TSTP Solution File: ITP409_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n022.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 : Tue Aug 22 10:44:37 EDT 2023
% Result : Theorem 23.33s 6.51s
% Output : CNFRefutation 23.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 18:40:48 EDT 2023
% 0.14/0.35 % CPUTime :
% 23.33/6.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.33/6.53
% 23.33/6.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.33/6.55 %$ fun_app$c > fun_app$ > antimono$a > antimono$ > fun_app$g > fun_app$f > fun_app$e > fun_app$d > fun_app$b > fun_app$a > #nlpp > times$a > times$ > greatest$a > greatest$ > zero$ > uu$ > tltrue > tlfalse > p$ > one$ > of_nat$a > of_nat$ > of_int$ > nat$ > n_0$ > less_eq$ > less$ > #skF_7 > #skF_34 > #skF_187 > #skF_198 > #skF_75 > #skF_191 > #skF_37 > #skF_140 > #skF_142 > #skF_116 > #skF_73 > #skF_130 > #skF_15 > #skF_71 > #skF_124 > #skF_21 > #skF_214 > #skF_134 > #skF_53 > #skF_203 > #skF_3 > #skF_38 > #skF_100 > #skF_93 > #skF_52 > #skF_155 > #skF_1 > #skF_41 > #skF_78 > #skF_168 > #skF_177 > #skF_65 > #skF_46 > #skF_181 > #skF_40 > #skF_28 > #skF_119 > #skF_77 > #skF_95 > #skF_48 > #skF_85 > #skF_196 > #skF_190 > #skF_107 > #skF_22 > #skF_111 > #skF_50 > #skF_26 > #skF_150 > #skF_98 > #skF_204 > #skF_121 > #skF_129 > #skF_195 > #skF_49 > #skF_183 > #skF_20 > #skF_2 > #skF_104 > #skF_126 > #skF_102 > #skF_122 > #skF_112 > #skF_137 > #skF_153 > #skF_70 > #skF_135 > #skF_29 > #skF_94 > #skF_54 > #skF_81 > #skF_164 > #skF_146 > #skF_120 > #skF_10 > #skF_184 > #skF_79 > #skF_174 > #skF_105 > #skF_58 > #skF_18 > #skF_125 > #skF_173 > #skF_51 > #skF_90 > #skF_76 > #skF_72 > #skF_131 > #skF_115 > #skF_158 > #skF_44 > #skF_159 > #skF_178 > #skF_163 > #skF_133 > #skF_194 > #skF_61 > #skF_66 > #skF_199 > #skF_59 > #skF_25 > #skF_47 > #skF_156 > #skF_19 > #skF_189 > #skF_152 > #skF_170 > #skF_17 > #skF_136 > #skF_97 > #skF_166 > #skF_69 > #skF_23 > #skF_148 > #skF_127 > #skF_175 > #skF_182 > #skF_161 > #skF_36 > #skF_13 > #skF_63 > #skF_62 > #skF_210 > #skF_92 > #skF_57 > #skF_180 > #skF_202 > #skF_197 > #skF_9 > #skF_5 > #skF_84 > #skF_201 > #skF_60 > #skF_149 > #skF_56 > #skF_33 > #skF_55 > #skF_207 > #skF_67 > #skF_14 > #skF_42 > #skF_212 > #skF_27 > #skF_143 > #skF_151 > #skF_186 > #skF_35 > #skF_87 > #skF_6 > #skF_139 > #skF_109 > #skF_64 > #skF_128 > #skF_176 > #skF_209 > #skF_82 > #skF_138 > #skF_108 > #skF_43 > #skF_213 > #skF_12 > #skF_45 > #skF_206 > #skF_113 > #skF_68 > #skF_30 > #skF_86 > #skF_4 > #skF_80 > #skF_205 > #skF_123 > #skF_24 > #skF_167 > #skF_208 > #skF_8 > #skF_91 > #skF_83 > #skF_141 > #skF_157 > #skF_171 > #skF_185 > #skF_132 > #skF_162 > #skF_154 > #skF_145 > #skF_211 > #skF_32 > #skF_160 > #skF_39 > #skF_110 > #skF_172 > #skF_16 > #skF_165 > #skF_99 > #skF_89 > #skF_96 > #skF_147 > #skF_169 > #skF_31 > #skF_200 > #skF_118 > #skF_114 > #skF_117 > #skF_144 > #skF_101 > #skF_192 > #skF_88 > #skF_179 > #skF_106 > #skF_11 > #skF_74 > #skF_193 > #skF_188 > #skF_103
% 23.33/6.55
% 23.33/6.55 %Foreground sorts:
% 23.33/6.55 tff(Nat_nat_bool_fun_fun$, type, Nat_nat_bool_fun_fun$: $tType ).
% 23.33/6.55 tff(Nat$, type, Nat$: $tType ).
% 23.33/6.55 tff(Int_nat_fun$, type, Int_nat_fun$: $tType ).
% 23.33/6.55 tff(tlbool, type, tlbool: $tType ).
% 23.33/6.55 tff(Int_int_fun$, type, Int_int_fun$: $tType ).
% 23.33/6.55 tff(Nat_nat_fun$, type, Nat_nat_fun$: $tType ).
% 23.33/6.55 tff(Nat_int_fun$, type, Nat_int_fun$: $tType ).
% 23.33/6.55 tff(Int_int_bool_fun_fun$, type, Int_int_bool_fun_fun$: $tType ).
% 23.33/6.55 tff(Nat_bool_fun$, type, Nat_bool_fun$: $tType ).
% 23.33/6.55 tff(Int_bool_fun$, type, Int_bool_fun$: $tType ).
% 23.33/6.55
% 23.33/6.55 %Background operators:
% 23.33/6.55 tff('#skE_2', type, '#skE_2': $int).
% 23.33/6.55 tff('#skE_1', type, '#skE_1': $int).
% 23.33/6.55 tff('#skE_5', type, '#skE_5': $int).
% 23.33/6.55 tff('#skE_4', type, '#skE_4': $int).
% 23.33/6.55 tff('#skE_3', type, '#skE_3': $int).
% 23.33/6.55
% 23.33/6.55 %Foreground operators:
% 23.33/6.55 tff('#skF_7', type, '#skF_7': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_34', type, '#skF_34': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_187', type, '#skF_187': Nat$ > Nat$).
% 23.33/6.55 tff('#skF_198', type, '#skF_198': $int > Nat$).
% 23.33/6.55 tff('#skF_75', type, '#skF_75': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_191', type, '#skF_191': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_37', type, '#skF_37': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_140', type, '#skF_140': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_142', type, '#skF_142': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_116', type, '#skF_116': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_73', type, '#skF_73': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_130', type, '#skF_130': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_15', type, '#skF_15': Nat_bool_fun$ > Nat$).
% 23.33/6.55 tff('#skF_71', type, '#skF_71': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_124', type, '#skF_124': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_21', type, '#skF_21': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_214', type, '#skF_214': $int > Nat$).
% 23.33/6.55 tff('#skF_134', type, '#skF_134': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_53', type, '#skF_53': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_203', type, '#skF_203': (Int_bool_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_3', type, '#skF_3': Nat$).
% 23.33/6.55 tff('#skF_38', type, '#skF_38': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_100', type, '#skF_100': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_93', type, '#skF_93': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_52', type, '#skF_52': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff(uu$, type, uu$: Int_int_bool_fun_fun$).
% 23.33/6.55 tff('#skF_155', type, '#skF_155': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_1', type, '#skF_1': Nat$).
% 23.33/6.55 tff(times$a, type, times$a: Nat$ > Nat_nat_fun$).
% 23.33/6.55 tff('#skF_41', type, '#skF_41': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_78', type, '#skF_78': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_168', type, '#skF_168': (Int_bool_fun$ * $int * Int_bool_fun$) > $int).
% 23.33/6.55 tff('#skF_177', type, '#skF_177': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff(nat$, type, nat$: Int_nat_fun$).
% 23.33/6.55 tff(less_eq$, type, less_eq$: Nat_nat_bool_fun_fun$).
% 23.33/6.55 tff('#skF_65', type, '#skF_65': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_46', type, '#skF_46': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_181', type, '#skF_181': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_40', type, '#skF_40': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_28', type, '#skF_28': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_119', type, '#skF_119': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_77', type, '#skF_77': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_95', type, '#skF_95': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_48', type, '#skF_48': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_85', type, '#skF_85': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_196', type, '#skF_196': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff(of_nat$a, type, of_nat$a: Nat_nat_fun$).
% 23.33/6.55 tff('#skF_190', type, '#skF_190': Nat$ > Nat$).
% 23.33/6.55 tff(antimono$a, type, antimono$a: Int_int_fun$ > $o).
% 23.33/6.55 tff('#skF_107', type, '#skF_107': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_22', type, '#skF_22': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_111', type, '#skF_111': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_50', type, '#skF_50': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_26', type, '#skF_26': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_150', type, '#skF_150': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_98', type, '#skF_98': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_204', type, '#skF_204': $int > Nat$).
% 23.33/6.55 tff(tlfalse, type, tlfalse: tlbool).
% 23.33/6.55 tff('#skF_121', type, '#skF_121': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_129', type, '#skF_129': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_195', type, '#skF_195': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff(fun_app$e, type, fun_app$e: (Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_49', type, '#skF_49': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff(fun_app$d, type, fun_app$d: (Nat_nat_bool_fun_fun$ * Nat$) > Nat_bool_fun$).
% 23.33/6.55 tff('#skF_183', type, '#skF_183': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_20', type, '#skF_20': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_2', type, '#skF_2': Nat$).
% 23.33/6.55 tff('#skF_104', type, '#skF_104': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_126', type, '#skF_126': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_102', type, '#skF_102': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_122', type, '#skF_122': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_112', type, '#skF_112': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff(fun_app$a, type, fun_app$a: (Int_int_bool_fun_fun$ * $int) > Int_bool_fun$).
% 23.33/6.55 tff('#skF_137', type, '#skF_137': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_153', type, '#skF_153': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_70', type, '#skF_70': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_135', type, '#skF_135': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_29', type, '#skF_29': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_94', type, '#skF_94': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_54', type, '#skF_54': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_81', type, '#skF_81': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_164', type, '#skF_164': (Nat$ * Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_146', type, '#skF_146': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff(times$, type, times$: $int > Int_int_fun$).
% 23.33/6.55 tff('#skF_120', type, '#skF_120': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_10', type, '#skF_10': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_184', type, '#skF_184': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_79', type, '#skF_79': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_174', type, '#skF_174': Int_int_fun$ > $int).
% 23.33/6.55 tff('#skF_105', type, '#skF_105': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_58', type, '#skF_58': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_18', type, '#skF_18': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_125', type, '#skF_125': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_173', type, '#skF_173': Int_int_fun$ > $int).
% 23.33/6.55 tff('#skF_51', type, '#skF_51': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff(greatest$, type, greatest$: Int_bool_fun$ > $int).
% 23.33/6.55 tff('#skF_90', type, '#skF_90': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_76', type, '#skF_76': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_72', type, '#skF_72': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_131', type, '#skF_131': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_115', type, '#skF_115': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_158', type, '#skF_158': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_44', type, '#skF_44': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_159', type, '#skF_159': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_178', type, '#skF_178': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_163', type, '#skF_163': (Nat$ * Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_133', type, '#skF_133': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_194', type, '#skF_194': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_61', type, '#skF_61': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_66', type, '#skF_66': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff(less$, type, less$: Nat_nat_bool_fun_fun$).
% 23.33/6.55 tff('#skF_199', type, '#skF_199': $int > Nat$).
% 23.33/6.55 tff('#skF_59', type, '#skF_59': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_25', type, '#skF_25': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_47', type, '#skF_47': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_156', type, '#skF_156': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff(of_nat$, type, of_nat$: Nat_int_fun$).
% 23.33/6.55 tff('#skF_19', type, '#skF_19': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_189', type, '#skF_189': (Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_152', type, '#skF_152': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_170', type, '#skF_170': (Nat_bool_fun$ * Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_17', type, '#skF_17': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_136', type, '#skF_136': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_97', type, '#skF_97': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_166', type, '#skF_166': (Int_bool_fun$ * $int) > $int).
% 23.33/6.55 tff(antimono$, type, antimono$: Nat_int_fun$ > $o).
% 23.33/6.55 tff('#skF_69', type, '#skF_69': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_23', type, '#skF_23': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_148', type, '#skF_148': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_127', type, '#skF_127': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff(one$, type, one$: Nat$).
% 23.33/6.55 tff('#skF_175', type, '#skF_175': Int_int_fun$ > $int).
% 23.33/6.55 tff('#skF_182', type, '#skF_182': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff(zero$, type, zero$: Nat$).
% 23.33/6.55 tff('#skF_161', type, '#skF_161': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff(greatest$a, type, greatest$a: Nat_bool_fun$ > Nat$).
% 23.33/6.55 tff('#skF_36', type, '#skF_36': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_13', type, '#skF_13': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_63', type, '#skF_63': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_62', type, '#skF_62': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_210', type, '#skF_210': $int > Nat$).
% 23.33/6.55 tff('#skF_92', type, '#skF_92': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_57', type, '#skF_57': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_180', type, '#skF_180': Nat$ > Nat$).
% 23.33/6.55 tff('#skF_202', type, '#skF_202': (Int_bool_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_197', type, '#skF_197': $int > Nat$).
% 23.33/6.55 tff('#skF_9', type, '#skF_9': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_5', type, '#skF_5': Nat$).
% 23.33/6.55 tff('#skF_84', type, '#skF_84': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_201', type, '#skF_201': $int > Nat$).
% 23.33/6.55 tff('#skF_60', type, '#skF_60': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_149', type, '#skF_149': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_56', type, '#skF_56': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_33', type, '#skF_33': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_55', type, '#skF_55': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_207', type, '#skF_207': $int > Nat$).
% 23.33/6.55 tff('#skF_67', type, '#skF_67': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_14', type, '#skF_14': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_42', type, '#skF_42': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_212', type, '#skF_212': $int > Nat$).
% 23.33/6.55 tff('#skF_27', type, '#skF_27': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_143', type, '#skF_143': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_151', type, '#skF_151': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_186', type, '#skF_186': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff(n_0$, type, n_0$: Nat$).
% 23.33/6.55 tff('#skF_35', type, '#skF_35': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_87', type, '#skF_87': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff(of_int$, type, of_int$: Int_int_fun$).
% 23.33/6.55 tff('#skF_6', type, '#skF_6': Nat$).
% 23.33/6.55 tff('#skF_139', type, '#skF_139': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_109', type, '#skF_109': (Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_64', type, '#skF_64': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_128', type, '#skF_128': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_176', type, '#skF_176': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_209', type, '#skF_209': $int > Nat$).
% 23.33/6.55 tff('#skF_82', type, '#skF_82': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_138', type, '#skF_138': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff(fun_app$b, type, fun_app$b: (Nat_int_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_108', type, '#skF_108': (Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_43', type, '#skF_43': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_213', type, '#skF_213': $int > Nat$).
% 23.33/6.55 tff(fun_app$c, type, fun_app$c: (Nat_bool_fun$ * Nat$) > $o).
% 23.33/6.55 tff('#skF_12', type, '#skF_12': Nat$ > Nat$).
% 23.33/6.55 tff('#skF_45', type, '#skF_45': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_206', type, '#skF_206': $int > Nat$).
% 23.33/6.55 tff('#skF_113', type, '#skF_113': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_68', type, '#skF_68': ($int * $int * Int_nat_fun$ * Nat$) > $int).
% 23.33/6.55 tff('#skF_30', type, '#skF_30': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_86', type, '#skF_86': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_4', type, '#skF_4': Nat$).
% 23.33/6.55 tff('#skF_80', type, '#skF_80': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff(p$, type, p$: Nat_bool_fun$).
% 23.33/6.55 tff('#skF_205', type, '#skF_205': $int > Nat$).
% 23.33/6.55 tff('#skF_123', type, '#skF_123': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_24', type, '#skF_24': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_167', type, '#skF_167': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_208', type, '#skF_208': $int > Nat$).
% 23.33/6.55 tff('#skF_8', type, '#skF_8': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff(fun_app$, type, fun_app$: (Int_bool_fun$ * $int) > $o).
% 23.33/6.55 tff(tltrue, type, tltrue: tlbool).
% 23.33/6.55 tff('#skF_91', type, '#skF_91': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_83', type, '#skF_83': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_141', type, '#skF_141': (Nat$ * Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_157', type, '#skF_157': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_171', type, '#skF_171': (Nat_bool_fun$ * Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_185', type, '#skF_185': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_132', type, '#skF_132': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_162', type, '#skF_162': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_154', type, '#skF_154': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_145', type, '#skF_145': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_211', type, '#skF_211': (Nat_bool_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_32', type, '#skF_32': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_160', type, '#skF_160': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_39', type, '#skF_39': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_110', type, '#skF_110': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_172', type, '#skF_172': Int_int_fun$ > $int).
% 23.33/6.55 tff('#skF_16', type, '#skF_16': Nat_bool_fun$ > Nat$).
% 23.33/6.55 tff(fun_app$g, type, fun_app$g: (Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_165', type, '#skF_165': Nat_int_fun$ > Nat$).
% 23.33/6.55 tff('#skF_99', type, '#skF_99': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_89', type, '#skF_89': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_96', type, '#skF_96': ($int * Int_int_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_147', type, '#skF_147': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_169', type, '#skF_169': (Int_bool_fun$ * $int * Int_bool_fun$) > $int).
% 23.33/6.55 tff('#skF_31', type, '#skF_31': ($int * Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_200', type, '#skF_200': $int > Nat$).
% 23.33/6.55 tff('#skF_118', type, '#skF_118': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_114', type, '#skF_114': (Nat$ * Nat$ * Nat_int_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_117', type, '#skF_117': (Nat$ * Nat$ * Nat_nat_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_144', type, '#skF_144': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_101', type, '#skF_101': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 23.33/6.55 tff('#skF_192', type, '#skF_192': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_88', type, '#skF_88': ($int * $int * Int_int_fun$ * $int) > $int).
% 23.33/6.55 tff('#skF_179', type, '#skF_179': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_106', type, '#skF_106': (Nat$ * Nat_bool_fun$) > Nat$).
% 23.33/6.55 tff('#skF_11', type, '#skF_11': (Nat$ * Nat$) > Nat$).
% 23.33/6.55 tff(fun_app$f, type, fun_app$f: (Int_nat_fun$ * $int) > Nat$).
% 23.33/6.55 tff('#skF_74', type, '#skF_74': (Nat$ * Int_nat_fun$ * $int * $int) > $int).
% 23.33/6.55 tff('#skF_193', type, '#skF_193': Nat$ > Nat$).
% 23.33/6.55 tff('#skF_188', type, '#skF_188': (Nat_bool_fun$ * Nat$) > Nat$).
% 23.33/6.55 tff('#skF_103', type, '#skF_103': (Nat$ * Nat$) > Nat$).
% 23.33/6.55
% 23.72/6.58 tff(f_50, negated_conjecture, ~((![A__questionmark_v0:Nat$]: ($lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, A__questionmark_v0)) => fun_app$c(p$, A__questionmark_v0))) <=> (fun_app$c(p$, n_0$) & (![A__questionmark_v0:Nat$]: ($lesseq($sum(fun_app$b(of_nat$, n_0$), 1), fun_app$b(of_nat$, A__questionmark_v0)) => fun_app$c(p$, A__questionmark_v0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conjecture1)).
% 23.72/6.58 tff(f_4524, axiom, (![A__questionmark_v0:Nat$]: $lesseq(0, fun_app$b(of_nat$, A__questionmark_v0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom612)).
% 23.72/6.58 tff(f_4527, axiom, (![A__questionmark_v0:Nat$]: (fun_app$f(nat$, fun_app$b(of_nat$, A__questionmark_v0)) = A__questionmark_v0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom613)).
% 23.72/6.58 tff(f_3925, axiom, (![A__questionmark_v0a:$int]: ($lesseq(0, A__questionmark_v0a) => (?[A__questionmark_v1:Nat$]: (A__questionmark_v0a = fun_app$b(of_nat$, A__questionmark_v1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom502)).
% 23.72/6.58 tff(f_3933, axiom, (![A__questionmark_v0a:$int]: (($lesseq(0, A__questionmark_v0a) & (![A__questionmark_v1:Nat$]: ((A__questionmark_v0a = fun_app$b(of_nat$, A__questionmark_v1)) => $false))) => $false)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom503)).
% 23.72/6.58 tff(f_3879, axiom, (![A__questionmark_v0a:$int]: ($less(0, A__questionmark_v0a) => (?[A__questionmark_v1:Nat$]: ($less(0, fun_app$b(of_nat$, A__questionmark_v1)) & (A__questionmark_v0a = fun_app$b(of_nat$, A__questionmark_v1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom494)).
% 23.72/6.58 tff(f_2531, axiom, (![A__questionmark_v0:Nat$]: ($less(fun_app$b(of_nat$, A__questionmark_v0), $sum(0, 1)) <=> (fun_app$b(of_nat$, A__questionmark_v0) = 0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom300)).
% 23.72/6.58 tff(c_30, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | ~$lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, A__questionmark_v0_3)) | fun_app$c(p$, n_0$))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2818, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), fun_app$b(of_nat$, n_0$)) | fun_app$c(p$, n_0$))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_30])).
% 23.72/6.58 tff(c_3089, plain, (fun_app$b(of_nat$, n_0$)='#skE_1'), inference(define, [status(thm), theory('equality')], [c_2818])).
% 23.72/6.58 tff(c_2109, plain, (![A__questionmark_v0_1410:Nat$]: ($lesseq(0, fun_app$b(of_nat$, A__questionmark_v0_1410)))), inference(cnfTransformation, [status(thm)], [f_4524])).
% 23.72/6.58 tff(c_2124, plain, (![A__questionmark_v0_1410:Nat$]: (~$less(fun_app$b(of_nat$, A__questionmark_v0_1410), 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_2109])).
% 23.72/6.58 tff(c_3099, plain, (~$less('#skE_1', 0)), inference(superposition, [status(thm), theory('equality')], [c_3089, c_2124])).
% 23.72/6.58 tff(c_15, plain, (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | $lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, '#skF_2'))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2823, plain, (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | ~$less(fun_app$b(of_nat$, '#skF_2'), fun_app$b(of_nat$, n_0$))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_15])).
% 23.72/6.58 tff(c_3248, plain, (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | ~$less(fun_app$b(of_nat$, '#skF_2'), '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_3089, c_2823])).
% 23.72/6.58 tff(c_3253, plain, (fun_app$b(of_nat$, '#skF_2')='#skE_2'), inference(define, [status(thm), theory('equality')], [c_3248])).
% 23.72/6.58 tff(c_12, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | ~$lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, A__questionmark_v0_3)) | $lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, '#skF_2')))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2824, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), fun_app$b(of_nat$, n_0$)) | ~$less(fun_app$b(of_nat$, '#skF_2'), fun_app$b(of_nat$, n_0$)))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_12])).
% 23.72/6.58 tff(c_3543, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), '#skE_1') | ~$less('#skE_2', '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_3253, c_3089, c_3089, c_2824])).
% 23.72/6.58 tff(c_3546, plain, (~$less('#skE_2', '#skE_1')), inference(splitLeft, [status(thm)], [c_3543])).
% 23.72/6.58 tff(c_3268, plain, (~$less('#skE_2', 0)), inference(superposition, [status(thm), theory('equality')], [c_3253, c_2124])).
% 23.72/6.58 tff(c_2123, plain, (![A__questionmark_v0_1411:Nat$]: (fun_app$f(nat$, fun_app$b(of_nat$, A__questionmark_v0_1411))=A__questionmark_v0_1411)), inference(cnfTransformation, [status(thm)], [f_4527])).
% 23.72/6.58 tff(c_3267, plain, (fun_app$f(nat$, '#skE_2')='#skF_2'), inference(superposition, [status(thm), theory('equality')], [c_3253, c_2123])).
% 23.72/6.58 tff(c_1796, plain, (![A__questionmark_v0_1280a:$int]: (fun_app$b(of_nat$, '#skF_199'(A__questionmark_v0_1280a))=A__questionmark_v0_1280a | ~$lesseq(0, A__questionmark_v0_1280a))), inference(cnfTransformation, [status(thm)], [f_3925])).
% 23.72/6.58 tff(c_3665, plain, (![A__questionmark_v0_2801a:$int]: (fun_app$b(of_nat$, '#skF_199'(A__questionmark_v0_2801a))=A__questionmark_v0_2801a | $less(A__questionmark_v0_2801a, 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1796])).
% 23.72/6.58 tff(c_6072, plain, (![A__questionmark_v0_3113a:$int]: (fun_app$f(nat$, A__questionmark_v0_3113a)='#skF_199'(A__questionmark_v0_3113a) | $less(A__questionmark_v0_3113a, 0))), inference(superposition, [status(thm), theory('equality')], [c_3665, c_2123])).
% 23.72/6.58 tff(c_6131, plain, ('#skF_2'='#skF_199'('#skE_2') | $less('#skE_2', 0)), inference(superposition, [status(thm), theory('equality')], [c_3267, c_6072])).
% 23.72/6.58 tff(c_6235, plain, ('#skF_2'='#skF_199'('#skE_2')), inference(negUnitSimplification, [status(thm)], [c_3268, c_6131])).
% 23.72/6.58 tff(c_1798, plain, (![A__questionmark_v0_1282a:$int]: (fun_app$b(of_nat$, '#skF_200'(A__questionmark_v0_1282a))=A__questionmark_v0_1282a | ~$lesseq(0, A__questionmark_v0_1282a))), inference(cnfTransformation, [status(thm)], [f_3933])).
% 23.72/6.58 tff(c_3596, plain, (![A__questionmark_v0_2798a:$int]: (fun_app$b(of_nat$, '#skF_200'(A__questionmark_v0_2798a))=A__questionmark_v0_2798a | $less(A__questionmark_v0_2798a, 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1798])).
% 23.72/6.58 tff(c_5923, plain, (![A__questionmark_v0_3096a:$int]: (fun_app$f(nat$, A__questionmark_v0_3096a)='#skF_200'(A__questionmark_v0_3096a) | $less(A__questionmark_v0_3096a, 0))), inference(superposition, [status(thm), theory('equality')], [c_3596, c_2123])).
% 23.72/6.58 tff(c_5958, plain, ('#skF_2'='#skF_200'('#skE_2') | $less('#skE_2', 0)), inference(superposition, [status(thm), theory('equality')], [c_3267, c_5923])).
% 23.72/6.58 tff(c_8494, plain, ('#skF_199'('#skE_2')='#skF_200'('#skE_2') | $less('#skE_2', 0)), inference(demodulation, [status(thm), theory('equality')], [c_6235, c_5958])).
% 23.72/6.58 tff(c_8499, plain, ('#skF_199'('#skE_2')='#skF_200'('#skE_2')), inference(negUnitSimplification, [status(thm)], [c_3268, c_8494])).
% 23.72/6.58 tff(c_6256, plain, (fun_app$b(of_nat$, '#skF_199'('#skE_2'))='#skE_2'), inference(demodulation, [status(thm), theory('equality')], [c_6235, c_3253])).
% 23.72/6.58 tff(c_8645, plain, (fun_app$b(of_nat$, '#skF_200'('#skE_2'))='#skE_2'), inference(demodulation, [status(thm), theory('equality')], [c_8499, c_6256])).
% 23.72/6.58 tff(c_7140, plain, ('#skF_199'('#skE_2')='#skF_200'('#skE_2') | $less('#skE_2', 0)), inference(demodulation, [status(thm), theory('equality')], [c_6235, c_5958])).
% 23.72/6.58 tff(c_7145, plain, ('#skF_199'('#skE_2')='#skF_200'('#skE_2')), inference(negUnitSimplification, [status(thm)], [c_3268, c_7140])).
% 23.72/6.58 tff(c_7290, plain, (fun_app$b(of_nat$, '#skF_200'('#skE_2'))='#skE_2'), inference(demodulation, [status(thm), theory('equality')], [c_7145, c_6256])).
% 23.72/6.58 tff(c_3152, plain, (![A__questionmark_v0_2319:Nat$]: (fun_app$f(nat$, fun_app$b(of_nat$, A__questionmark_v0_2319))=A__questionmark_v0_2319)), inference(cnfTransformation, [status(thm)], [f_4527])).
% 23.72/6.58 tff(c_3175, plain, (fun_app$f(nat$, '#skE_1')=n_0$), inference(superposition, [status(thm), theory('equality')], [c_3089, c_3152])).
% 23.72/6.58 tff(c_5961, plain, (n_0$='#skF_200'('#skE_1') | $less('#skE_1', 0)), inference(superposition, [status(thm), theory('equality')], [c_3175, c_5923])).
% 23.72/6.58 tff(c_6145, plain, (n_0$='#skF_200'('#skE_1')), inference(negUnitSimplification, [status(thm)], [c_3099, c_5961])).
% 23.72/6.58 tff(c_6188, plain, (fun_app$b(of_nat$, '#skF_200'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_6145, c_3089])).
% 23.72/6.58 tff(c_21, plain, (![A__questionmark_v0_3:Nat$, A__questionmark_v0_4:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | ~$lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, A__questionmark_v0_3)) | fun_app$c(p$, A__questionmark_v0_4) | ~$lesseq($sum(fun_app$b(of_nat$, n_0$), 1), fun_app$b(of_nat$, A__questionmark_v0_4)))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2821, plain, (![A__questionmark_v0_3:Nat$, A__questionmark_v0_4:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), fun_app$b(of_nat$, n_0$)) | fun_app$c(p$, A__questionmark_v0_4) | $less(fun_app$b(of_nat$, A__questionmark_v0_4), $sum(1, fun_app$b(of_nat$, n_0$))))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_21])).
% 23.72/6.58 tff(c_6275, plain, (![A__questionmark_v0_3:Nat$, A__questionmark_v0_4:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), '#skE_1') | fun_app$c(p$, A__questionmark_v0_4) | $less(fun_app$b(of_nat$, A__questionmark_v0_4), $sum(1, '#skE_1')))), inference(demodulation, [status(thm), theory('equality')], [c_6188, c_6145, c_6188, c_6145, c_2821])).
% 23.72/6.58 tff(c_7820, plain, (![A__questionmark_v0_3768:Nat$]: (fun_app$c(p$, A__questionmark_v0_3768) | $less(fun_app$b(of_nat$, A__questionmark_v0_3768), $sum(1, '#skE_1')))), inference(splitLeft, [status(thm)], [c_6275])).
% 23.72/6.58 tff(c_7, plain, (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | ~fun_app$c(p$, '#skF_2')), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_3005, plain, (~fun_app$c(p$, '#skF_2')), inference(splitLeft, [status(thm)], [c_7])).
% 23.72/6.58 tff(c_6259, plain, (~fun_app$c(p$, '#skF_199'('#skE_2'))), inference(demodulation, [status(thm), theory('equality')], [c_6235, c_3005])).
% 23.72/6.58 tff(c_7174, plain, (~fun_app$c(p$, '#skF_200'('#skE_2'))), inference(demodulation, [status(thm), theory('equality')], [c_7145, c_6259])).
% 23.72/6.58 tff(c_7823, plain, ($less(fun_app$b(of_nat$, '#skF_200'('#skE_2')), $sum(1, '#skE_1'))), inference(resolution, [status(thm)], [c_7820, c_7174])).
% 23.72/6.58 tff(c_7851, plain, ($less('#skE_2', $sum(1, '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_7290, c_7823])).
% 23.72/6.58 tff(c_3273, plain, (fun_app$f(nat$, '#skE_2')='#skF_2'), inference(superposition, [status(thm), theory('equality')], [c_3253, c_2123])).
% 23.72/6.58 tff(c_3296, plain, (n_0$='#skF_2' | '#skE_2'!='#skE_1'), inference(superposition, [status(thm), theory('equality')], [c_3273, c_3175])).
% 23.72/6.58 tff(c_3307, plain, ('#skE_2'!='#skE_1'), inference(splitLeft, [status(thm)], [c_3296])).
% 23.72/6.58 tff(c_7875, plain, $false, inference(close, [status(thm), theory('LIA')], [c_7851, c_3546, c_3307])).
% 23.72/6.58 tff(c_9225, plain, (![A__questionmark_v0_3965:Nat$]: (fun_app$c(p$, A__questionmark_v0_3965) | $less(fun_app$b(of_nat$, A__questionmark_v0_3965), '#skE_1'))), inference(splitRight, [status(thm)], [c_6275])).
% 23.72/6.58 tff(c_8529, plain, (~fun_app$c(p$, '#skF_200'('#skE_2'))), inference(demodulation, [status(thm), theory('equality')], [c_8499, c_6259])).
% 23.72/6.58 tff(c_9228, plain, ($less(fun_app$b(of_nat$, '#skF_200'('#skE_2')), '#skE_1')), inference(resolution, [status(thm)], [c_9225, c_8529])).
% 23.72/6.58 tff(c_9255, plain, ($less('#skE_2', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_8645, c_9228])).
% 23.72/6.58 tff(c_9257, plain, $false, inference(negUnitSimplification, [status(thm)], [c_3546, c_9255])).
% 23.72/6.58 tff(c_9263, plain, ($less('#skE_2', '#skE_1')), inference(splitRight, [status(thm)], [c_3543])).
% 23.72/6.58 tff(c_3308, plain, (![A__questionmark_v0_2776a:$int]: (fun_app$b(of_nat$, '#skF_197'(A__questionmark_v0_2776a))=A__questionmark_v0_2776a | ~$less(0, A__questionmark_v0_2776a))), inference(cnfTransformation, [status(thm)], [f_3879])).
% 23.72/6.58 tff(c_9661, plain, (![A__questionmark_v0_3987a:$int]: (fun_app$f(nat$, A__questionmark_v0_3987a)='#skF_197'(A__questionmark_v0_3987a) | ~$less(0, A__questionmark_v0_3987a))), inference(superposition, [status(thm), theory('equality')], [c_3308, c_2123])).
% 23.72/6.58 tff(c_9692, plain, (n_0$='#skF_197'('#skE_1') | ~$less(0, '#skE_1')), inference(superposition, [status(thm), theory('equality')], [c_9661, c_3175])).
% 23.72/6.58 tff(c_9881, plain, (~$less(0, '#skE_1')), inference(splitLeft, [status(thm)], [c_9692])).
% 23.72/6.58 tff(c_9882, plain, $false, inference(close, [status(thm), theory('LIA')], [c_9881, c_9263, c_3268])).
% 23.72/6.58 tff(c_9971, plain, (n_0$='#skF_197'('#skE_1')), inference(splitRight, [status(thm)], [c_9692])).
% 23.72/6.58 tff(c_10007, plain, (fun_app$b(of_nat$, '#skF_197'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_9971, c_3089])).
% 23.72/6.58 tff(c_10543, plain, (![A__questionmark_v0_4091:Nat$]: (fun_app$c(p$, A__questionmark_v0_4091) | $less(fun_app$b(of_nat$, A__questionmark_v0_4091), '#skE_1'))), inference(splitRight, [status(thm)], [c_3543])).
% 23.72/6.58 tff(c_24, plain, (![A__questionmark_v0_4:Nat$]: (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | fun_app$c(p$, A__questionmark_v0_4) | ~$lesseq($sum(fun_app$b(of_nat$, n_0$), 1), fun_app$b(of_nat$, A__questionmark_v0_4)))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2820, plain, (![A__questionmark_v0_4:Nat$]: (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | fun_app$c(p$, A__questionmark_v0_4) | $less(fun_app$b(of_nat$, A__questionmark_v0_4), $sum(1, fun_app$b(of_nat$, n_0$))))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_24])).
% 23.72/6.58 tff(c_9412, plain, (![A__questionmark_v0_4:Nat$]: (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | fun_app$c(p$, A__questionmark_v0_4) | $less(fun_app$b(of_nat$, A__questionmark_v0_4), $sum(1, '#skE_1')))), inference(demodulation, [status(thm), theory('equality')], [c_3089, c_2820])).
% 23.72/6.58 tff(c_9414, plain, (~fun_app$c(p$, n_0$)), inference(splitLeft, [status(thm)], [c_9412])).
% 23.72/6.58 tff(c_9989, plain, (~fun_app$c(p$, '#skF_197'('#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_9971, c_9414])).
% 23.72/6.58 tff(c_10546, plain, ($less(fun_app$b(of_nat$, '#skF_197'('#skE_1')), '#skE_1')), inference(resolution, [status(thm)], [c_10543, c_9989])).
% 23.72/6.58 tff(c_10576, plain, ($less('#skE_1', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_10007, c_10546])).
% 23.72/6.58 tff(c_10579, plain, $false, inference(backgroundSimplification, [status(thm), theory('LIA')], [c_10576])).
% 23.72/6.58 tff(c_10581, plain, (fun_app$c(p$, n_0$)), inference(splitRight, [status(thm)], [c_9412])).
% 23.72/6.58 tff(c_18, plain, ($lesseq($sum(fun_app$b(of_nat$, n_0$), 1), fun_app$b(of_nat$, '#skF_1')) | ~fun_app$c(p$, n_0$) | $lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, '#skF_2'))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2822, plain, (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, fun_app$b(of_nat$, n_0$))) | ~fun_app$c(p$, n_0$) | ~$less(fun_app$b(of_nat$, '#skF_2'), fun_app$b(of_nat$, n_0$))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_18])).
% 23.72/6.58 tff(c_10890, plain, (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_9263, c_3089, c_3253, c_10581, c_3089, c_2822])).
% 23.72/6.58 tff(c_10895, plain, (fun_app$b(of_nat$, '#skF_1')='#skE_3'), inference(define, [status(thm), theory('equality')], [c_10890])).
% 23.72/6.58 tff(c_11879, plain, (![A__questionmark_v0_4229:Nat$]: (fun_app$c(p$, A__questionmark_v0_4229) | $less(fun_app$b(of_nat$, A__questionmark_v0_4229), '#skE_1'))), inference(splitRight, [status(thm)], [c_3543])).
% 23.72/6.58 tff(c_3250, plain, (fun_app$b(of_nat$, '#skF_2')='#skE_2'), inference(define, [status(thm), theory('equality')], [c_3248])).
% 23.72/6.58 tff(c_3249, plain, (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | ~$less(fun_app$b(of_nat$, '#skF_2'), '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_3089, c_2823])).
% 23.72/6.58 tff(c_3254, plain, (~fun_app$c(p$, '#skF_1') | ~fun_app$c(p$, n_0$) | ~$less('#skE_2', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_3250, c_3249])).
% 23.72/6.58 tff(c_11140, plain, (~fun_app$c(p$, '#skF_1')), inference(demodulation, [status(thm), theory('equality')], [c_9263, c_10581, c_3254])).
% 23.72/6.58 tff(c_11885, plain, ($less(fun_app$b(of_nat$, '#skF_1'), '#skE_1')), inference(resolution, [status(thm)], [c_11879, c_11140])).
% 23.72/6.58 tff(c_11915, plain, ($less('#skE_3', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_10895, c_11885])).
% 23.72/6.58 tff(c_10892, plain, (fun_app$b(of_nat$, '#skF_1')='#skE_3'), inference(define, [status(thm), theory('equality')], [c_10890])).
% 23.72/6.58 tff(c_10891, plain, (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_9263, c_3089, c_3253, c_10581, c_3089, c_2822])).
% 23.72/6.58 tff(c_10896, plain, (~$less('#skE_3', $sum(1, '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_10892, c_10891])).
% 23.72/6.58 tff(c_11939, plain, $false, inference(close, [status(thm), theory('LIA')], [c_11915, c_10896])).
% 23.72/6.58 tff(c_11942, plain, ('#skE_2'='#skE_1'), inference(splitRight, [status(thm)], [c_3296])).
% 23.72/6.58 tff(c_11969, plain, (fun_app$f(nat$, '#skE_1')='#skF_2'), inference(demodulation, [status(thm), theory('equality')], [c_11942, c_3267])).
% 23.72/6.58 tff(c_12344, plain, (![A__questionmark_v0_4263a:$int]: (fun_app$b(of_nat$, '#skF_199'(A__questionmark_v0_4263a))=A__questionmark_v0_4263a | $less(A__questionmark_v0_4263a, 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1796])).
% 23.72/6.58 tff(c_12659, plain, (![A__questionmark_v0_4287a:$int]: (fun_app$f(nat$, A__questionmark_v0_4287a)='#skF_199'(A__questionmark_v0_4287a) | $less(A__questionmark_v0_4287a, 0))), inference(superposition, [status(thm), theory('equality')], [c_12344, c_2123])).
% 23.72/6.58 tff(c_12709, plain, ('#skF_2'='#skF_199'('#skE_1') | $less('#skE_1', 0)), inference(superposition, [status(thm), theory('equality')], [c_11969, c_12659])).
% 23.72/6.58 tff(c_12721, plain, ('#skF_2'='#skF_199'('#skE_1')), inference(negUnitSimplification, [status(thm)], [c_3099, c_12709])).
% 23.72/6.58 tff(c_11940, plain, (n_0$='#skF_2'), inference(splitRight, [status(thm)], [c_3296])).
% 23.72/6.58 tff(c_11953, plain, (fun_app$b(of_nat$, '#skF_2')='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_11940, c_3089])).
% 23.72/6.58 tff(c_12804, plain, (fun_app$b(of_nat$, '#skF_199'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_12721, c_11953])).
% 23.72/6.58 tff(c_12805, plain, (fun_app$b(of_nat$, '#skF_199'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_12721, c_11953])).
% 23.72/6.58 tff(c_1100, plain, (![A__questionmark_v0_800:Nat$]: (fun_app$b(of_nat$, A__questionmark_v0_800)=0 | ~$less(fun_app$b(of_nat$, A__questionmark_v0_800), $sum(0, 1)))), inference(cnfTransformation, [status(thm)], [f_2531])).
% 23.72/6.58 tff(c_2562, plain, (![A__questionmark_v0_800:Nat$]: (fun_app$b(of_nat$, A__questionmark_v0_800)=0 | ~$less(fun_app$b(of_nat$, A__questionmark_v0_800), 1))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1100])).
% 23.72/6.58 tff(c_12811, plain, (fun_app$b(of_nat$, '#skF_199'('#skE_1'))=0 | ~$less('#skE_1', 1)), inference(superposition, [status(thm), theory('equality')], [c_12805, c_2562])).
% 23.72/6.58 tff(c_12836, plain, ('#skE_1'=0 | ~$less('#skE_1', 1)), inference(demodulation, [status(thm), theory('equality')], [c_12804, c_12811])).
% 23.72/6.58 tff(c_12853, plain, (~$less('#skE_1', 1)), inference(splitLeft, [status(thm)], [c_12836])).
% 23.72/6.58 tff(c_11988, plain, (![A__questionmark_v0_4246a:$int]: (fun_app$b(of_nat$, '#skF_197'(A__questionmark_v0_4246a))=A__questionmark_v0_4246a | ~$less(0, A__questionmark_v0_4246a))), inference(cnfTransformation, [status(thm)], [f_3879])).
% 23.72/6.58 tff(c_12543, plain, (![A__questionmark_v0_4276a:$int]: (fun_app$f(nat$, A__questionmark_v0_4276a)='#skF_197'(A__questionmark_v0_4276a) | ~$less(0, A__questionmark_v0_4276a))), inference(superposition, [status(thm), theory('equality')], [c_11988, c_2123])).
% 23.72/6.58 tff(c_12569, plain, ('#skF_2'='#skF_197'('#skE_1') | ~$less(0, '#skE_1')), inference(superposition, [status(thm), theory('equality')], [c_11969, c_12543])).
% 23.72/6.58 tff(c_12715, plain, (~$less(0, '#skE_1')), inference(splitLeft, [status(thm)], [c_12569])).
% 23.72/6.58 tff(c_12854, plain, $false, inference(close, [status(thm), theory('LIA')], [c_12853, c_12715])).
% 23.72/6.58 tff(c_12857, plain, ('#skE_1'=0), inference(splitRight, [status(thm)], [c_12836])).
% 23.72/6.58 tff(c_12747, plain, (fun_app$b(of_nat$, '#skF_199'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_12721, c_11953])).
% 23.72/6.58 tff(c_12887, plain, (fun_app$b(of_nat$, '#skF_199'(0))=0), inference(demodulation, [status(thm), theory('equality')], [c_12857, c_12857, c_12747])).
% 23.72/6.58 tff(c_12989, plain, (fun_app$f(nat$, 0)='#skF_199'(0)), inference(superposition, [status(thm), theory('equality')], [c_12887, c_2123])).
% 23.72/6.58 tff(c_12366, plain, (![A__questionmark_v0_4264a:$int]: (fun_app$b(of_nat$, '#skF_200'(A__questionmark_v0_4264a))=A__questionmark_v0_4264a | $less(A__questionmark_v0_4264a, 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1798])).
% 23.72/6.58 tff(c_12384, plain, (![A__questionmark_v0_4264a:$int]: (fun_app$f(nat$, A__questionmark_v0_4264a)='#skF_200'(A__questionmark_v0_4264a) | $less(A__questionmark_v0_4264a, 0))), inference(superposition, [status(thm), theory('equality')], [c_12366, c_2123])).
% 23.72/6.58 tff(c_13011, plain, ('#skF_199'(0)='#skF_200'(0) | $less(0, 0)), inference(superposition, [status(thm), theory('equality')], [c_12989, c_12384])).
% 23.72/6.58 tff(c_13037, plain, ('#skF_199'(0)='#skF_200'(0)), inference(backgroundSimplification, [status(thm), theory('LIA')], [c_13011])).
% 23.72/6.58 tff(c_12753, plain, (~fun_app$c(p$, '#skF_199'('#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_12721, c_3005])).
% 23.72/6.58 tff(c_12888, plain, (~fun_app$c(p$, '#skF_199'(0))), inference(demodulation, [status(thm), theory('equality')], [c_12857, c_12753])).
% 23.72/6.58 tff(c_13063, plain, (~fun_app$c(p$, '#skF_200'(0))), inference(demodulation, [status(thm), theory('equality')], [c_13037, c_12888])).
% 23.72/6.58 tff(c_12750, plain, (n_0$='#skF_199'('#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_12721, c_11940])).
% 23.72/6.58 tff(c_12889, plain, (n_0$='#skF_199'(0)), inference(demodulation, [status(thm), theory('equality')], [c_12857, c_12750])).
% 23.72/6.58 tff(c_13065, plain, (n_0$='#skF_200'(0)), inference(demodulation, [status(thm), theory('equality')], [c_13037, c_12889])).
% 23.72/6.58 tff(c_3085, plain, (fun_app$b(of_nat$, n_0$)='#skE_1'), inference(define, [status(thm), theory('equality')], [c_2818])).
% 23.72/6.58 tff(c_3092, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), '#skE_1') | fun_app$c(p$, n_0$))), inference(demodulation, [status(thm), theory('equality')], [c_3085, c_2818])).
% 23.72/6.58 tff(c_13203, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), 0) | fun_app$c(p$, '#skF_200'(0)))), inference(demodulation, [status(thm), theory('equality')], [c_13065, c_12857, c_3092])).
% 23.72/6.58 tff(c_13204, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3))), inference(negUnitSimplification, [status(thm)], [c_13063, c_2124, c_13203])).
% 23.72/6.58 tff(c_13209, plain, $false, inference(demodulation, [status(thm), theory('equality')], [c_13204, c_13063])).
% 23.72/6.58 tff(c_13217, plain, ('#skF_2'='#skF_197'('#skE_1')), inference(splitRight, [status(thm)], [c_12569])).
% 23.72/6.58 tff(c_12581, plain, (![A__questionmark_v0_4281a:$int]: (fun_app$f(nat$, A__questionmark_v0_4281a)='#skF_200'(A__questionmark_v0_4281a) | $less(A__questionmark_v0_4281a, 0))), inference(superposition, [status(thm), theory('equality')], [c_12366, c_2123])).
% 23.72/6.58 tff(c_12610, plain, ('#skF_2'='#skF_200'('#skE_1') | $less('#skE_1', 0)), inference(superposition, [status(thm), theory('equality')], [c_12581, c_11969])).
% 23.72/6.58 tff(c_13516, plain, ('#skF_197'('#skE_1')='#skF_200'('#skE_1') | $less('#skE_1', 0)), inference(demodulation, [status(thm), theory('equality')], [c_13217, c_12610])).
% 23.72/6.58 tff(c_13519, plain, ($less('#skE_1', 0)), inference(splitLeft, [status(thm)], [c_13516])).
% 23.72/6.58 tff(c_13270, plain, (fun_app$b(of_nat$, '#skF_197'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_13217, c_11953])).
% 23.72/6.58 tff(c_13243, plain, (fun_app$b(of_nat$, '#skF_197'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_13217, c_11953])).
% 23.72/6.58 tff(c_13316, plain, (![A__questionmark_v0_4353:Nat$]: (fun_app$b(of_nat$, A__questionmark_v0_4353)=0 | ~$less(fun_app$b(of_nat$, A__questionmark_v0_4353), 1))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1100])).
% 23.72/6.58 tff(c_13319, plain, (fun_app$b(of_nat$, '#skF_197'('#skE_1'))=0 | ~$less('#skE_1', 1)), inference(superposition, [status(thm), theory('equality')], [c_13243, c_13316])).
% 23.72/6.58 tff(c_13340, plain, ('#skE_1'=0 | ~$less('#skE_1', 1)), inference(demodulation, [status(thm), theory('equality')], [c_13270, c_13319])).
% 23.72/6.58 tff(c_13352, plain, (~$less('#skE_1', 1)), inference(splitLeft, [status(thm)], [c_13340])).
% 23.72/6.58 tff(c_13520, plain, $false, inference(close, [status(thm), theory('LIA')], [c_13519, c_13352])).
% 23.72/6.58 tff(c_13602, plain, ('#skF_197'('#skE_1')='#skF_200'('#skE_1')), inference(splitRight, [status(thm)], [c_13516])).
% 23.72/6.58 tff(c_13246, plain, (n_0$='#skF_197'('#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_13217, c_11940])).
% 23.72/6.58 tff(c_13671, plain, (n_0$='#skF_200'('#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_13602, c_13246])).
% 23.72/6.58 tff(c_27, plain, (![A__questionmark_v0_4:Nat$]: ($lesseq($sum(fun_app$b(of_nat$, n_0$), 1), fun_app$b(of_nat$, '#skF_1')) | ~fun_app$c(p$, n_0$) | fun_app$c(p$, A__questionmark_v0_4) | ~$lesseq($sum(fun_app$b(of_nat$, n_0$), 1), fun_app$b(of_nat$, A__questionmark_v0_4)))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2819, plain, (![A__questionmark_v0_4:Nat$]: (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, fun_app$b(of_nat$, n_0$))) | ~fun_app$c(p$, n_0$) | fun_app$c(p$, A__questionmark_v0_4) | $less(fun_app$b(of_nat$, A__questionmark_v0_4), $sum(1, fun_app$b(of_nat$, n_0$))))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_27])).
% 23.72/6.58 tff(c_13683, plain, (![A__questionmark_v0_4:Nat$]: (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, fun_app$b(of_nat$, '#skF_200'('#skE_1')))) | ~fun_app$c(p$, '#skF_200'('#skE_1')) | fun_app$c(p$, A__questionmark_v0_4) | $less(fun_app$b(of_nat$, A__questionmark_v0_4), $sum(1, fun_app$b(of_nat$, '#skF_200'('#skE_1')))))), inference(demodulation, [status(thm), theory('equality')], [c_13671, c_13671, c_13671, c_2819])).
% 23.72/6.58 tff(c_13742, plain, (fun_app$b(of_nat$, '#skF_200'('#skE_1'))='#skE_4'), inference(define, [status(thm), theory('equality')], [c_13683])).
% 23.72/6.58 tff(c_2289, plain, (![A__questionmark_v0_1282a:$int]: (fun_app$b(of_nat$, '#skF_200'(A__questionmark_v0_1282a))=A__questionmark_v0_1282a | $less(A__questionmark_v0_1282a, 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1798])).
% 23.72/6.58 tff(c_13775, plain, ('#skE_4'='#skE_1' | $less('#skE_1', 0)), inference(superposition, [status(thm), theory('equality')], [c_13742, c_2289])).
% 23.72/6.58 tff(c_14146, plain, ($less('#skE_1', 0)), inference(splitLeft, [status(thm)], [c_13775])).
% 23.72/6.58 tff(c_14147, plain, $false, inference(close, [status(thm), theory('LIA')], [c_14146, c_13352])).
% 23.72/6.58 tff(c_14150, plain, ('#skE_4'='#skE_1'), inference(splitRight, [status(thm)], [c_13775])).
% 23.72/6.58 tff(c_13694, plain, (fun_app$b(of_nat$, '#skF_200'('#skE_1'))='#skE_4'), inference(define, [status(thm), theory('equality')], [c_13683])).
% 23.72/6.58 tff(c_14371, plain, (fun_app$b(of_nat$, '#skF_200'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_14150, c_13694])).
% 23.72/6.58 tff(c_13798, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), '#skE_1') | fun_app$c(p$, '#skF_200'('#skE_1')))), inference(demodulation, [status(thm), theory('equality')], [c_13671, c_3092])).
% 23.72/6.58 tff(c_14137, plain, (fun_app$c(p$, '#skF_200'('#skE_1'))), inference(splitLeft, [status(thm)], [c_13798])).
% 23.72/6.58 tff(c_13249, plain, (~fun_app$c(p$, '#skF_197'('#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_13217, c_3005])).
% 23.72/6.58 tff(c_13644, plain, (~fun_app$c(p$, '#skF_200'('#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_13602, c_13249])).
% 23.72/6.58 tff(c_14140, plain, $false, inference(demodulation, [status(thm), theory('equality')], [c_14137, c_13644])).
% 23.72/6.58 tff(c_15314, plain, (![A__questionmark_v0_5502:Nat$]: (fun_app$c(p$, A__questionmark_v0_5502) | $less(fun_app$b(of_nat$, A__questionmark_v0_5502), '#skE_1'))), inference(splitRight, [status(thm)], [c_13798])).
% 23.72/6.58 tff(c_15317, plain, ($less(fun_app$b(of_nat$, '#skF_200'('#skE_1')), '#skE_1')), inference(resolution, [status(thm)], [c_15314, c_13644])).
% 23.72/6.58 tff(c_15344, plain, ($less('#skE_1', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_14371, c_15317])).
% 23.72/6.58 tff(c_15347, plain, $false, inference(backgroundSimplification, [status(thm), theory('LIA')], [c_15344])).
% 23.72/6.58 tff(c_15350, plain, ('#skE_1'=0), inference(splitRight, [status(thm)], [c_13340])).
% 23.72/6.58 tff(c_13215, plain, ($less(0, '#skE_1')), inference(splitRight, [status(thm)], [c_12569])).
% 23.72/6.58 tff(c_15360, plain, ($less(0, 0)), inference(demodulation, [status(thm), theory('equality')], [c_15350, c_13215])).
% 23.72/6.58 tff(c_15374, plain, $false, inference(backgroundSimplification, [status(thm), theory('LIA')], [c_15360])).
% 23.72/6.58 tff(c_15376, plain, (fun_app$c(p$, '#skF_2')), inference(splitRight, [status(thm)], [c_7])).
% 23.72/6.58 tff(c_4, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | ~$lesseq(fun_app$b(of_nat$, n_0$), fun_app$b(of_nat$, A__questionmark_v0_3)) | ~fun_app$c(p$, '#skF_2'))), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2826, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), fun_app$b(of_nat$, n_0$)) | ~fun_app$c(p$, '#skF_2'))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_4])).
% 23.72/6.58 tff(c_20367, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), fun_app$b(of_nat$, n_0$)))), inference(demodulation, [status(thm), theory('equality')], [c_15376, c_2826])).
% 23.72/6.58 tff(c_20372, plain, (fun_app$b(of_nat$, n_0$)='#skE_1'), inference(define, [status(thm), theory('equality')], [c_20367])).
% 23.72/6.58 tff(c_15540, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), fun_app$b(of_nat$, n_0$)))), inference(demodulation, [status(thm), theory('equality')], [c_15376, c_2826])).
% 23.72/6.58 tff(c_15545, plain, (fun_app$b(of_nat$, n_0$)='#skE_1'), inference(define, [status(thm), theory('equality')], [c_15540])).
% 23.72/6.58 tff(c_15562, plain, (~$less('#skE_1', 0)), inference(superposition, [status(thm), theory('equality')], [c_15545, c_2124])).
% 23.72/6.58 tff(c_17490, plain, (![A__questionmark_v0_5709a:$int]: (fun_app$b(of_nat$, '#skF_200'(A__questionmark_v0_5709a))=A__questionmark_v0_5709a | $less(A__questionmark_v0_5709a, 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_1798])).
% 23.72/6.58 tff(c_17586, plain, (![A__questionmark_v0_5719a:$int]: (fun_app$f(nat$, A__questionmark_v0_5719a)='#skF_200'(A__questionmark_v0_5719a) | $less(A__questionmark_v0_5719a, 0))), inference(superposition, [status(thm), theory('equality')], [c_17490, c_2123])).
% 23.72/6.58 tff(c_15561, plain, (fun_app$f(nat$, '#skE_1')=n_0$), inference(superposition, [status(thm), theory('equality')], [c_15545, c_2123])).
% 23.72/6.58 tff(c_17615, plain, (n_0$='#skF_200'('#skE_1') | $less('#skE_1', 0)), inference(superposition, [status(thm), theory('equality')], [c_17586, c_15561])).
% 23.72/6.58 tff(c_17973, plain, (n_0$='#skF_200'('#skE_1')), inference(negUnitSimplification, [status(thm)], [c_15562, c_17615])).
% 23.72/6.58 tff(c_18043, plain, (fun_app$b(of_nat$, '#skF_200'('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_17973, c_15545])).
% 23.72/6.58 tff(c_15541, plain, (fun_app$b(of_nat$, n_0$)='#skE_1'), inference(define, [status(thm), theory('equality')], [c_15540])).
% 23.72/6.58 tff(c_20245, plain, (![A__questionmark_v0_6093:Nat$]: (fun_app$c(p$, A__questionmark_v0_6093) | $less(fun_app$b(of_nat$, A__questionmark_v0_6093), '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_15541, c_15540])).
% 23.72/6.58 tff(c_15873, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), '#skE_1') | fun_app$c(p$, n_0$))), inference(demodulation, [status(thm), theory('equality')], [c_15545, c_2818])).
% 23.72/6.58 tff(c_15875, plain, (fun_app$c(p$, n_0$)), inference(splitLeft, [status(thm)], [c_15873])).
% 23.72/6.58 tff(c_9, plain, ($lesseq($sum(fun_app$b(of_nat$, n_0$), 1), fun_app$b(of_nat$, '#skF_1')) | ~fun_app$c(p$, n_0$) | ~fun_app$c(p$, '#skF_2')), inference(cnfTransformation, [status(thm)], [f_50])).
% 23.72/6.58 tff(c_2825, plain, (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, fun_app$b(of_nat$, n_0$))) | ~fun_app$c(p$, n_0$) | ~fun_app$c(p$, '#skF_2')), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_9])).
% 23.72/6.58 tff(c_16089, plain, (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_15376, c_15875, c_15545, c_2825])).
% 23.72/6.58 tff(c_16094, plain, (fun_app$b(of_nat$, '#skF_1')='#skE_3'), inference(define, [status(thm), theory('equality')], [c_16089])).
% 23.72/6.58 tff(c_16118, plain, (fun_app$f(nat$, '#skE_3')='#skF_1'), inference(superposition, [status(thm), theory('equality')], [c_16094, c_2123])).
% 23.72/6.58 tff(c_16062, plain, (![A__questionmark_v0_5554a:$int]: (fun_app$b(of_nat$, '#skF_197'(A__questionmark_v0_5554a))=A__questionmark_v0_5554a | ~$less(0, A__questionmark_v0_5554a))), inference(cnfTransformation, [status(thm)], [f_3879])).
% 23.72/6.58 tff(c_16688, plain, (![A__questionmark_v0_5607a:$int]: (fun_app$f(nat$, A__questionmark_v0_5607a)='#skF_197'(A__questionmark_v0_5607a) | ~$less(0, A__questionmark_v0_5607a))), inference(superposition, [status(thm), theory('equality')], [c_16062, c_2123])).
% 23.72/6.58 tff(c_16759, plain, ('#skF_1'='#skF_197'('#skE_3') | ~$less(0, '#skE_3')), inference(superposition, [status(thm), theory('equality')], [c_16118, c_16688])).
% 23.72/6.58 tff(c_16843, plain, (~$less(0, '#skE_3')), inference(splitLeft, [status(thm)], [c_16759])).
% 23.72/6.58 tff(c_16091, plain, (fun_app$b(of_nat$, '#skF_1')='#skE_3'), inference(define, [status(thm), theory('equality')], [c_16089])).
% 23.72/6.58 tff(c_16090, plain, (~$less(fun_app$b(of_nat$, '#skF_1'), $sum(1, '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_15376, c_15875, c_15545, c_2825])).
% 23.72/6.58 tff(c_16095, plain, (~$less('#skE_3', $sum(1, '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_16091, c_16090])).
% 23.72/6.58 tff(c_16844, plain, $false, inference(close, [status(thm), theory('LIA')], [c_16843, c_16095, c_15562])).
% 23.72/6.58 tff(c_16862, plain, ('#skF_1'='#skF_197'('#skE_3')), inference(splitRight, [status(thm)], [c_16759])).
% 23.72/6.58 tff(c_16898, plain, (fun_app$b(of_nat$, '#skF_197'('#skE_3'))='#skE_3'), inference(demodulation, [status(thm), theory('equality')], [c_16862, c_16094])).
% 23.72/6.58 tff(c_17222, plain, (![A__questionmark_v0_5687:Nat$]: (fun_app$c(p$, A__questionmark_v0_5687) | $less(fun_app$b(of_nat$, A__questionmark_v0_5687), '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_15541, c_15540])).
% 23.72/6.58 tff(c_15375, plain, (~fun_app$c(p$, n_0$) | ~fun_app$c(p$, '#skF_1')), inference(splitRight, [status(thm)], [c_7])).
% 23.72/6.58 tff(c_15455, plain, (~fun_app$c(p$, '#skF_1')), inference(splitLeft, [status(thm)], [c_15375])).
% 23.72/6.58 tff(c_16886, plain, (~fun_app$c(p$, '#skF_197'('#skE_3'))), inference(demodulation, [status(thm), theory('equality')], [c_16862, c_15455])).
% 23.72/6.58 tff(c_17225, plain, ($less(fun_app$b(of_nat$, '#skF_197'('#skE_3')), '#skE_1')), inference(resolution, [status(thm)], [c_17222, c_16886])).
% 23.72/6.58 tff(c_17253, plain, ($less('#skE_3', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_16898, c_17225])).
% 23.72/6.58 tff(c_17277, plain, $false, inference(close, [status(thm), theory('LIA')], [c_17253, c_16095])).
% 23.72/6.58 tff(c_17279, plain, (~fun_app$c(p$, n_0$)), inference(splitRight, [status(thm)], [c_15873])).
% 23.72/6.58 tff(c_17991, plain, (~fun_app$c(p$, '#skF_200'('#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_17973, c_17279])).
% 23.72/6.58 tff(c_20248, plain, ($less(fun_app$b(of_nat$, '#skF_200'('#skE_1')), '#skE_1')), inference(resolution, [status(thm)], [c_20245, c_17991])).
% 23.72/6.58 tff(c_20278, plain, ($less('#skE_1', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_18043, c_20248])).
% 23.72/6.58 tff(c_20281, plain, $false, inference(backgroundSimplification, [status(thm), theory('LIA')], [c_20278])).
% 23.72/6.58 tff(c_20282, plain, (~fun_app$c(p$, n_0$)), inference(splitRight, [status(thm)], [c_15375])).
% 23.72/6.58 tff(c_20581, plain, (![A__questionmark_v0_3:Nat$]: (fun_app$c(p$, A__questionmark_v0_3) | $less(fun_app$b(of_nat$, A__questionmark_v0_3), '#skE_1') | fun_app$c(p$, n_0$))), inference(demodulation, [status(thm), theory('equality')], [c_20372, c_2818])).
% 23.72/6.58 tff(c_20587, plain, (![A__questionmark_v0_6129:Nat$]: (fun_app$c(p$, A__questionmark_v0_6129) | $less(fun_app$b(of_nat$, A__questionmark_v0_6129), '#skE_1'))), inference(negUnitSimplification, [status(thm)], [c_20282, c_20581])).
% 23.72/6.58 tff(c_20608, plain, ($less(fun_app$b(of_nat$, n_0$), '#skE_1')), inference(resolution, [status(thm)], [c_20587, c_20282])).
% 23.72/6.58 tff(c_20630, plain, ($less('#skE_1', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_20372, c_20608])).
% 23.72/6.58 tff(c_20633, plain, $false, inference(backgroundSimplification, [status(thm), theory('LIA')], [c_20630])).
% 23.72/6.58 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.72/6.58
% 23.72/6.58 Inference rules
% 23.72/6.58 ----------------------
% 23.72/6.58 #Ref : 0
% 23.72/6.58 #Sup : 3000
% 23.72/6.58 #Fact : 1
% 23.72/6.58 #Define : 17
% 23.72/6.58 #Split : 108
% 23.72/6.58 #Chain : 0
% 23.72/6.58 #Close : 42
% 23.72/6.58
% 23.72/6.58 Ordering : LPO
% 23.72/6.58
% 23.72/6.58 Simplification rules
% 23.72/6.58 ----------------------
% 23.72/6.58 #Subsume : 467
% 23.72/6.58 #Demod : 1220
% 23.72/6.58 #Tautology : 2026
% 23.72/6.58 #SimpNegUnit : 81
% 23.72/6.58 #BackRed : 166
% 23.72/6.58
% 23.72/6.58 #Partial instantiations: 497
% 23.72/6.58 #Strategies tried : 1
% 23.72/6.58
% 23.72/6.58 Timing (in seconds)
% 23.72/6.58 ----------------------
% 23.72/6.58 Preprocessing : 2.19
% 23.72/6.58 Parsing : 0.95
% 23.72/6.58 CNF conversion : 0.19
% 23.72/6.58 Main loop : 3.22
% 23.72/6.58 Inferencing : 0.68
% 23.72/6.58 Reduction : 1.06
% 23.72/6.58 Demodulation : 0.75
% 23.72/6.58 BG Simplification : 0.51
% 23.72/6.58 Subsumption : 0.71
% 23.72/6.58 Abstraction : 0.10
% 23.72/6.58 MUC search : 0.04
% 23.72/6.58 Cooper : 0.19
% 23.72/6.58 Total : 5.51
% 23.72/6.58 Index Insertion : 0.00
% 23.72/6.58 Index Deletion : 0.00
% 23.72/6.59 Index Matching : 0.00
% 23.72/6.59 BG Taut test : 0.00
%------------------------------------------------------------------------------