TSTP Solution File: ITP328_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 : n007.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 10:44:29 EDT 2023
% Result : Theorem 26.81s 7.73s
% Output : CNFRefutation 26.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n007.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 : Thu Aug 3 18:33:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 26.81/7.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.81/7.73
% 26.81/7.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.86/7.76 %$ member$d > member$c > member$b > member$ > less_eq$c > less_eq$b > fun_app$j > fun_app$d > fun_app$c > fun_app$ > plus$e > plus$d > plus$c > plus$a > fun_app$r > fun_app$q > fun_app$p > fun_app$o > fun_app$n > fun_app$m > fun_app$l > fun_app$k > fun_app$i > fun_app$h > fun_app$g > fun_app$f > fun_app$e > fun_app$b > fun_app$a > #nlpp > uud$ > uub$ > uua$ > uu$ > to_nat$ > plus$b > plus$ > nat$ > minus$a > minus$ > member$a > less_eq$a > less$a > iterate_add$ > collect$b > collect$a > collect$ > zero$a > zero$ > x$ > uuc$ > triangle$ > tltrue > tlfalse > of_nat$ > less_eq$ > less$ > ja$ > i$ > from_nat$ > a$ > #skF_129 > #skF_62 > #skF_74 > #skF_174 > #skF_204 > #skF_178 > #skF_5 > #skF_205 > #skF_100 > #skF_220 > #skF_176 > #skF_103 > #skF_191 > #skF_71 > #skF_101 > #skF_183 > #skF_136 > #skF_92 > #skF_116 > #skF_88 > #skF_83 > #skF_38 > #skF_114 > #skF_13 > #skF_59 > #skF_108 > #skF_34 > #skF_10 > #skF_39 > #skF_109 > #skF_21 > #skF_53 > #skF_117 > #skF_121 > #skF_12 > #skF_149 > #skF_15 > #skF_104 > #skF_50 > #skF_63 > #skF_133 > #skF_16 > #skF_141 > #skF_78 > #skF_211 > #skF_140 > #skF_45 > #skF_22 > #skF_158 > #skF_95 > #skF_187 > #skF_3 > #skF_23 > #skF_70 > #skF_18 > #skF_61 > #skF_1 > #skF_215 > #skF_137 > #skF_160 > #skF_198 > #skF_44 > #skF_208 > #skF_217 > #skF_32 > #skF_37 > #skF_69 > #skF_84 > #skF_8 > #skF_199 > #skF_171 > #skF_173 > #skF_20 > #skF_42 > #skF_76 > #skF_47 > #skF_132 > #skF_43 > #skF_122 > #skF_96 > #skF_36 > #skF_81 > #skF_52 > #skF_79 > #skF_90 > #skF_54 > #skF_168 > #skF_190 > #skF_167 > #skF_17 > #skF_162 > #skF_180 > #skF_2 > #skF_48 > #skF_206 > #skF_153 > #skF_24 > #skF_197 > #skF_172 > #skF_157 > #skF_65 > #skF_40 > #skF_192 > #skF_119 > #skF_219 > #skF_85 > #skF_200 > #skF_14 > #skF_212 > #skF_46 > #skF_186 > #skF_102 > #skF_145 > #skF_113 > #skF_218 > #skF_110 > #skF_107 > #skF_166 > #skF_73 > #skF_177 > #skF_213 > #skF_169 > #skF_55 > #skF_147 > #skF_123 > #skF_51 > #skF_155 > #skF_97 > #skF_126 > #skF_125 > #skF_72 > #skF_66 > #skF_207 > #skF_30 > #skF_216 > #skF_35 > #skF_152 > #skF_6 > #skF_156 > #skF_151 > #skF_49 > #skF_134 > #skF_105 > #skF_93 > #skF_41 > #skF_124 > #skF_25 > #skF_11 > #skF_188 > #skF_128 > #skF_67 > #skF_163 > #skF_150 > #skF_146 > #skF_64 > #skF_4 > #skF_106 > #skF_182 > #skF_164 > #skF_184 > #skF_165 > #skF_179 > #skF_202 > #skF_175 > #skF_159 > #skF_196 > #skF_209 > #skF_127 > #skF_28 > #skF_9 > #skF_56 > #skF_77 > #skF_111 > #skF_27 > #skF_26 > #skF_154 > #skF_148 > #skF_144 > #skF_201 > #skF_31 > #skF_57 > #skF_120 > #skF_181 > #skF_131 > #skF_68 > #skF_194 > #skF_94 > #skF_185 > #skF_89 > #skF_87 > #skF_7 > #skF_193 > #skF_210 > #skF_86 > #skF_91 > #skF_60 > #skF_214 > #skF_139 > #skF_75 > #skF_112 > #skF_115 > #skF_135 > #skF_58 > #skF_130 > #skF_170 > #skF_33 > #skF_82 > #skF_138 > #skF_118 > #skF_203 > #skF_189 > #skF_161 > #skF_98 > #skF_143 > #skF_195 > #skF_142 > #skF_19 > #skF_99 > #skF_29 > #skF_80
% 26.86/7.76
% 26.86/7.76 %Foreground sorts:
% 26.86/7.76 tff(Int_set$, type, Int_set$: $tType ).
% 26.86/7.76 tff(Nat_nat_bool_fun_fun$, type, Nat_nat_bool_fun_fun$: $tType ).
% 26.86/7.76 tff(Int_n_fun$, type, Int_n_fun$: $tType ).
% 26.86/7.76 tff(N_n_bool_fun_fun$, type, N_n_bool_fun_fun$: $tType ).
% 26.86/7.76 tff(Nat$, type, Nat$: $tType ).
% 26.86/7.76 tff(Int_set_int_set_fun$, type, Int_set_int_set_fun$: $tType ).
% 26.86/7.76 tff(N$, type, N$: $tType ).
% 26.86/7.76 tff(tlbool, type, tlbool: $tType ).
% 26.86/7.76 tff(Int_set_int_fun$, type, Int_set_int_fun$: $tType ).
% 26.86/7.76 tff(Int_int_fun$, type, Int_int_fun$: $tType ).
% 26.86/7.76 tff(Int_set_set$, type, Int_set_set$: $tType ).
% 26.86/7.76 tff(Nat_nat_fun$, type, Nat_nat_fun$: $tType ).
% 26.86/7.76 tff(Nat_int_fun$, type, Nat_int_fun$: $tType ).
% 26.86/7.76 tff(Int_int_bool_fun_fun$, type, Int_int_bool_fun_fun$: $tType ).
% 26.86/7.76 tff(Int_set_n_fun$, type, Int_set_n_fun$: $tType ).
% 26.86/7.76 tff(N_set$, type, N_set$: $tType ).
% 26.86/7.76 tff(N_bool_fun$, type, N_bool_fun$: $tType ).
% 26.86/7.76 tff(N_int_fun$, type, N_int_fun$: $tType ).
% 26.86/7.76 tff(Nat_bool_fun$, type, Nat_bool_fun$: $tType ).
% 26.86/7.76 tff(N_set_set$, type, N_set_set$: $tType ).
% 26.86/7.76 tff(Int_int_set_fun$, type, Int_int_set_fun$: $tType ).
% 26.86/7.76 tff(N_n_fun$, type, N_n_fun$: $tType ).
% 26.86/7.76 tff(Int_set_set_set$, type, Int_set_set_set$: $tType ).
% 26.86/7.76 tff(Int_set_bool_fun$, type, Int_set_bool_fun$: $tType ).
% 26.86/7.76 tff(N_int_set_fun$, type, N_int_set_fun$: $tType ).
% 26.86/7.76 tff(Int_bool_fun$, type, Int_bool_fun$: $tType ).
% 26.86/7.76 tff(Nat_n_fun$, type, Nat_n_fun$: $tType ).
% 26.86/7.76
% 26.86/7.76 %Background operators:
% 26.86/7.76 tff('#skE_2', type, '#skE_2': $int).
% 26.86/7.76 tff('#skE_1', type, '#skE_1': $int).
% 26.86/7.76 tff('#skE_3', type, '#skE_3': $int).
% 26.86/7.76
% 26.86/7.76 %Foreground operators:
% 26.86/7.76 tff('#skF_129', type, '#skF_129': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_62', type, '#skF_62': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_74', type, '#skF_74': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_174', type, '#skF_174': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_204', type, '#skF_204': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_178', type, '#skF_178': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_5', type, '#skF_5': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(i$, type, i$: N$).
% 26.86/7.76 tff('#skF_205', type, '#skF_205': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_100', type, '#skF_100': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_220', type, '#skF_220': (Int_set$ * Int_set$) > $int).
% 26.86/7.76 tff('#skF_176', type, '#skF_176': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_103', type, '#skF_103': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_191', type, '#skF_191': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_71', type, '#skF_71': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_101', type, '#skF_101': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_183', type, '#skF_183': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_136', type, '#skF_136': N_bool_fun$ > N$).
% 26.86/7.76 tff('#skF_92', type, '#skF_92': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff(collect$a, type, collect$a: Int_set_bool_fun$ > Int_set_set$).
% 26.86/7.76 tff(iterate_add$, type, iterate_add$: Nat$ > Int_int_fun$).
% 26.86/7.76 tff(member$a, type, member$a: $int > Int_set_bool_fun$).
% 26.86/7.76 tff('#skF_116', type, '#skF_116': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_88', type, '#skF_88': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_83', type, '#skF_83': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff('#skF_38', type, '#skF_38': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_114', type, '#skF_114': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_13', type, '#skF_13': (Int_set$ * Int_set$ * Int_set_int_fun$ * $int) > Int_set$).
% 26.86/7.76 tff('#skF_59', type, '#skF_59': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(fun_app$e, type, fun_app$e: (Nat_int_fun$ * Nat$) > $int).
% 26.86/7.76 tff('#skF_108', type, '#skF_108': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_34', type, '#skF_34': (Int_set$ * Int_set_int_set_fun$ * Int_set$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_10', type, '#skF_10': ($int * $int * Int_int_set_fun$ * Int_set$) > $int).
% 26.86/7.76 tff('#skF_39', type, '#skF_39': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(less_eq$, type, less_eq$: N_n_bool_fun_fun$).
% 26.86/7.76 tff('#skF_109', type, '#skF_109': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_21', type, '#skF_21': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_53', type, '#skF_53': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_117', type, '#skF_117': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_121', type, '#skF_121': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_12', type, '#skF_12': (Int_set$ * Int_set$ * Int_set_n_fun$ * N$) > Int_set$).
% 26.86/7.76 tff(fun_app$d, type, fun_app$d: (N_bool_fun$ * N$) > $o).
% 26.86/7.76 tff('#skF_149', type, '#skF_149': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff('#skF_15', type, '#skF_15': (Int_set$ * Int_set$ * Int_set_int_set_fun$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_104', type, '#skF_104': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_50', type, '#skF_50': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_63', type, '#skF_63': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_133', type, '#skF_133': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_16', type, '#skF_16': (Int_set$ * Int_set$ * Int_set_int_set_fun$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_141', type, '#skF_141': (N_bool_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_78', type, '#skF_78': (Int_set$ * Int_set_set$ * Int_set_set$) > Int_set$).
% 26.86/7.76 tff('#skF_211', type, '#skF_211': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_140', type, '#skF_140': (N_bool_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_45', type, '#skF_45': (Int_set$ * Int_set$ * Int_set_int_fun$ * $int) > Int_set$).
% 26.86/7.76 tff('#skF_22', type, '#skF_22': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_158', type, '#skF_158': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(minus$a, type, minus$a: Int_set$ > Int_set_int_set_fun$).
% 26.86/7.76 tff('#skF_95', type, '#skF_95': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_187', type, '#skF_187': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_3', type, '#skF_3': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(fun_app$o, type, fun_app$o: (N_int_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_23', type, '#skF_23': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_70', type, '#skF_70': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_18', type, '#skF_18': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_61', type, '#skF_61': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(tlfalse, type, tlfalse: tlbool).
% 26.86/7.76 tff('#skF_1', type, '#skF_1': (Int_bool_fun$ * Int_bool_fun$) > $int).
% 26.86/7.76 tff(member$, type, member$: (Int_set$ * Int_set_set$) > $o).
% 26.86/7.76 tff(less$, type, less$: N_n_bool_fun_fun$).
% 26.86/7.76 tff('#skF_215', type, '#skF_215': (Int_set$ * Int_set$) > $int).
% 26.86/7.76 tff('#skF_137', type, '#skF_137': (N_bool_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_160', type, '#skF_160': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_198', type, '#skF_198': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff('#skF_44', type, '#skF_44': (Int_set$ * Int_set$ * Int_set_n_fun$ * N$) > Int_set$).
% 26.86/7.76 tff('#skF_208', type, '#skF_208': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_217', type, '#skF_217': (Nat$ * Nat_bool_fun$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_32', type, '#skF_32': ($int * Int_set_int_fun$ * Int_set$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_37', type, '#skF_37': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_69', type, '#skF_69': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(fun_app$a, type, fun_app$a: (Int_int_bool_fun_fun$ * $int) > Int_bool_fun$).
% 26.86/7.76 tff('#skF_84', type, '#skF_84': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff(plus$c, type, plus$c: (N_set$ * N_set$) > N_set$).
% 26.86/7.76 tff('#skF_8', type, '#skF_8': (N$ * N$ * N_int_set_fun$ * Int_set$) > N$).
% 26.86/7.76 tff('#skF_199', type, '#skF_199': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff('#skF_171', type, '#skF_171': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_173', type, '#skF_173': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_20', type, '#skF_20': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_42', type, '#skF_42': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(fun_app$b, type, fun_app$b: (Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_76', type, '#skF_76': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_47', type, '#skF_47': (Int_set$ * Int_set$ * Int_set_int_set_fun$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_132', type, '#skF_132': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(fun_app$m, type, fun_app$m: (Int_set_n_fun$ * Int_set$) > N$).
% 26.86/7.76 tff('#skF_43', type, '#skF_43': (Int_set$ * Int_set$ * Int_set_n_fun$ * N$) > Int_set$).
% 26.86/7.76 tff('#skF_122', type, '#skF_122': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_96', type, '#skF_96': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_36', type, '#skF_36': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_81', type, '#skF_81': ($int * Int_set$ * Int_set$) > $int).
% 26.86/7.76 tff('#skF_52', type, '#skF_52': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_79', type, '#skF_79': (N$ * N_set$ * N_set$) > N$).
% 26.86/7.76 tff('#skF_90', type, '#skF_90': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_54', type, '#skF_54': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff(zero$a, type, zero$a: N$).
% 26.86/7.76 tff('#skF_168', type, '#skF_168': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_190', type, '#skF_190': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_167', type, '#skF_167': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_17', type, '#skF_17': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_162', type, '#skF_162': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(a$, type, a$: Nat$).
% 26.86/7.76 tff(ja$, type, ja$: Nat$).
% 26.86/7.76 tff('#skF_180', type, '#skF_180': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(less$a, type, less$a: Int_set$ > Int_set_bool_fun$).
% 26.86/7.76 tff('#skF_2', type, '#skF_2': (Int_bool_fun$ * Int_bool_fun$) > $int).
% 26.86/7.76 tff('#skF_48', type, '#skF_48': (Int_set$ * Int_set$ * Int_set_int_set_fun$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_206', type, '#skF_206': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_153', type, '#skF_153': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_24', type, '#skF_24': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff(fun_app$h, type, fun_app$h: (Int_set_int_set_fun$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_197', type, '#skF_197': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff(fun_app$g, type, fun_app$g: (N_n_bool_fun_fun$ * N$) > N_bool_fun$).
% 26.86/7.76 tff('#skF_172', type, '#skF_172': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_157', type, '#skF_157': (Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff(of_nat$, type, of_nat$: Nat_int_fun$).
% 26.86/7.76 tff('#skF_65', type, '#skF_65': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_40', type, '#skF_40': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(plus$e, type, plus$e: (Int_set_set_set$ * Int_set_set_set$) > Int_set_set_set$).
% 26.86/7.76 tff('#skF_192', type, '#skF_192': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff(fun_app$c, type, fun_app$c: (Int_set_bool_fun$ * Int_set$) > $o).
% 26.86/7.76 tff(uuc$, type, uuc$: Int_int_bool_fun_fun$).
% 26.86/7.76 tff('#skF_119', type, '#skF_119': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_219', type, '#skF_219': (Int_set$ * Int_set$) > $int).
% 26.86/7.76 tff('#skF_85', type, '#skF_85': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_200', type, '#skF_200': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff('#skF_14', type, '#skF_14': (Int_set$ * Int_set$ * Int_set_int_fun$ * $int) > Int_set$).
% 26.86/7.76 tff('#skF_212', type, '#skF_212': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_46', type, '#skF_46': (Int_set$ * Int_set$ * Int_set_int_fun$ * $int) > Int_set$).
% 26.86/7.76 tff('#skF_186', type, '#skF_186': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_102', type, '#skF_102': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff(collect$b, type, collect$b: Int_bool_fun$ > Int_set$).
% 26.86/7.76 tff(to_nat$, type, to_nat$: N$ > Nat$).
% 26.86/7.76 tff('#skF_145', type, '#skF_145': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff('#skF_113', type, '#skF_113': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_218', type, '#skF_218': (Int_set$ * Int_set$) > $int).
% 26.86/7.76 tff(fun_app$i, type, fun_app$i: (Nat_n_fun$ * Nat$) > N$).
% 26.86/7.76 tff('#skF_110', type, '#skF_110': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_107', type, '#skF_107': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_166', type, '#skF_166': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_73', type, '#skF_73': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_177', type, '#skF_177': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_213', type, '#skF_213': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_169', type, '#skF_169': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(member$b, type, member$b: (N$ * N_set$) > $o).
% 26.86/7.76 tff(zero$, type, zero$: Int_set$).
% 26.86/7.76 tff('#skF_55', type, '#skF_55': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_147', type, '#skF_147': (Nat_bool_fun$ * Nat$) > Nat$).
% 26.86/7.76 tff(member$d, type, member$d: (Int_set_set$ * Int_set_set_set$) > $o).
% 26.86/7.76 tff('#skF_123', type, '#skF_123': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(fun_app$n, type, fun_app$n: (Int_set_int_fun$ * Int_set$) > $int).
% 26.86/7.76 tff('#skF_51', type, '#skF_51': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_155', type, '#skF_155': (Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff('#skF_97', type, '#skF_97': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_126', type, '#skF_126': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_125', type, '#skF_125': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_72', type, '#skF_72': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_66', type, '#skF_66': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(fun_app$r, type, fun_app$r: (Nat_nat_fun$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_207', type, '#skF_207': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_30', type, '#skF_30': (N$ * Int_set_n_fun$ * Int_set$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_216', type, '#skF_216': (Nat$ * Nat_bool_fun$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_35', type, '#skF_35': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_152', type, '#skF_152': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff(plus$b, type, plus$b: Int_set$ > Int_set_int_set_fun$).
% 26.86/7.76 tff('#skF_6', type, '#skF_6': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_156', type, '#skF_156': (Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff('#skF_151', type, '#skF_151': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff('#skF_49', type, '#skF_49': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_134', type, '#skF_134': (N_bool_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_105', type, '#skF_105': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_93', type, '#skF_93': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(member$c, type, member$c: (N_set$ * N_set_set$) > $o).
% 26.86/7.76 tff('#skF_41', type, '#skF_41': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_124', type, '#skF_124': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_25', type, '#skF_25': (Int_set$ * N_int_set_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_11', type, '#skF_11': (Int_set$ * Int_set$ * Int_set_n_fun$ * N$) > Int_set$).
% 26.86/7.76 tff('#skF_188', type, '#skF_188': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_128', type, '#skF_128': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_67', type, '#skF_67': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_163', type, '#skF_163': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(minus$, type, minus$: N$ > N_n_fun$).
% 26.86/7.76 tff(from_nat$, type, from_nat$: Nat_n_fun$).
% 26.86/7.76 tff('#skF_150', type, '#skF_150': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff('#skF_146', type, '#skF_146': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff(less_eq$b, type, less_eq$b: (N_set$ * N_set$) > $o).
% 26.86/7.76 tff('#skF_64', type, '#skF_64': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(uu$, type, uu$: N_set$ > N_bool_fun$).
% 26.86/7.76 tff('#skF_4', type, '#skF_4': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_106', type, '#skF_106': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_182', type, '#skF_182': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(fun_app$p, type, fun_app$p: (Int_n_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_164', type, '#skF_164': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_184', type, '#skF_184': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_165', type, '#skF_165': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_179', type, '#skF_179': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff(fun_app$q, type, fun_app$q: (Nat_nat_bool_fun_fun$ * Nat$) > Nat_bool_fun$).
% 26.86/7.76 tff('#skF_202', type, '#skF_202': (Nat_bool_fun$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_175', type, '#skF_175': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_159', type, '#skF_159': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_196', type, '#skF_196': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 26.86/7.76 tff('#skF_209', type, '#skF_209': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(uua$, type, uua$: Int_set_set$ > Int_set_bool_fun$).
% 26.86/7.76 tff('#skF_127', type, '#skF_127': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_28', type, '#skF_28': (Int_set$ * Int_int_set_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(nat$, type, nat$: $int > Nat$).
% 26.86/7.76 tff('#skF_9', type, '#skF_9': ($int * $int * Int_int_set_fun$ * Int_set$) > $int).
% 26.86/7.76 tff('#skF_56', type, '#skF_56': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_77', type, '#skF_77': (Int_set$ * Int_set_set$ * Int_set_set$) > Int_set$).
% 26.86/7.76 tff('#skF_111', type, '#skF_111': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_27', type, '#skF_27': (Int_set$ * Int_int_set_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_26', type, '#skF_26': (Int_set$ * N_int_set_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(x$, type, x$: N$).
% 26.86/7.76 tff('#skF_154', type, '#skF_154': (Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff('#skF_148', type, '#skF_148': (Nat_bool_fun$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_144', type, '#skF_144': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_201', type, '#skF_201': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 26.86/7.76 tff('#skF_31', type, '#skF_31': ($int * Int_set_int_fun$ * Int_set$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_57', type, '#skF_57': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(collect$, type, collect$: N_bool_fun$ > N_set$).
% 26.86/7.76 tff('#skF_120', type, '#skF_120': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(less_eq$a, type, less_eq$a: Int_set$ > Int_set_bool_fun$).
% 26.86/7.76 tff('#skF_181', type, '#skF_181': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_131', type, '#skF_131': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_68', type, '#skF_68': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_194', type, '#skF_194': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_94', type, '#skF_94': ($int * Int_int_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_185', type, '#skF_185': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(fun_app$l, type, fun_app$l: (Int_int_set_fun$ * $int) > Int_set$).
% 26.86/7.76 tff(fun_app$, type, fun_app$: (Int_bool_fun$ * $int) > $o).
% 26.86/7.76 tff(plus$a, type, plus$a: (Int_set_set$ * Int_set_set$) > Int_set_set$).
% 26.86/7.76 tff(tltrue, type, tltrue: tlbool).
% 26.86/7.76 tff('#skF_89', type, '#skF_89': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_87', type, '#skF_87': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_7', type, '#skF_7': (N$ * N$ * N_int_set_fun$ * Int_set$) > N$).
% 26.86/7.76 tff('#skF_193', type, '#skF_193': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_210', type, '#skF_210': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_86', type, '#skF_86': ($int * $int * Int_int_fun$ * $int) > $int).
% 26.86/7.76 tff('#skF_91', type, '#skF_91': (N$ * N$ * N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_60', type, '#skF_60': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff(uud$, type, uud$: $int > Int_int_fun$).
% 26.86/7.76 tff('#skF_214', type, '#skF_214': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_139', type, '#skF_139': N_bool_fun$ > N$).
% 26.86/7.76 tff(triangle$, type, triangle$: Nat_nat_fun$).
% 26.86/7.76 tff('#skF_75', type, '#skF_75': (Int_int_bool_fun_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_112', type, '#skF_112': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_115', type, '#skF_115': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_135', type, '#skF_135': N_bool_fun$ > N$).
% 26.86/7.76 tff(uub$, type, uub$: Int_set$ > Int_bool_fun$).
% 26.86/7.76 tff('#skF_58', type, '#skF_58': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff(less_eq$c, type, less_eq$c: (Int_set_set$ * Int_set_set$) > $o).
% 26.86/7.76 tff(plus$, type, plus$: N$ > N_n_fun$).
% 26.86/7.76 tff('#skF_130', type, '#skF_130': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_170', type, '#skF_170': ($int * N_int_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_33', type, '#skF_33': (Int_set$ * Int_set_int_set_fun$ * Int_set$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_82', type, '#skF_82': ($int * Int_set$ * Int_set$) > $int).
% 26.86/7.76 tff(plus$d, type, plus$d: (N_set_set$ * N_set_set$) > N_set_set$).
% 26.86/7.76 tff('#skF_138', type, '#skF_138': N_bool_fun$ > N$).
% 26.86/7.76 tff('#skF_118', type, '#skF_118': (N_n_bool_fun_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_203', type, '#skF_203': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_189', type, '#skF_189': ($int * $int * Int_n_fun$ * N$) > $int).
% 26.86/7.76 tff('#skF_161', type, '#skF_161': (Nat_n_fun$ * Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(fun_app$f, type, fun_app$f: (N_n_fun$ * N$) > N$).
% 26.86/7.76 tff('#skF_98', type, '#skF_98': (N$ * Int_n_fun$ * $int * $int) > $int).
% 26.86/7.76 tff('#skF_143', type, '#skF_143': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff(fun_app$j, type, fun_app$j: (Nat_bool_fun$ * Nat$) > $o).
% 26.86/7.76 tff(fun_app$k, type, fun_app$k: (N_int_set_fun$ * N$) > Int_set$).
% 26.86/7.76 tff('#skF_195', type, '#skF_195': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_142', type, '#skF_142': (Nat$ * Nat$) > Nat$).
% 26.86/7.76 tff('#skF_19', type, '#skF_19': (N$ * N$ * N_int_fun$ * $int) > N$).
% 26.86/7.76 tff('#skF_99', type, '#skF_99': (N$ * N_n_fun$ * N$ * N$) > N$).
% 26.86/7.76 tff('#skF_29', type, '#skF_29': (N$ * Int_set_n_fun$ * Int_set$ * Int_set$) > Int_set$).
% 26.86/7.76 tff('#skF_80', type, '#skF_80': (N$ * N_set$ * N_set$) > N$).
% 26.86/7.76
% 26.86/7.77 tff(f_65, negated_conjecture, ~(($less(fun_app$e(of_nat$, to_nat$(x$)), fun_app$e(of_nat$, to_nat$(i$))) => ($sum(fun_app$e(of_nat$, to_nat$(i$)), 0) = fun_app$e(of_nat$, to_nat$(x$)))) & (~$less(fun_app$e(of_nat$, to_nat$(x$)), fun_app$e(of_nat$, to_nat$(i$))) => ($sum(fun_app$e(of_nat$, to_nat$(i$)), $difference(fun_app$e(of_nat$, to_nat$(x$)), fun_app$e(of_nat$, to_nat$(i$)))) = fun_app$e(of_nat$, to_nat$(x$))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conjecture5)).
% 26.86/7.77 tff(f_5418, axiom, (![A__questionmark_v0:Nat$]: (nat$(fun_app$e(of_nat$, A__questionmark_v0)) = A__questionmark_v0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom616)).
% 26.86/7.77 tff(f_4793, axiom, (![A__questionmark_v0:Nat$, A__questionmark_v1:Nat$]: ($less(fun_app$e(of_nat$, A__questionmark_v0), fun_app$e(of_nat$, A__questionmark_v1)) <=> ($lesseq(fun_app$e(of_nat$, A__questionmark_v0), fun_app$e(of_nat$, A__questionmark_v1)) & ~(fun_app$e(of_nat$, A__questionmark_v0) = fun_app$e(of_nat$, A__questionmark_v1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom534)).
% 26.86/7.77 tff(f_5415, axiom, (![A__questionmark_v0:Nat$]: $lesseq(0, fun_app$e(of_nat$, A__questionmark_v0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom615)).
% 26.86/7.77 tff(f_3453, axiom, (![A__questionmark_v0:N$, A__questionmark_v1:N$]: (((~(A__questionmark_v0 = A__questionmark_v1) & (fun_app$d(fun_app$g(less$, A__questionmark_v1), A__questionmark_v0) => $false)) & (fun_app$d(fun_app$g(less$, A__questionmark_v0), A__questionmark_v1) => $false)) => $false)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom364)).
% 26.86/7.77 tff(f_152, axiom, fun_app$d(fun_app$g(less_eq$, i$), x$), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom16)).
% 26.86/7.77 tff(f_5172, axiom, (![A__questionmark_v0:N$, A__questionmark_v1:N$]: (~fun_app$d(fun_app$g(less_eq$, A__questionmark_v0), A__questionmark_v1) <=> fun_app$d(fun_app$g(less$, A__questionmark_v1), A__questionmark_v0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom570)).
% 26.86/7.77 tff(f_5428, axiom, (![A__questionmark_v0a:$int]: (($lesseq(0, A__questionmark_v0a) => (fun_app$e(of_nat$, nat$(A__questionmark_v0a)) = A__questionmark_v0a)) & (~$lesseq(0, A__questionmark_v0a) => (fun_app$e(of_nat$, nat$(A__questionmark_v0a)) = 0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom617)).
% 26.86/7.77 tff(f_3528, axiom, (![A__questionmark_v0:N$, A__questionmark_v1:N$]: (fun_app$d(fun_app$g(less$, A__questionmark_v0), A__questionmark_v1) => $less(fun_app$e(of_nat$, to_nat$(A__questionmark_v0)), fun_app$e(of_nat$, to_nat$(A__questionmark_v1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom374)).
% 26.86/7.77 tff(c_19, plain, (fun_app$e(of_nat$, to_nat$(x$))!=$sum(fun_app$e(of_nat$, to_nat$(i$)), 0) | $sum(fun_app$e(of_nat$, to_nat$(i$)), $sum($uminus(fun_app$e(of_nat$, to_nat$(i$))), fun_app$e(of_nat$, to_nat$(x$))))!=fun_app$e(of_nat$, to_nat$(x$))), inference(cnfTransformation, [status(thm)], [f_65])).
% 26.86/7.77 tff(c_4478, plain, (fun_app$e(of_nat$, to_nat$(x$))!=fun_app$e(of_nat$, to_nat$(i$))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_19])).
% 26.86/7.77 tff(c_4614, plain, (fun_app$e(of_nat$, to_nat$(x$))='#skE_1'), inference(define, [status(thm), theory('equality')], [c_4478])).
% 26.86/7.77 tff(c_4615, plain, (fun_app$e(of_nat$, to_nat$(i$))='#skE_2'), inference(define, [status(thm), theory('equality')], [c_4478])).
% 26.86/7.77 tff(c_22, plain, ($less(fun_app$e(of_nat$, to_nat$(x$)), fun_app$e(of_nat$, to_nat$(i$))) | $sum(fun_app$e(of_nat$, to_nat$(i$)), $sum($uminus(fun_app$e(of_nat$, to_nat$(i$))), fun_app$e(of_nat$, to_nat$(x$))))!=fun_app$e(of_nat$, to_nat$(x$))), inference(cnfTransformation, [status(thm)], [f_65])).
% 26.86/7.77 tff(c_4477, plain, ($less(fun_app$e(of_nat$, to_nat$(x$)), fun_app$e(of_nat$, to_nat$(i$)))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_22])).
% 26.86/7.77 tff(c_4696, plain, ($less('#skE_1', '#skE_2')), inference(demodulation, [status(thm), theory('equality')], [c_4614, c_4615, c_4477])).
% 26.86/7.77 tff(c_3433, plain, (![A__questionmark_v0_1459:Nat$]: (nat$(fun_app$e(of_nat$, A__questionmark_v0_1459))=A__questionmark_v0_1459)), inference(cnfTransformation, [status(thm)], [f_5418])).
% 26.86/7.77 tff(c_4752, plain, (to_nat$(i$)=nat$('#skE_2')), inference(superposition, [status(thm), theory('equality')], [c_4615, c_3433])).
% 26.86/7.77 tff(c_4805, plain, (fun_app$e(of_nat$, nat$('#skE_2'))='#skE_2'), inference(demodulation, [status(thm), theory('equality')], [c_4752, c_4615])).
% 26.86/7.77 tff(c_4760, plain, (fun_app$e(of_nat$, nat$('#skE_2'))='#skE_2'), inference(demodulation, [status(thm), theory('equality')], [c_4752, c_4615])).
% 26.86/7.77 tff(c_4775, plain, (to_nat$(x$)=nat$('#skE_1')), inference(superposition, [status(thm), theory('equality')], [c_4614, c_3433])).
% 26.86/7.77 tff(c_4873, plain, (fun_app$e(of_nat$, nat$('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_4775, c_4614])).
% 26.86/7.77 tff(c_4783, plain, (fun_app$e(of_nat$, nat$('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_4775, c_4614])).
% 26.86/7.77 tff(c_3021, plain, (![A__questionmark_v0_1293:Nat$, A__questionmark_v1_1294:Nat$]: ($lesseq(fun_app$e(of_nat$, A__questionmark_v0_1293), fun_app$e(of_nat$, A__questionmark_v1_1294)) | ~$less(fun_app$e(of_nat$, A__questionmark_v0_1293), fun_app$e(of_nat$, A__questionmark_v1_1294)))), inference(cnfTransformation, [status(thm)], [f_4793])).
% 26.86/7.77 tff(c_15009, plain, (![A__questionmark_v1_3654:Nat$, A__questionmark_v0_3655:Nat$]: (~$less(fun_app$e(of_nat$, A__questionmark_v1_3654), fun_app$e(of_nat$, A__questionmark_v0_3655)) | ~$less(fun_app$e(of_nat$, A__questionmark_v0_3655), fun_app$e(of_nat$, A__questionmark_v1_3654)))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_3021])).
% 26.86/7.77 tff(c_15030, plain, (![A__questionmark_v0_3655:Nat$]: (~$less('#skE_1', fun_app$e(of_nat$, A__questionmark_v0_3655)) | ~$less(fun_app$e(of_nat$, A__questionmark_v0_3655), fun_app$e(of_nat$, nat$('#skE_1'))))), inference(superposition, [status(thm), theory('equality')], [c_4783, c_15009])).
% 26.86/7.77 tff(c_15341, plain, (![A__questionmark_v0_3691:Nat$]: (~$less('#skE_1', fun_app$e(of_nat$, A__questionmark_v0_3691)) | ~$less(fun_app$e(of_nat$, A__questionmark_v0_3691), '#skE_1'))), inference(demodulation, [status(thm), theory('equality')], [c_4873, c_15030])).
% 26.86/7.77 tff(c_15359, plain, (~$less('#skE_1', fun_app$e(of_nat$, nat$('#skE_2'))) | ~$less('#skE_2', '#skE_1')), inference(superposition, [status(thm), theory('equality')], [c_4760, c_15341])).
% 26.86/7.77 tff(c_15382, plain, (~$less('#skE_2', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_4696, c_4805, c_15359])).
% 26.86/7.77 tff(c_3419, plain, (![A__questionmark_v0_1458:Nat$]: ($lesseq(0, fun_app$e(of_nat$, A__questionmark_v0_1458)))), inference(cnfTransformation, [status(thm)], [f_5415])).
% 26.86/7.77 tff(c_4643, plain, (![A__questionmark_v0_2624:Nat$]: (~$less(fun_app$e(of_nat$, A__questionmark_v0_2624), 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_3419])).
% 26.86/7.77 tff(c_4648, plain, (~$less('#skE_2', 0)), inference(superposition, [status(thm), theory('equality')], [c_4615, c_4643])).
% 26.86/7.77 tff(c_4611, plain, (fun_app$e(of_nat$, to_nat$(i$))='#skE_2'), inference(define, [status(thm), theory('equality')], [c_4478])).
% 26.86/7.77 tff(c_4610, plain, (fun_app$e(of_nat$, to_nat$(x$))='#skE_1'), inference(define, [status(thm), theory('equality')], [c_4478])).
% 26.86/7.77 tff(c_4616, plain, ('#skE_2'!='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_4611, c_4610, c_4478])).
% 26.86/7.77 tff(c_4631, plain, (to_nat$(i$)=nat$('#skE_2')), inference(superposition, [status(thm), theory('equality')], [c_4615, c_3433])).
% 26.86/7.77 tff(c_9708, plain, (![A__questionmark_v0_3426:N$, A__questionmark_v1_3427:N$]: (fun_app$d(fun_app$g(less$, A__questionmark_v0_3426), A__questionmark_v1_3427) | fun_app$d(fun_app$g(less$, A__questionmark_v1_3427), A__questionmark_v0_3426) | A__questionmark_v1_3427=A__questionmark_v0_3426)), inference(cnfTransformation, [status(thm)], [f_3453])).
% 26.86/7.77 tff(c_89, plain, (fun_app$d(fun_app$g(less_eq$, i$), x$)), inference(cnfTransformation, [status(thm)], [f_152])).
% 26.86/7.77 tff(c_6011, plain, (![A__questionmark_v0_3335:N$, A__questionmark_v1_3336:N$]: (~fun_app$d(fun_app$g(less_eq$, A__questionmark_v0_3335), A__questionmark_v1_3336) | ~fun_app$d(fun_app$g(less$, A__questionmark_v1_3336), A__questionmark_v0_3335))), inference(cnfTransformation, [status(thm)], [f_5172])).
% 26.86/7.77 tff(c_6041, plain, (~fun_app$d(fun_app$g(less$, x$), i$)), inference(resolution, [status(thm)], [c_89, c_6011])).
% 26.86/7.77 tff(c_9782, plain, (fun_app$d(fun_app$g(less$, i$), x$) | x$=i$), inference(resolution, [status(thm)], [c_9708, c_6041])).
% 26.86/7.77 tff(c_9805, plain, (x$=i$), inference(splitLeft, [status(thm)], [c_9782])).
% 26.86/7.77 tff(c_4692, plain, (to_nat$(x$)=nat$('#skE_1')), inference(superposition, [status(thm), theory('equality')], [c_4614, c_3433])).
% 26.86/7.77 tff(c_9846, plain, (to_nat$(i$)=nat$('#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_9805, c_4692])).
% 26.86/7.77 tff(c_10049, plain, (nat$('#skE_2')=nat$('#skE_1')), inference(superposition, [status(thm), theory('equality')], [c_4631, c_9846])).
% 26.86/7.77 tff(c_3423, plain, (![A__questionmark_v0_1460a:$int]: (fun_app$e(of_nat$, nat$(A__questionmark_v0_1460a))=A__questionmark_v0_1460a | ~$lesseq(0, A__questionmark_v0_1460a))), inference(cnfTransformation, [status(thm)], [f_5428])).
% 26.86/7.77 tff(c_3432, plain, (![A__questionmark_v0_1460a:$int]: (fun_app$e(of_nat$, nat$(A__questionmark_v0_1460a))=A__questionmark_v0_1460a | $less(A__questionmark_v0_1460a, 0))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_3423])).
% 26.86/7.77 tff(c_10091, plain, (fun_app$e(of_nat$, nat$('#skE_1'))='#skE_2' | $less('#skE_2', 0)), inference(superposition, [status(thm), theory('equality')], [c_10049, c_3432])).
% 26.86/7.77 tff(c_10171, plain, ('#skE_2'='#skE_1' | $less('#skE_2', 0)), inference(demodulation, [status(thm), theory('equality')], [c_4873, c_10091])).
% 26.86/7.77 tff(c_10173, plain, $false, inference(negUnitSimplification, [status(thm)], [c_4648, c_4616, c_10171])).
% 26.86/7.77 tff(c_10174, plain, (fun_app$d(fun_app$g(less$, i$), x$)), inference(splitRight, [status(thm)], [c_9782])).
% 26.86/7.77 tff(c_16157, plain, (![A__questionmark_v0_3728:N$, A__questionmark_v1_3729:N$]: ($less(fun_app$e(of_nat$, to_nat$(A__questionmark_v0_3728)), fun_app$e(of_nat$, to_nat$(A__questionmark_v1_3729))) | ~fun_app$d(fun_app$g(less$, A__questionmark_v0_3728), A__questionmark_v1_3729))), inference(cnfTransformation, [status(thm)], [f_3528])).
% 26.86/7.77 tff(c_16177, plain, ($less(fun_app$e(of_nat$, to_nat$(i$)), fun_app$e(of_nat$, to_nat$(x$)))), inference(resolution, [status(thm)], [c_10174, c_16157])).
% 26.86/7.77 tff(c_16219, plain, ($less('#skE_2', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_4805, c_4752, c_4873, c_4775, c_16177])).
% 26.86/7.77 tff(c_16221, plain, $false, inference(negUnitSimplification, [status(thm)], [c_15382, c_16219])).
% 26.86/7.77 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.86/7.77
% 26.86/7.77 Inference rules
% 26.86/7.77 ----------------------
% 26.86/7.77 #Ref : 10
% 26.86/7.77 #Sup : 2754
% 26.86/7.77 #Fact : 5
% 26.86/7.77 #Define : 3
% 26.86/7.77 #Split : 13
% 26.86/7.77 #Chain : 0
% 26.86/7.77 #Close : 0
% 26.86/7.77
% 26.86/7.77 Ordering : LPO
% 26.86/7.77
% 26.86/7.77 Simplification rules
% 26.86/7.77 ----------------------
% 26.86/7.77 #Subsume : 1095
% 26.86/7.77 #Demod : 1999
% 26.86/7.77 #Tautology : 1348
% 26.86/7.77 #SimpNegUnit : 86
% 26.86/7.77 #BackRed : 29
% 26.86/7.77
% 26.86/7.77 #Partial instantiations: 251
% 26.86/7.77 #Strategies tried : 1
% 26.86/7.77
% 26.86/7.77 Timing (in seconds)
% 26.86/7.77 ----------------------
% 26.86/7.77 Preprocessing : 2.68
% 26.86/7.77 Parsing : 1.21
% 26.86/7.77 CNF conversion : 0.21
% 26.86/7.77 Main loop : 4.01
% 26.86/7.77 Inferencing : 0.80
% 26.86/7.78 Reduction : 1.82
% 26.86/7.78 Demodulation : 1.49
% 26.86/7.78 BG Simplification : 0.69
% 26.86/7.78 Subsumption : 0.89
% 26.86/7.78 Abstraction : 0.13
% 26.86/7.78 MUC search : 0.00
% 26.86/7.78 Cooper : 0.13
% 26.86/7.78 Total : 6.75
% 26.86/7.78 Index Insertion : 0.00
% 26.86/7.78 Index Deletion : 0.00
% 26.86/7.78 Index Matching : 0.00
% 26.86/7.78 BG Taut test : 0.00
%------------------------------------------------------------------------------