff(f2246,plain,
! [X0: 'Num$'] : $less($uminus('sub$'('inc$'(X0),'one$')),1),
inference(definition_unfolding,[],[f1384,f1403]) ).
tff(f1384,plain,
! [X0: 'Num$'] : $less($uminus('numeral$'(X0)),1),
inference(cnf_transformation,[],[f260]) ).
tff(f260,axiom,
! [X0: 'Num$'] : $less($uminus('numeral$'(X0)),1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom258) ).
tff(f3150,plain,
spl107_85,
inference(avatar_split_clause,[],[f2243,f3148]) ).
tff(f3148,plain,
( spl107_85
<=> ! [X0: 'Num$'] : ~ $less(0,$uminus('sub$'('inc$'(X0),'one$'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_85])]) ).
tff(f2243,plain,
! [X0: 'Num$'] : ~ $less(0,$uminus('sub$'('inc$'(X0),'one$'))),
inference(definition_unfolding,[],[f1361,f1403]) ).
tff(f1361,plain,
! [X0: 'Num$'] : ~ $less(0,$uminus('numeral$'(X0))),
inference(cnf_transformation,[],[f259]) ).
tff(f259,axiom,
! [X0: 'Num$'] : ~ $less(0,$uminus('numeral$'(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).
tff(f3146,plain,
spl107_84,
inference(avatar_split_clause,[],[f2242,f3144]) ).
tff(f3144,plain,
( spl107_84
<=> ! [X0: 'Num$'] : ~ $less(1,$uminus('sub$'('inc$'(X0),'one$'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_84])]) ).
tff(f2242,plain,
! [X0: 'Num$'] : ~ $less(1,$uminus('sub$'('inc$'(X0),'one$'))),
inference(definition_unfolding,[],[f1360,f1403]) ).
tff(f1360,plain,
! [X0: 'Num$'] : ~ $less(1,$uminus('numeral$'(X0))),
inference(cnf_transformation,[],[f263]) ).
tff(f263,axiom,
! [X0: 'Num$'] : ~ $less(1,$uminus('numeral$'(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
tff(f3142,plain,
spl107_83,
inference(avatar_split_clause,[],[f2240,f3140]) ).
tff(f3140,plain,
( spl107_83
<=> ! [X0: 'Num$'] : ( 0 != $uminus('sub$'('inc$'(X0),'one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_83])]) ).
tff(f2240,plain,
! [X0: 'Num$'] : ( 0 != $uminus('sub$'('inc$'(X0),'one$')) ),
inference(definition_unfolding,[],[f1358,f1403]) ).
tff(f1358,plain,
! [X0: 'Num$'] : ( 0 != $uminus('numeral$'(X0)) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,axiom,
! [X0: 'Num$'] : ( 0 != $uminus('numeral$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom245) ).
tff(f3138,plain,
spl107_82,
inference(avatar_split_clause,[],[f2239,f3136]) ).
tff(f3136,plain,
( spl107_82
<=> ! [X0: 'Num$'] : ( 1 != $uminus('sub$'('inc$'(X0),'one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_82])]) ).
tff(f2239,plain,
! [X0: 'Num$'] : ( 1 != $uminus('sub$'('inc$'(X0),'one$')) ),
inference(definition_unfolding,[],[f1357,f1403]) ).
tff(f1357,plain,
! [X0: 'Num$'] : ( 1 != $uminus('numeral$'(X0)) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,axiom,
! [X0: 'Num$'] : ( 1 != $uminus('numeral$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom251) ).
tff(f3134,plain,
spl107_81,
inference(avatar_split_clause,[],[f1926,f3132]) ).
tff(f1926,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP17(X1,X0)
| ~ 'fun_app$c'(X1,'nat$'(0)) ),
inference(cnf_transformation,[],[f1180]) ).
tff(f1180,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP17(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
| ~ $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,'nat$'(0)) ) )
& ( ( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',sK89(X0,X1)),1)))
& $less('fun_app$k'('of_nat$',sK89(X0,X1)),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,'nat$'(0))
| ~ sP17(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f1178,f1179]) ).
tff(f1179,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
=> ( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',sK89(X0,X1)),1)))
& $less('fun_app$k'('of_nat$',sK89(X0,X1)),'fun_app$k'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1178,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP17(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
| ~ $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,'nat$'(0)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,'nat$'(0))
| ~ sP17(X1,X0) ) ),
inference(rectify,[],[f1177]) ).
tff(f1177,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP17(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,'nat$'(0)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,'nat$'(0))
| ~ sP17(X1,X0) ) ),
inference(flattening,[],[f1176]) ).
tff(f1176,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP17(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& ~ 'fun_app$c'(X1,'nat$'(0)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,'nat$'(0))
| ~ sP17(X1,X0) ) ),
inference(nnf_transformation,[],[f918]) ).
tff(f918,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP17(X1,X0)
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,'nat$'(0)) ) ),
inference(definition_folding,[],[f680,f917]) ).
tff(f680,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,'nat$'(0)) ) ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
& $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
<=> ( ? [X2: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
| 'fun_app$c'(X1,'nat$'(0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).
tff(f3130,plain,
spl107_80,
inference(avatar_split_clause,[],[f1910,f3128]) ).
tff(f3128,plain,
( spl107_80
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'(X1,'nat$'(0))
| ~ sP15(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_80])]) ).
tff(f1910,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'(X1,'nat$'(0))
| ~ sP15(X1,X0) ),
inference(cnf_transformation,[],[f1162]) ).
tff(f1162,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP15(X1,X0)
| ( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',sK85(X0,X1)),1)))
& $less('fun_app$k'('of_nat$',sK85(X0,X1)),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,'nat$'(0)) )
| ~ sP15(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f1160,f1161]) ).
tff(f1161,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
=> ( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',sK85(X0,X1)),1)))
& $less('fun_app$k'('of_nat$',sK85(X0,X1)),'fun_app$k'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1160,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP15(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),1)))
& $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,'nat$'(0)) )
| ~ sP15(X1,X0) ) ),
inference(rectify,[],[f1159]) ).
tff(f1159,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP15(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,'nat$'(0)) )
| ~ sP15(X1,X0) ) ),
inference(flattening,[],[f1158]) ).
tff(f1158,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP15(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
| ~ 'fun_app$c'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,'nat$'(0)) )
| ~ sP15(X1,X0) ) ),
inference(nnf_transformation,[],[f914]) ).
tff(f914,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP15(X1,X0)
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,'nat$'(0)) ) ),
inference(definition_folding,[],[f797,f913]) ).
tff(f797,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( 'fun_app$c'(X1,X2)
| ~ $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1)) )
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1)))
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0)) )
& 'fun_app$c'(X1,'nat$'(0)) ) ),
inference(ennf_transformation,[],[f678]) ).
tff(f678,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1))
=> 'fun_app$c'(X1,X2) )
<=> ( ! [X3: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X0))
=> 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X3),1))) )
& 'fun_app$c'(X1,'nat$'(0)) ) ),
inference(rectify,[],[f119]) ).
tff(f119,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),$sum('fun_app$k'('of_nat$',X0),1))
=> 'fun_app$c'(X1,X2) )
<=> ( ! [X2: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X2),'fun_app$k'('of_nat$',X0))
=> 'fun_app$c'(X1,'nat$'($sum('fun_app$k'('of_nat$',X2),1))) )
& 'fun_app$c'(X1,'nat$'(0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).
tff(f3126,plain,
spl107_79,
inference(avatar_split_clause,[],[f1776,f3124]) ).
tff(f3124,plain,
( spl107_79
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('uu$'(X0),X1)
| ~ 'semantics_ltln$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_79])]) ).
tff(f1776,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('uu$'(X0),X1)
| ~ 'semantics_ltln$'(X1,X0) ),
inference(cnf_transformation,[],[f1072]) ).
tff(f1072,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ( 'fun_app$b'('uu$'(X0),X1)
| ~ 'semantics_ltln$'(X1,X0) )
& ( 'semantics_ltln$'(X1,X0)
| ~ 'fun_app$b'('uu$'(X0),X1) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('uu$'(X0),X1)
<=> 'semantics_ltln$'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
tff(f3121,plain,
spl107_78,
inference(avatar_split_clause,[],[f1775,f3119]) ).
tff(f3119,plain,
( spl107_78
<=> ! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'semantics_ltln$'(X1,X0)
| ~ 'fun_app$b'('uu$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_78])]) ).
tff(f1775,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( 'semantics_ltln$'(X1,X0)
| ~ 'fun_app$b'('uu$'(X0),X1) ),
inference(cnf_transformation,[],[f1072]) ).
tff(f3117,plain,
spl107_77,
inference(avatar_split_clause,[],[f1774,f3115]) ).
tff(f3115,plain,
( spl107_77
<=> ! [X0: 'Nat_a_set_fun_set$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('uua$'(X0),X1)
| ~ 'member$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_77])]) ).
tff(f1774,plain,
! [X0: 'Nat_a_set_fun_set$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('uua$'(X0),X1)
| ~ 'member$'(X1,X0) ),
inference(cnf_transformation,[],[f1071]) ).
tff(f1071,plain,
! [X0: 'Nat_a_set_fun_set$',X1: 'Nat_a_set_fun$'] :
( ( 'fun_app$b'('uua$'(X0),X1)
| ~ 'member$'(X1,X0) )
& ( 'member$'(X1,X0)
| ~ 'fun_app$b'('uua$'(X0),X1) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f4,axiom,
! [X0: 'Nat_a_set_fun_set$',X1: 'Nat_a_set_fun$'] :
( 'fun_app$b'('uua$'(X0),X1)
<=> 'member$'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
tff(f3113,plain,
spl107_76,
inference(avatar_split_clause,[],[f1773,f3111]) ).
tff(f3111,plain,
( spl107_76
<=> ! [X0: 'Nat_a_set_fun_set$',X1: 'Nat_a_set_fun$'] :
( 'member$'(X1,X0)
| ~ 'fun_app$b'('uua$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_76])]) ).
tff(f1773,plain,
! [X0: 'Nat_a_set_fun_set$',X1: 'Nat_a_set_fun$'] :
( 'member$'(X1,X0)
| ~ 'fun_app$b'('uua$'(X0),X1) ),
inference(cnf_transformation,[],[f1071]) ).
tff(f3109,plain,
spl107_75,
inference(avatar_split_clause,[],[f1772,f3107]) ).
tff(f3107,plain,
( spl107_75
<=> ! [X0: 'Nat_a_set_fun$',X1: 'Nat_a_set_fun_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$b'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_75])]) ).
tff(f1772,plain,
! [X0: 'Nat_a_set_fun$',X1: 'Nat_a_set_fun_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$b'(X1,X0) ),
inference(cnf_transformation,[],[f1070]) ).
tff(f1070,plain,
! [X0: 'Nat_a_set_fun$',X1: 'Nat_a_set_fun_bool_fun$'] :
( ( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$b'(X1,X0) )
& ( 'fun_app$b'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ) ),
inference(nnf_transformation,[],[f54]) ).
tff(f54,axiom,
! [X0: 'Nat_a_set_fun$',X1: 'Nat_a_set_fun_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
<=> 'fun_app$b'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).
tff(f3105,plain,
spl107_74,
inference(avatar_split_clause,[],[f1771,f3103]) ).
tff(f3103,plain,
( spl107_74
<=> ! [X0: 'Nat_a_set_fun$',X1: 'Nat_a_set_fun_bool_fun$'] :
( 'fun_app$b'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_74])]) ).
tff(f1771,plain,
! [X0: 'Nat_a_set_fun$',X1: 'Nat_a_set_fun_bool_fun$'] :
( 'fun_app$b'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ),
inference(cnf_transformation,[],[f1070]) ).
tff(f3101,plain,
spl107_73,
inference(avatar_split_clause,[],[f1770,f3099]) ).
tff(f3099,plain,
( spl107_73
<=> ! [X0: $int,X1: $int] :
( 'fun_app$'('uub$'(X0),X1)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_73])]) ).
tff(f1770,plain,
! [X0: $int,X1: $int] :
( 'fun_app$'('uub$'(X0),X1)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1069]) ).
tff(f1069,plain,
! [X0: $int,X1: $int] :
( ( 'fun_app$'('uub$'(X0),X1)
| ~ $less(X0,X1) )
& ( $less(X0,X1)
| ~ 'fun_app$'('uub$'(X0),X1) ) ),
inference(nnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int,X1: $int] :
( 'fun_app$'('uub$'(X0),X1)
<=> $less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
tff(f3097,plain,
spl107_72,
inference(avatar_split_clause,[],[f1769,f3095]) ).
tff(f3095,plain,
( spl107_72
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ 'fun_app$'('uub$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_72])]) ).
tff(f1769,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ 'fun_app$'('uub$'(X0),X1) ),
inference(cnf_transformation,[],[f1069]) ).
tff(f3093,plain,
spl107_71,
inference(avatar_split_clause,[],[f1750,f3091]) ).
tff(f3091,plain,
( spl107_71
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ~ 'fun_app$c'(X0,sK76(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_71])]) ).
tff(f1750,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ~ 'fun_app$c'(X0,sK76(X0)) ),
inference(cnf_transformation,[],[f1057]) ).
tff(f1057,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( ~ 'fun_app$c'(X0,sK76(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',sK76(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f792,f1056]) ).
tff(f1056,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) ) )
=> ( ~ 'fun_app$c'(X0,sK76(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',sK76(X0))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f792,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) ) ) ),
inference(ennf_transformation,[],[f83]) ).
tff(f83,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2))
=> 'fun_app$c'(X0,X3) )
=> 'fun_app$c'(X0,X2) )
=> 'fun_app$c'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom81) ).
tff(f3089,plain,
spl107_70,
inference(avatar_split_clause,[],[f1747,f3087]) ).
tff(f3087,plain,
( spl107_70
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ~ 'fun_app$c'(X0,sK75(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_70])]) ).
tff(f1747,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ~ 'fun_app$c'(X0,sK75(X0)) ),
inference(cnf_transformation,[],[f1055]) ).
tff(f1055,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',sK75(X0))) )
& ~ 'fun_app$c'(X0,sK75(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f791,f1054]) ).
tff(f1054,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) )
& ~ 'fun_app$c'(X0,X2) )
=> ( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',sK75(X0))) )
& ~ 'fun_app$c'(X0,sK75(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f791,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$c'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$c'(X0,X3)
| ~ $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) )
& ~ 'fun_app$c'(X0,X2) ) ),
inference(ennf_transformation,[],[f82]) ).
tff(f82,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ~ 'fun_app$c'(X0,X2)
=> ? [X3: 'Nat$'] :
( ~ 'fun_app$c'(X0,X3)
& $less('fun_app$k'('of_nat$',X3),'fun_app$k'('of_nat$',X2)) ) )
=> 'fun_app$c'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).
tff(f3085,plain,
spl107_69,
inference(avatar_split_clause,[],[f1529,f3083]) ).
tff(f3083,plain,
( spl107_69
<=> ! [X0: $int] :
( $less($uminus(X0),0)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_69])]) ).
tff(f1529,plain,
! [X0: $int] :
( $less($uminus(X0),0)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f985]) ).
tff(f985,plain,
! [X0: $int] :
( ( $less($uminus(X0),0)
| ~ $less(0,X0) )
& ( $less(0,X0)
| ~ $less($uminus(X0),0) ) ),
inference(nnf_transformation,[],[f75]) ).
tff(f75,axiom,
! [X0: $int] :
( $less($uminus(X0),0)
<=> $less(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).
tff(f3081,plain,
( spl107_68
| ~ spl107_36
| ~ spl107_43 ),
inference(avatar_split_clause,[],[f2989,f2961,f2932,f3079]) ).
tff(f3079,plain,
( spl107_68
<=> ! [X0: 'Nat_bool_fun$'] : sP16('case_nat$a'(tltrue,X0),'nat$'(0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_68])]) ).
tff(f2932,plain,
( spl107_36
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP16(X1,X0)
| ~ 'fun_app$c'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_36])]) ).
tff(f2989,plain,
( ! [X0: 'Nat_bool_fun$'] : sP16('case_nat$a'(tltrue,X0),'nat$'(0))
| ~ spl107_36
| ~ spl107_43 ),
inference(resolution,[],[f2962,f2933]) ).
tff(f2933,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$c'(X1,X0)
| sP16(X1,X0) )
| ~ spl107_36 ),
inference(avatar_component_clause,[],[f2932]) ).
tff(f3077,plain,
spl107_67,
inference(avatar_split_clause,[],[f1528,f3075]) ).
tff(f3075,plain,
( spl107_67
<=> ! [X0: $int] :
( $less(0,X0)
| ~ $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_67])]) ).
tff(f1528,plain,
! [X0: $int] :
( $less(0,X0)
| ~ $less($uminus(X0),0) ),
inference(cnf_transformation,[],[f985]) ).
tff(f3073,plain,
spl107_66,
inference(avatar_split_clause,[],[f1527,f3071]) ).
tff(f3071,plain,
( spl107_66
<=> ! [X0: $int] :
( $less($uminus(X0),X0)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_66])]) ).
tff(f1527,plain,
! [X0: $int] :
( $less($uminus(X0),X0)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f984]) ).
tff(f984,plain,
! [X0: $int] :
( ( $less($uminus(X0),X0)
| ~ $less(0,X0) )
& ( $less(0,X0)
| ~ $less($uminus(X0),X0) ) ),
inference(nnf_transformation,[],[f73]) ).
tff(f73,axiom,
! [X0: $int] :
( $less($uminus(X0),X0)
<=> $less(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).
tff(f3069,plain,
spl107_65,
inference(avatar_split_clause,[],[f1526,f3067]) ).
tff(f3067,plain,
( spl107_65
<=> ! [X0: $int] :
( $less(0,X0)
| ~ $less($uminus(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_65])]) ).
tff(f1526,plain,
! [X0: $int] :
( $less(0,X0)
| ~ $less($uminus(X0),X0) ),
inference(cnf_transformation,[],[f984]) ).
tff(f3065,plain,
spl107_64,
inference(avatar_split_clause,[],[f1525,f3063]) ).
tff(f3063,plain,
( spl107_64
<=> ! [X0: $int] :
( $less('sgn$'(X0),0)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_64])]) ).
tff(f1525,plain,
! [X0: $int] :
( $less('sgn$'(X0),0)
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f983]) ).
tff(f983,plain,
! [X0: $int] :
( ( $less('sgn$'(X0),0)
| ~ $less(X0,0) )
& ( $less(X0,0)
| ~ $less('sgn$'(X0),0) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,axiom,
! [X0: $int] :
( $less('sgn$'(X0),0)
<=> $less(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).
tff(f3061,plain,
spl107_63,
inference(avatar_split_clause,[],[f1524,f3059]) ).
tff(f3059,plain,
( spl107_63
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less('sgn$'(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_63])]) ).
tff(f1524,plain,
! [X0: $int] :
( $less(X0,0)
| ~ $less('sgn$'(X0),0) ),
inference(cnf_transformation,[],[f983]) ).
tff(f3057,plain,
spl107_62,
inference(avatar_split_clause,[],[f1523,f3055]) ).
tff(f3055,plain,
( spl107_62
<=> ! [X0: $int] :
( $less(0,$uminus(X0))
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_62])]) ).
tff(f1523,plain,
! [X0: $int] :
( $less(0,$uminus(X0))
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f982]) ).
tff(f982,plain,
! [X0: $int] :
( ( $less(0,$uminus(X0))
| ~ $less(X0,0) )
& ( $less(X0,0)
| ~ $less(0,$uminus(X0)) ) ),
inference(nnf_transformation,[],[f74]) ).
tff(f74,axiom,
! [X0: $int] :
( $less(0,$uminus(X0))
<=> $less(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).
tff(f3053,plain,
spl107_61,
inference(avatar_split_clause,[],[f1522,f3051]) ).
tff(f3051,plain,
( spl107_61
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less(0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_61])]) ).
tff(f1522,plain,
! [X0: $int] :
( $less(X0,0)
| ~ $less(0,$uminus(X0)) ),
inference(cnf_transformation,[],[f982]) ).
tff(f3049,plain,
spl107_60,
inference(avatar_split_clause,[],[f1521,f3047]) ).
tff(f3047,plain,
( spl107_60
<=> ! [X0: $int] :
( $less(0,'sgn$'(X0))
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_60])]) ).
tff(f1521,plain,
! [X0: $int] :
( $less(0,'sgn$'(X0))
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f981]) ).
tff(f981,plain,
! [X0: $int] :
( ( $less(0,'sgn$'(X0))
| ~ $less(0,X0) )
& ( $less(0,X0)
| ~ $less(0,'sgn$'(X0)) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,axiom,
! [X0: $int] :
( $less(0,'sgn$'(X0))
<=> $less(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom176) ).
tff(f3045,plain,
spl107_59,
inference(avatar_split_clause,[],[f1520,f3043]) ).
tff(f3043,plain,
( spl107_59
<=> ! [X0: $int] :
( $less(0,X0)
| ~ $less(0,'sgn$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_59])]) ).
tff(f1520,plain,
! [X0: $int] :
( $less(0,X0)
| ~ $less(0,'sgn$'(X0)) ),
inference(cnf_transformation,[],[f981]) ).
tff(f3041,plain,
spl107_58,
inference(avatar_split_clause,[],[f1517,f3039]) ).
tff(f3039,plain,
( spl107_58
<=> ! [X0: $int] :
( $less(X0,$uminus(X0))
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_58])]) ).
tff(f1517,plain,
! [X0: $int] :
( $less(X0,$uminus(X0))
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f979]) ).
tff(f979,plain,
! [X0: $int] :
( ( $less(X0,$uminus(X0))
| ~ $less(X0,0) )
& ( $less(X0,0)
| ~ $less(X0,$uminus(X0)) ) ),
inference(nnf_transformation,[],[f72]) ).
tff(f72,axiom,
! [X0: $int] :
( $less(X0,$uminus(X0))
<=> $less(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
tff(f3037,plain,
spl107_57,
inference(avatar_split_clause,[],[f1516,f3035]) ).
tff(f3035,plain,
( spl107_57
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_57])]) ).
tff(f1516,plain,
! [X0: $int] :
( $less(X0,0)
| ~ $less(X0,$uminus(X0)) ),
inference(cnf_transformation,[],[f979]) ).
tff(f3033,plain,
spl107_56,
inference(avatar_split_clause,[],[f1512,f3031]) ).
tff(f3031,plain,
( spl107_56
<=> ! [X0: $int] :
( ( 0 = X0 )
| ( $uminus(X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_56])]) ).
tff(f1512,plain,
! [X0: $int] :
( ( 0 = X0 )
| ( $uminus(X0) != X0 ) ),
inference(cnf_transformation,[],[f977]) ).
tff(f977,plain,
! [X0: $int] :
( ( ( $uminus(X0) = X0 )
| ( 0 != X0 ) )
& ( ( 0 = X0 )
| ( $uminus(X0) != X0 ) ) ),
inference(nnf_transformation,[],[f60]) ).
tff(f60,axiom,
! [X0: $int] :
( ( $uminus(X0) = X0 )
<=> ( 0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
tff(f3029,plain,
spl107_55,
inference(avatar_split_clause,[],[f1508,f3027]) ).
tff(f3027,plain,
( spl107_55
<=> ! [X0: $int] :
( ( 0 = X0 )
| ( 0 != $uminus(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_55])]) ).
tff(f1508,plain,
! [X0: $int] :
( ( 0 = X0 )
| ( 0 != $uminus(X0) ) ),
inference(cnf_transformation,[],[f975]) ).
tff(f975,plain,
! [X0: $int] :
( ( ( 0 = $uminus(X0) )
| ( 0 != X0 ) )
& ( ( 0 = X0 )
| ( 0 != $uminus(X0) ) ) ),
inference(nnf_transformation,[],[f62]) ).
tff(f62,axiom,
! [X0: $int] :
( ( 0 = $uminus(X0) )
<=> ( 0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).
tff(f3025,plain,
spl107_54,
inference(avatar_split_clause,[],[f1504,f3023]) ).
tff(f3023,plain,
( spl107_54
<=> ! [X0: $int] :
( ( 0 = X0 )
| ( 0 != 'sgn$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_54])]) ).
tff(f1504,plain,
! [X0: $int] :
( ( 0 = X0 )
| ( 0 != 'sgn$'(X0) ) ),
inference(cnf_transformation,[],[f973]) ).
tff(f973,plain,
! [X0: $int] :
( ( ( 0 = 'sgn$'(X0) )
| ( 0 != X0 ) )
& ( ( 0 = X0 )
| ( 0 != 'sgn$'(X0) ) ) ),
inference(nnf_transformation,[],[f182]) ).
tff(f182,axiom,
! [X0: $int] :
( ( 0 = 'sgn$'(X0) )
<=> ( 0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom180) ).
tff(f3021,plain,
spl107_53,
inference(avatar_split_clause,[],[f1498,f3019]) ).
tff(f3019,plain,
( spl107_53
<=> ! [X0: $int] :
( $less(0,X0)
| ( 1 != 'sgn$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_53])]) ).
tff(f1498,plain,
! [X0: $int] :
( $less(0,X0)
| ( 1 != 'sgn$'(X0) ) ),
inference(cnf_transformation,[],[f970]) ).
tff(f970,plain,
! [X0: $int] :
( ( ( 1 = 'sgn$'(X0) )
| ~ $less(0,X0) )
& ( $less(0,X0)
| ( 1 != 'sgn$'(X0) ) ) ),
inference(nnf_transformation,[],[f186]) ).
tff(f186,axiom,
! [X0: $int] :
( ( 1 = 'sgn$'(X0) )
<=> $less(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom184) ).
tff(f3017,plain,
spl107_52,
inference(avatar_split_clause,[],[f1468,f3015]) ).
tff(f1468,plain,
! [X0: $int] :
( ( 1 = 'sgn$'(X0) )
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f707]) ).
tff(f707,plain,
! [X0: $int] :
( ( 1 = 'sgn$'(X0) )
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,axiom,
! [X0: $int] :
( $less(0,X0)
=> ( 1 = 'sgn$'(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom177) ).
tff(f3013,plain,
spl107_51,
inference(avatar_split_clause,[],[f1408,f3011]) ).
tff(f3011,plain,
( spl107_51
<=> ! [X0: 'Num$'] : ( 'plus$'(X0,'one$') = 'plus$'('one$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_51])]) ).
tff(f1408,plain,
! [X0: 'Num$'] : ( 'plus$'(X0,'one$') = 'plus$'('one$',X0) ),
inference(cnf_transformation,[],[f424]) ).
tff(f424,axiom,
! [X0: 'Num$'] : ( 'plus$'(X0,'one$') = 'plus$'('one$',X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom422) ).
tff(f3009,plain,
spl107_50,
inference(avatar_split_clause,[],[f1407,f3007]) ).
tff(f3007,plain,
( spl107_50
<=> ! [X0: $int] : ( 'sgn$'($uminus(X0)) = $uminus('sgn$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_50])]) ).
tff(f1407,plain,
! [X0: $int] : ( 'sgn$'($uminus(X0)) = $uminus('sgn$'(X0)) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,axiom,
! [X0: $int] : ( 'sgn$'($uminus(X0)) = $uminus('sgn$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).
tff(f3005,plain,
spl107_49,
inference(avatar_split_clause,[],[f1398,f3003]) ).
tff(f1398,plain,
! [X0: 'Nat$'] : ( 0 != $sum('fun_app$k'('of_nat$',X0),1) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,axiom,
! [X0: 'Nat$'] : ( 0 != $sum('fun_app$k'('of_nat$',X0),1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom139) ).
tff(f3001,plain,
spl107_48,
inference(avatar_split_clause,[],[f611,f2999]) ).
tff(f2997,plain,
( spl107_47
| ~ spl107_4
| ~ spl107_36 ),
inference(avatar_split_clause,[],[f2984,f2932,f2790,f2995]) ).
tff(f2995,plain,
( spl107_47
<=> ! [X0: 'Nat$'] : sP16('uuj$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_47])]) ).
tff(f2984,plain,
( ! [X0: 'Nat$'] : sP16('uuj$',X0)
| ~ spl107_4
| ~ spl107_36 ),
inference(resolution,[],[f2933,f2791]) ).
tff(f2975,plain,
spl107_46,
inference(avatar_split_clause,[],[f2501,f2973]) ).
tff(f2973,plain,
( spl107_46
<=> ! [X0: 'Num$'] : ( 'sub$'('inc$'(X0),'one$') != -1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_46])]) ).
tff(f2501,plain,
! [X0: 'Num$'] : ( 'sub$'('inc$'(X0),'one$') != -1 ),
inference(evaluation,[],[f2241]) ).
tff(f2241,plain,
! [X0: 'Num$'] : ( $uminus(1) != 'sub$'('inc$'(X0),'one$') ),
inference(definition_unfolding,[],[f1359,f1403]) ).
tff(f1359,plain,
! [X0: 'Num$'] : ( $uminus(1) != 'numeral$'(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,axiom,
! [X0: 'Num$'] : ( $uminus(1) != 'numeral$'(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).
tff(f2971,plain,
spl107_45,
inference(avatar_split_clause,[],[f2500,f2969]) ).
tff(f2969,plain,
( spl107_45
<=> ! [X0: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_45])]) ).
tff(f2500,plain,
! [X0: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),-1),
inference(evaluation,[],[f2244]) ).
tff(f2244,plain,
! [X0: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),$uminus(1)),
inference(definition_unfolding,[],[f1362,f1403]) ).
tff(f1362,plain,
! [X0: 'Num$'] : ~ $less('numeral$'(X0),$uminus(1)),
inference(cnf_transformation,[],[f262]) ).
tff(f262,axiom,
! [X0: 'Num$'] : ~ $less('numeral$'(X0),$uminus(1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).
tff(f2967,plain,
spl107_44,
inference(avatar_split_clause,[],[f2499,f2965]) ).
tff(f2965,plain,
( spl107_44
<=> ! [X0: 'Num$'] : $less(-1,'sub$'('inc$'(X0),'one$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_44])]) ).
tff(f2499,plain,
! [X0: 'Num$'] : $less(-1,'sub$'('inc$'(X0),'one$')),
inference(evaluation,[],[f2245]) ).
tff(f2245,plain,
! [X0: 'Num$'] : $less($uminus(1),'sub$'('inc$'(X0),'one$')),
inference(definition_unfolding,[],[f1383,f1403]) ).
tff(f1383,plain,
! [X0: 'Num$'] : $less($uminus(1),'numeral$'(X0)),
inference(cnf_transformation,[],[f261]) ).
tff(f261,axiom,
! [X0: 'Num$'] : $less($uminus(1),'numeral$'(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).
tff(f2963,plain,
spl107_43,
inference(avatar_split_clause,[],[f2360,f2961]) ).
tff(f2360,plain,
! [X1: 'Nat_bool_fun$'] : 'fun_app$c'('case_nat$a'(tltrue,X1),'nat$'(0)),
inference(equality_resolution,[],[f1840]) ).
tff(f1840,plain,
! [X0: tlbool,X1: 'Nat_bool_fun$'] :
( 'fun_app$c'('case_nat$a'(X0,X1),'nat$'(0))
| ( tltrue != X0 ) ),
inference(cnf_transformation,[],[f1104]) ).
tff(f2959,plain,
spl107_42,
inference(avatar_split_clause,[],[f2330,f2956]) ).
tff(f2956,plain,
( spl107_42
<=> ( 1 = 'sub$'('inc$'('one$'),'one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_42])]) ).
tff(f2330,plain,
1 = 'sub$'('inc$'('one$'),'one$'),
inference(equality_resolution,[],[f2284]) ).
tff(f2284,plain,
! [X0: 'Num$'] :
( ( 1 = 'sub$'('inc$'(X0),'one$') )
| ( 'one$' != X0 ) ),
inference(definition_unfolding,[],[f1501,f1403]) ).
tff(f1501,plain,
! [X0: 'Num$'] :
( ( 1 = 'numeral$'(X0) )
| ( 'one$' != X0 ) ),
inference(cnf_transformation,[],[f971]) ).
tff(f2954,plain,
spl107_41,
inference(avatar_split_clause,[],[f2296,f2952]) ).
tff(f2952,plain,
( spl107_41
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'bit0$'(X0) != 'inc$'('bit0$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_41])]) ).
tff(f2296,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'bit0$'(X0) != 'inc$'('bit0$'(X1)) ),
inference(definition_unfolding,[],[f1564,f1391]) ).
tff(f1564,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'bit0$'(X0) != 'bit1$'(X1) ),
inference(cnf_transformation,[],[f449]) ).
tff(f449,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'bit0$'(X0) != 'bit1$'(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom447) ).
tff(f2950,plain,
spl107_40,
inference(avatar_split_clause,[],[f2238,f2948]) ).
tff(f2238,plain,
! [X0: 'Num$'] : $less(0,'sub$'('inc$'(X0),'one$')),
inference(definition_unfolding,[],[f1356,f1403]) ).
tff(f1356,plain,
! [X0: 'Num$'] : $less(0,'numeral$'(X0)),
inference(cnf_transformation,[],[f245]) ).
tff(f245,axiom,
! [X0: 'Num$'] : $less(0,'numeral$'(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom243) ).
tff(f2946,plain,
spl107_39,
inference(avatar_split_clause,[],[f2237,f2944]) ).
tff(f2944,plain,
( spl107_39
<=> ! [X0: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_39])]) ).
tff(f2237,plain,
! [X0: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),0),
inference(definition_unfolding,[],[f1355,f1403]) ).
tff(f1355,plain,
! [X0: 'Num$'] : ~ $less('numeral$'(X0),0),
inference(cnf_transformation,[],[f244]) ).
tff(f244,axiom,
! [X0: 'Num$'] : ~ $less('numeral$'(X0),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom242) ).
tff(f2942,plain,
spl107_38,
inference(avatar_split_clause,[],[f2236,f2940]) ).
tff(f2940,plain,
( spl107_38
<=> ! [X0: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_38])]) ).
tff(f2236,plain,
! [X0: 'Num$'] : ~ $less('sub$'('inc$'(X0),'one$'),1),
inference(definition_unfolding,[],[f1354,f1403]) ).
tff(f1354,plain,
! [X0: 'Num$'] : ~ $less('numeral$'(X0),1),
inference(cnf_transformation,[],[f246]) ).
tff(f246,axiom,
! [X0: 'Num$'] : ~ $less('numeral$'(X0),1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).
tff(f2938,plain,
spl107_37,
inference(avatar_split_clause,[],[f2235,f2936]) ).
tff(f2936,plain,
( spl107_37
<=> ! [X0: 'Num$'] : ( 0 != 'sub$'('inc$'(X0),'one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_37])]) ).
tff(f2235,plain,
! [X0: 'Num$'] : ( 0 != 'sub$'('inc$'(X0),'one$') ),
inference(definition_unfolding,[],[f1353,f1403]) ).
tff(f1353,plain,
! [X0: 'Num$'] : ( 0 != 'numeral$'(X0) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,axiom,
! [X0: 'Num$'] : ( 0 != 'numeral$'(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom230) ).
tff(f2934,plain,
spl107_36,
inference(avatar_split_clause,[],[f1919,f2932]) ).
tff(f1919,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP16(X1,X0)
| ~ 'fun_app$c'(X1,X0) ),
inference(cnf_transformation,[],[f1171]) ).
tff(f2930,plain,
spl107_35,
inference(avatar_split_clause,[],[f1903,f2928]) ).
tff(f2928,plain,
( spl107_35
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'(X1,X0)
| ~ sP14(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_35])]) ).
tff(f1903,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$c'(X1,X0)
| ~ sP14(X1,X0) ),
inference(cnf_transformation,[],[f1153]) ).
tff(f2926,plain,
spl107_34,
inference(avatar_split_clause,[],[f1466,f2924]) ).
tff(f2924,plain,
( spl107_34
<=> ! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_34])]) ).
tff(f1466,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(cnf_transformation,[],[f633]) ).
tff(f633,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(rectify,[],[f516]) ).
tff(f516,axiom,
! [X6: tlbool] :
( ( tlfalse = X6 )
| ( tltrue = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_515) ).
tff(f2922,plain,
spl107_33,
inference(avatar_split_clause,[],[f1397,f2920]) ).
tff(f2920,plain,
( spl107_33
<=> ! [X0: 'Nat_a_set_fun$'] : ( 'suffix$'('nat$'(0),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_33])]) ).
tff(f1397,plain,
! [X0: 'Nat_a_set_fun$'] : ( 'suffix$'('nat$'(0),X0) = X0 ),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
! [X0: 'Nat_a_set_fun$'] : ( 'suffix$'('nat$'(0),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14) ).
tff(f2918,plain,
spl107_32,
inference(avatar_split_clause,[],[f1396,f2916]) ).
tff(f2916,plain,
( spl107_32
<=> ! [X0: 'Nat$'] : ( 'nat$'('fun_app$k'('of_nat$',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_32])]) ).
tff(f1396,plain,
! [X0: 'Nat$'] : ( 'nat$'('fun_app$k'('of_nat$',X0)) = X0 ),
inference(cnf_transformation,[],[f504]) ).
tff(f504,axiom,
! [X0: 'Nat$'] : ( 'nat$'('fun_app$k'('of_nat$',X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).
tff(f2914,plain,
spl107_31,
inference(avatar_split_clause,[],[f1392,f2912]) ).
tff(f2912,plain,
( spl107_31
<=> ! [X0: $int] : ( 'sgn$'(X0) = 'sgn$'('sgn$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_31])]) ).
tff(f1392,plain,
! [X0: $int] : ( 'sgn$'(X0) = 'sgn$'('sgn$'(X0)) ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,axiom,
! [X0: $int] : ( 'sgn$'(X0) = 'sgn$'('sgn$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom171) ).
tff(f2910,plain,
spl107_30,
inference(avatar_split_clause,[],[f1388,f2908]) ).
tff(f1388,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(cnf_transformation,[],[f485]) ).
tff(f485,axiom,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).
tff(f2906,plain,
spl107_29,
inference(avatar_split_clause,[],[f1339,f2903]) ).
tff(f2903,plain,
( spl107_29
<=> ( 'one$' = 'fun_app$p'('num_of_nat$','nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_29])]) ).
tff(f1339,plain,
'one$' = 'fun_app$p'('num_of_nat$','nat$'(0)),
inference(cnf_transformation,[],[f316]) ).
tff(f316,axiom,
'one$' = 'fun_app$p'('num_of_nat$','nat$'(0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).
tff(f2901,plain,
spl107_28,
inference(avatar_split_clause,[],[f615,f2899]) ).
tff(f2899,plain,
( spl107_28
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_28])]) ).
tff(f615,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f2897,plain,
spl107_27,
inference(avatar_split_clause,[],[f2234,f2895]) ).
tff(f2895,plain,
( spl107_27
<=> ! [X0: 'Num$'] : ( 'one$' != 'inc$'('bit0$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_27])]) ).
tff(f2234,plain,
! [X0: 'Num$'] : ( 'one$' != 'inc$'('bit0$'(X0)) ),
inference(definition_unfolding,[],[f1351,f1391]) ).
tff(f1351,plain,
! [X0: 'Num$'] : ( 'one$' != 'bit1$'(X0) ),
inference(cnf_transformation,[],[f425]) ).
tff(f425,axiom,
! [X0: 'Num$'] : ( 'one$' != 'bit1$'(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).
tff(f2893,plain,
spl107_26,
inference(avatar_split_clause,[],[f1382,f2891]) ).
tff(f1382,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(cnf_transformation,[],[f479]) ).
tff(f479,axiom,
! [X0: $int] : $less(X0,$sum(X0,1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).
tff(f2889,plain,
spl107_25,
inference(avatar_split_clause,[],[f1371,f2887]) ).
tff(f2887,plain,
( spl107_25
<=> ! [X0: 'Nat$'] : ( 'fun_app$e'('uud$',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_25])]) ).
tff(f1371,plain,
! [X0: 'Nat$'] : ( 'fun_app$e'('uud$',X0) = X0 ),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: 'Nat$'] : ( 'fun_app$e'('uud$',X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
tff(f2885,plain,
spl107_24,
inference(avatar_split_clause,[],[f1370,f2883]) ).
tff(f2883,plain,
( spl107_24
<=> ! [X0: 'A_ltln$'] : ( 'fun_app$i'('id$',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_24])]) ).
tff(f1370,plain,
! [X0: 'A_ltln$'] : ( 'fun_app$i'('id$',X0) = X0 ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,axiom,
! [X0: 'A_ltln$'] : ( 'fun_app$i'('id$',X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).
tff(f2881,plain,
spl107_23,
inference(avatar_split_clause,[],[f1367,f2879]) ).
tff(f2879,plain,
( spl107_23
<=> ! [X0: 'Nat_a_set_fun_set$'] : ( 'collect$'('uua$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_23])]) ).
tff(f1367,plain,
! [X0: 'Nat_a_set_fun_set$'] : ( 'collect$'('uua$'(X0)) = X0 ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,axiom,
! [X0: 'Nat_a_set_fun_set$'] : ( 'collect$'('uua$'(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).
tff(f2877,plain,
spl107_22,
inference(avatar_split_clause,[],[f1363,f2875]) ).
tff(f2875,plain,
( spl107_22
<=> ! [X0: 'Nat$'] : ~ $less('fun_app$k'('of_nat$',X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_22])]) ).
tff(f1363,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$k'('of_nat$',X0),0),
inference(cnf_transformation,[],[f145]) ).
tff(f145,axiom,
! [X0: 'Nat$'] : ~ $less('fun_app$k'('of_nat$',X0),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).
tff(f2873,plain,
spl107_21,
inference(avatar_split_clause,[],[f1334,f2870]) ).
tff(f2870,plain,
( spl107_21
<=> ( 0 = 'sub$'('one$','one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_21])]) ).
tff(f1334,plain,
0 = 'sub$'('one$','one$'),
inference(cnf_transformation,[],[f309]) ).
tff(f309,axiom,
0 = 'sub$'('one$','one$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom307) ).
tff(f2868,plain,
spl107_20,
inference(avatar_split_clause,[],[f621,f2866]) ).
tff(f2866,plain,
( spl107_20
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_20])]) ).
tff(f621,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f2864,plain,
spl107_19,
inference(avatar_split_clause,[],[f613,f2862]) ).
tff(f2862,plain,
( spl107_19
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_19])]) ).
tff(f613,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f2860,plain,
( ~ spl107_18
| spl107_17 ),
inference(avatar_split_clause,[],[f2855,f2851,f2857]) ).
tff(f2851,plain,
( spl107_17
<=> 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_17])]) ).
tff(f2855,plain,
( ~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('phi$','x$'))
| spl107_17 ),
inference(forward_demodulation,[],[f2853,f1592]) ).
tff(f2853,plain,
( ~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$'))
| spl107_17 ),
inference(avatar_component_clause,[],[f2851]) ).
tff(f2854,plain,
~ spl107_17,
inference(avatar_split_clause,[],[f1303,f2851]) ).
tff(f1303,plain,
~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
inference(cnf_transformation,[],[f632]) ).
tff(f632,plain,
~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
inference(flattening,[],[f13]) ).
tff(f13,negated_conjecture,
~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
inference(negated_conjecture,[],[f12]) ).
tff(f12,conjecture,
'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture11) ).
tff(f2849,plain,
spl107_16,
inference(avatar_split_clause,[],[f2505,f2846]) ).
tff(f2846,plain,
( spl107_16
<=> ( 'dbl_dec$'(0) = -1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_16])]) ).
tff(f2505,plain,
'dbl_dec$'(0) = -1,
inference(evaluation,[],[f1336]) ).
tff(f1336,plain,
$uminus(1) = 'dbl_dec$'(0),
inference(cnf_transformation,[],[f78]) ).
tff(f78,axiom,
$uminus(1) = 'dbl_dec$'(0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).
tff(f2844,plain,
spl107_15,
inference(avatar_split_clause,[],[f2504,f2841]) ).
tff(f2841,plain,
( spl107_15
<=> ( -1 = 'dbl_inc$'(-1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_15])]) ).
tff(f2504,plain,
-1 = 'dbl_inc$'(-1),
inference(evaluation,[],[f1342]) ).
tff(f1342,plain,
$uminus(1) = 'dbl_inc$'($uminus(1)),
inference(cnf_transformation,[],[f50]) ).
tff(f50,axiom,
$uminus(1) = 'dbl_inc$'($uminus(1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
tff(f2839,plain,
spl107_14,
inference(avatar_split_clause,[],[f2503,f2836]) ).
tff(f2836,plain,
( spl107_14
<=> ( -1 = 'sgn$'(-1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_14])]) ).
tff(f2503,plain,
-1 = 'sgn$'(-1),
inference(evaluation,[],[f1343]) ).
tff(f1343,plain,
$uminus(1) = 'sgn$'($uminus(1)),
inference(cnf_transformation,[],[f185]) ).
tff(f185,axiom,
$uminus(1) = 'sgn$'($uminus(1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom183) ).
tff(f2834,plain,
spl107_13,
inference(avatar_split_clause,[],[f2502,f2831]) ).
tff(f2831,plain,
( spl107_13
<=> ( 'dbl_dec$'(-1) = -3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_13])]) ).
tff(f2502,plain,
'dbl_dec$'(-1) = -3,
inference(evaluation,[],[f1344]) ).
tff(f1344,plain,
'dbl_dec$'($uminus(1)) = $uminus(3),
inference(cnf_transformation,[],[f322]) ).
tff(f322,axiom,
'dbl_dec$'($uminus(1)) = $uminus(3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).
tff(f2829,plain,
spl107_12,
inference(avatar_split_clause,[],[f1530,f2827]) ).
tff(f2827,plain,
( spl107_12
<=> ! [X0: 'Num$'] : ~ 'fun_app$o'('less$'(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_12])]) ).
tff(f1530,plain,
! [X0: 'Num$'] : ~ 'fun_app$o'('less$'(X0),X0),
inference(cnf_transformation,[],[f657]) ).
tff(f657,plain,
! [X0: 'Num$'] : ~ 'fun_app$o'('less$'(X0),X0),
inference(flattening,[],[f656]) ).
tff(f656,plain,
! [X0: 'Num$'] : ~ 'fun_app$o'('less$'(X0),X0),
inference(true_and_false_elimination,[],[f164]) ).
tff(f164,axiom,
! [X0: 'Num$'] :
( 'fun_app$o'('less$'(X0),X0)
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).
tff(f2825,plain,
spl107_11,
inference(avatar_split_clause,[],[f1352,f2823]) ).
tff(f2823,plain,
( spl107_11
<=> ! [X0: 'Num$'] : ( 'one$' != 'bit0$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_11])]) ).
tff(f1352,plain,
! [X0: 'Num$'] : ( 'one$' != 'bit0$'(X0) ),
inference(cnf_transformation,[],[f426]) ).
tff(f426,axiom,
! [X0: 'Num$'] : ( 'one$' != 'bit0$'(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).
tff(f2821,plain,
spl107_10,
inference(avatar_split_clause,[],[f1326,f2818]) ).
tff(f2818,plain,
( spl107_10
<=> ( 0 = 'sgn$'(0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_10])]) ).
tff(f1326,plain,
0 = 'sgn$'(0),
inference(cnf_transformation,[],[f174]) ).
tff(f174,axiom,
0 = 'sgn$'(0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom172) ).
tff(f2816,plain,
spl107_9,
inference(avatar_split_clause,[],[f1324,f2813]) ).
tff(f2813,plain,
( spl107_9
<=> ( 1 = 'sgn$'(1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_9])]) ).
tff(f1324,plain,
1 = 'sgn$'(1),
inference(cnf_transformation,[],[f175]) ).
tff(f175,axiom,
1 = 'sgn$'(1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom173) ).
tff(f2811,plain,
spl107_8,
inference(avatar_split_clause,[],[f1323,f2808]) ).
tff(f2808,plain,
( spl107_8
<=> ( 1 = 'dbl_inc$'(0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_8])]) ).
tff(f1323,plain,
1 = 'dbl_inc$'(0),
inference(cnf_transformation,[],[f37]) ).
tff(f37,axiom,
1 = 'dbl_inc$'(0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom35) ).
tff(f2806,plain,
spl107_7,
inference(avatar_split_clause,[],[f1322,f2803]) ).
tff(f2803,plain,
( spl107_7
<=> ( 1 = 'dbl_dec$'(1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_7])]) ).
tff(f1322,plain,
1 = 'dbl_dec$'(1),
inference(cnf_transformation,[],[f46]) ).
tff(f46,axiom,
1 = 'dbl_dec$'(1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).
tff(f2801,plain,
spl107_6,
inference(avatar_split_clause,[],[f1320,f2798]) ).
tff(f2798,plain,
( spl107_6
<=> ( 3 = 'dbl_inc$'(1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_6])]) ).
tff(f1320,plain,
3 = 'dbl_inc$'(1),
inference(cnf_transformation,[],[f393]) ).
tff(f393,axiom,
3 = 'dbl_inc$'(1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
tff(f2796,plain,
spl107_5,
inference(avatar_split_clause,[],[f2442,f2794]) ).
tff(f2794,plain,
( spl107_5
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ~ sP8(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_5])]) ).
tff(f2442,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ~ sP8(X0,X1),
inference(trivial_inequality_removal,[],[f1736]) ).
tff(f1736,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 != 0 )
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f1044]) ).
tff(f1044,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 0 != 0 )
& $less('fun_app$k'('of_nat$',X1),'fun_app$k'('of_nat$',X0)) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f1043]) ).
tff(f1043,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( ( 0 != 0 )
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP8(X1,X0) ),
inference(nnf_transformation,[],[f900]) ).
tff(f900,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( ( 0 != 0 )
& $less('fun_app$k'('of_nat$',X0),'fun_app$k'('of_nat$',X1)) )
| ~ sP8(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
tff(f2792,plain,
spl107_4,
inference(avatar_split_clause,[],[f1496,f2790]) ).
tff(f1496,plain,
! [X0: 'Nat$'] : 'fun_app$c'('uuj$',X0),
inference(cnf_transformation,[],[f653]) ).
tff(f653,plain,
! [X0: 'Nat$'] : 'fun_app$c'('uuj$',X0),
inference(true_and_false_elimination,[],[f11]) ).
tff(f11,axiom,
! [X0: 'Nat$'] :
( 'fun_app$c'('uuj$',X0)
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
tff(f2788,plain,
spl107_3,
inference(avatar_split_clause,[],[f1495,f2786]) ).
tff(f1495,plain,
! [X0: 'Nat$'] : ~ 'fun_app$c'('uui$',X0),
inference(cnf_transformation,[],[f652]) ).
tff(f652,plain,
! [X0: 'Nat$'] : ~ 'fun_app$c'('uui$',X0),
inference(flattening,[],[f651]) ).
tff(f651,plain,
! [X0: 'Nat$'] : ~ 'fun_app$c'('uui$',X0),
inference(true_and_false_elimination,[],[f10]) ).
tff(f10,axiom,
! [X0: 'Nat$'] :
( 'fun_app$c'('uui$',X0)
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
tff(f2784,plain,
~ spl107_2,
inference(avatar_split_clause,[],[f1304,f2781]) ).
tff(f2781,plain,
( spl107_2
<=> ( tltrue = tlfalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_2])]) ).
tff(f1304,plain,
tltrue != tlfalse,
inference(cnf_transformation,[],[f517]) ).
tff(f517,axiom,
tltrue != tlfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_516) ).
tff(f2779,plain,
spl107_1,
inference(avatar_split_clause,[],[f616,f2777]) ).
tff(f2777,plain,
( spl107_1
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_1])]) ).
tff(f616,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 15:35:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (13422)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.41 % (13447)WARNING: value z3 for option sas not known
% 0.14/0.41 % (13445)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.41 % (13448)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.41 % (13450)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)
% 0.14/0.41 % (13451)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)
% 0.14/0.41 % (13449)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)
% 0.14/0.41 % (13446)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.41 % (13447)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)
% 0.20/0.45 % (13445)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.45 % (13445)Terminated due to inappropriate strategy.
% 0.20/0.45 % (13445)------------------------------
% 0.20/0.45 % (13445)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.45 % (13445)Termination reason: Inappropriate
% 0.20/0.45
% 0.20/0.45 % (13445)Memory used [KB]: 1783
% 0.20/0.45 % (13445)Time elapsed: 0.043 s
% 0.20/0.45 % (13445)Instructions burned: 108 (million)
% 0.20/0.45 % (13446)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.45 % (13446)Terminated due to inappropriate strategy.
% 0.20/0.45 % (13446)------------------------------
% 0.20/0.45 % (13446)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.45 % (13446)Termination reason: Inappropriate
% 0.20/0.45
% 0.20/0.45 % (13446)Memory used [KB]: 1783
% 0.20/0.45 % (13446)Time elapsed: 0.042 s
% 0.20/0.45 % (13446)Instructions burned: 107 (million)
% 0.20/0.45 % (13445)------------------------------
% 0.20/0.45 % (13445)------------------------------
% 0.20/0.45 % (13446)------------------------------
% 0.20/0.45 % (13446)------------------------------
% 0.20/0.45 % (13448)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.45 % (13448)Terminated due to inappropriate strategy.
% 0.20/0.45 % (13448)------------------------------
% 0.20/0.45 % (13448)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.45 % (13448)Termination reason: Inappropriate
% 0.20/0.45
% 0.20/0.45 % (13448)Memory used [KB]: 1795
% 0.20/0.45 % (13448)Time elapsed: 0.045 s
% 0.20/0.45 % (13448)Instructions burned: 112 (million)
% 0.20/0.46 % (13448)------------------------------
% 0.20/0.46 % (13448)------------------------------
% 0.20/0.47 % (13465)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)
% 0.20/0.47 % (13464)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.47 % (13466)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.50 % (13464)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.50 % (13464)Terminated due to inappropriate strategy.
% 0.20/0.50 % (13464)------------------------------
% 0.20/0.50 % (13464)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.50 % (13464)Termination reason: Inappropriate
% 0.20/0.50
% 0.20/0.50 % (13464)Memory used [KB]: 1836
% 0.20/0.50 % (13464)Time elapsed: 0.033 s
% 0.20/0.50 % (13464)Instructions burned: 77 (million)
% 0.20/0.50 % (13464)------------------------------
% 0.20/0.50 % (13464)------------------------------
% 0.20/0.52 % (13470)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.20/0.53 % (13449)First to succeed.
% 0.20/0.54 % (13449)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13422"
% 0.20/0.54 % (13449)Refutation found. Thanks to Tanya!
% 0.20/0.54 % SZS status Theorem for theBenchmark
% 0.20/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55 % (13449)------------------------------
% 0.20/0.55 % (13449)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.55 % (13449)Termination reason: Refutation
% 0.20/0.55
% 0.20/0.55 % (13449)Memory used [KB]: 3393
% 0.20/0.55 % (13449)Time elapsed: 0.132 s
% 0.20/0.55 % (13449)Instructions burned: 290 (million)
% 0.20/0.55 % (13422)Success in time 0.188 s
%------------------------------------------------------------------------------