%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SCT171+7 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n021.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 : Wed Apr 9 08:34:32 PM UTC 2025
% Result : Theorem 27.92s 9.95s
% Output : CNFRefutation 27.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 19 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 57 ( 56 usr; 1 prp; 0-1 aty)
% Number of functors : 276 ( 276 usr; 39 con; 0-11 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ zero_neq_one > zero > top > semiring_0 > semiring > semiri456707255roduct > semilattice_sup > semilattice_inf > ring_n68954251visors > ring_char_0 > ring_1 > preorder > ordered_semiring > ordered_ring > ordere779506340up_add > ordere453448008miring > ordere236663937imp_le > ordere223160158up_add > ordere216010020id_add > ordere1490568538miring > order > ord > one > no_zero_divisors > mult_zero > monoid_mult > monoid_add > linordered_semiring > linordered_semidom > linordered_ring > linordered_idom > linordered_field > linorder > linord893533164strict > linord626643107strict > linord581940658strict > linord219039673up_add > linord20386208strict > linord1278240602ring_1 > linord1117847801e_zero > lattice > hBOOL > finite_finite > distrib_lattice > dense_linorder > comm_semiring_1 > comm_semiring > comm_monoid_mult > comm_monoid_add > cancel_semigroup_add > cancel146912293up_add > bounded_lattice_top > bounded_lattice > ab_semigroup_mult > ab_semigroup_add > ab_sem1668676832m_mult > hAPP > product_prod_rec > compose > comp > combs > combc > combb > ti > the_inv_into > sum_sum > sum_Plus > restrict > product_prod > product_Pair > pi > inj_on > in_rel > image > hilbert_inv_into > fun > finite_folding_image > finite_folding_idem > finite_fold_image > finite908156982e_idem > extensional > combk > big_co1399186613setsum > #nlpp > zero_zero > undefined > top_top > times_times > size_size > semilattice_sup_sup > semilattice_inf_inf > ring_1_Ints > plus_plus > ord_less_eq > ord_less > ord_greaterThan > ord_gr676655987ssThan > ord_gr1471790799AtMost > ord_atLeastLessThan > ord_atLeastAtMost > ord_atLeast > option > one_one > nat_case > mlex_prod > member > measure > if > finite_psubset > finite_finite_1 > finite_card > fequal > combi > collect > suc > product_unit > p > nat_size > nat > n > lba > lab > h > fdisj > fconj > fTrue > fNot > fFalse > f > e > d > c > bool_size > bool > b > arrow_708804735ctator > arrow_357225482_above > arrow_301600364e_Prof > arrow_2142409994le_alt > arrow_1998540521e_indi > arrow_1770777252_mktop > arrow_1665824030_below > arrow_1622070166_mkbot > arrow_1568854078le_Lin > arrow_1541970350le_IIA > arrow_1066301521nimity > a > #skF_13 > #skF_139 > #skF_108 > #skF_114 > #skF_118 > #skF_19 > #skF_183 > #skF_146 > #skF_132 > #skF_69 > #skF_35 > #skF_130 > #skF_140 > #skF_75 > #skF_21 > #skF_16 > #skF_110 > #skF_30 > #skF_65 > #skF_62 > #skF_144 > #skF_63 > #skF_105 > #skF_129 > #skF_49 > #skF_116 > #skF_85 > #skF_44 > #skF_165 > #skF_2 > #skF_54 > #skF_155 > #skF_50 > #skF_73 > #skF_1 > #skF_66 > #skF_180 > #skF_91 > #skF_145 > #skF_109 > #skF_27 > #skF_48 > #skF_93 > #skF_178 > #skF_122 > #skF_126 > #skF_177 > #skF_174 > #skF_25 > #skF_10 > #skF_88 > #skF_9 > #skF_143 > #skF_171 > #skF_57 > #skF_22 > #skF_181 > #skF_72 > #skF_32 > #skF_179 > #skF_154 > #skF_36 > #skF_77 > #skF_47 > #skF_135 > #skF_112 > #skF_151 > #skF_97 > #skF_64 > #skF_87 > #skF_12 > #skF_147 > #skF_39 > #skF_121 > #skF_6 > #skF_37 > #skF_5 > #skF_90 > #skF_99 > #skF_134 > #skF_117 > #skF_34 > #skF_51 > #skF_162 > #skF_142 > #skF_156 > #skF_15 > #skF_26 > #skF_101 > #skF_113 > #skF_42 > #skF_78 > #skF_172 > #skF_68 > #skF_56 > #skF_173 > #skF_45 > #skF_153 > #skF_98 > #skF_161 > #skF_33 > #skF_163 > #skF_82 > #skF_8 > #skF_137 > #skF_166 > #skF_167 > #skF_84 > #skF_175 > #skF_7 > #skF_184 > #skF_100 > #skF_107 > #skF_92 > #skF_80 > #skF_133 > #skF_128 > #skF_94 > #skF_11 > #skF_148 > #skF_29 > #skF_43 > #skF_170 > #skF_52 > #skF_131 > #skF_41 > #skF_55 > #skF_31 > #skF_24 > #skF_71 > #skF_182 > #skF_3 > #skF_46 > #skF_67 > #skF_141 > #skF_83 > #skF_103 > #skF_76 > #skF_28 > #skF_149 > #skF_102 > #skF_95 > #skF_185 > #skF_60 > #skF_81 > #skF_17 > #skF_61 > #skF_136 > #skF_125 > #skF_14 > #skF_157 > #skF_38 > #skF_127 > #skF_168 > #skF_169 > #skF_59 > #skF_70 > #skF_159 > #skF_53 > #skF_106 > #skF_58 > #skF_123 > #skF_138 > #skF_176 > #skF_89 > #skF_119 > #skF_186 > #skF_115 > #skF_160 > #skF_120 > #skF_124 > #skF_150 > #skF_40 > #skF_96 > #skF_164 > #skF_86 > #skF_158 > #skF_4 > #skF_23 > #skF_20 > #skF_111 > #skF_79 > #skF_18 > #skF_152 > #skF_74 > #skF_104
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(fconj,type,
fconj: $i ).
tff(measure,type,
measure: $i > $i ).
tff(linord1278240602ring_1,type,
linord1278240602ring_1: $i > $o ).
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(arrow_301600364e_Prof,type,
arrow_301600364e_Prof: $i ).
tff('#skF_139',type,
'#skF_139': ( $i * $i * $i * $i * $i ) > $i ).
tff(size_size,type,
size_size: $i > $i ).
tff('#skF_108',type,
'#skF_108': ( $i * $i * $i ) > $i ).
tff(hAPP,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(ordered_semiring,type,
ordered_semiring: $i > $o ).
tff('#skF_114',type,
'#skF_114': ( $i * $i * $i ) > $i ).
tff('#skF_118',type,
'#skF_118': ( $i * $i * $i * $i ) > $i ).
tff(ab_semigroup_mult,type,
ab_semigroup_mult: $i > $o ).
tff(finite908156982e_idem,type,
finite908156982e_idem: ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i * $i * $i ) > $i ).
tff(arrow_1770777252_mktop,type,
arrow_1770777252_mktop: $i ).
tff('#skF_183',type,
'#skF_183': ( $i * $i * $i ) > $i ).
tff('#skF_146',type,
'#skF_146': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(semiri456707255roduct,type,
semiri456707255roduct: $i > $o ).
tff('#skF_132',type,
'#skF_132': ( $i * $i * $i * $i * $i ) > $i ).
tff(comm_semiring,type,
comm_semiring: $i > $o ).
tff('#skF_69',type,
'#skF_69': ( $i * $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff(ord_less_eq,type,
ord_less_eq: $i > $i ).
tff('#skF_130',type,
'#skF_130': ( $i * $i ) > $i ).
tff('#skF_140',type,
'#skF_140': ( $i * $i * $i * $i * $i ) > $i ).
tff(semilattice_sup_sup,type,
semilattice_sup_sup: $i > $i ).
tff(product_unit,type,
product_unit: $i ).
tff('#skF_75',type,
'#skF_75': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff(finite_finite_1,type,
finite_finite_1: $i > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff('#skF_110',type,
'#skF_110': ( $i * $i * $i * $i * $i ) > $i ).
tff(product_prod_rec,type,
product_prod_rec: ( $i * $i * $i ) > $i ).
tff(h,type,
h: $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i * $i * $i ) > $i ).
tff(suc,type,
suc: $i ).
tff('#skF_65',type,
'#skF_65': ( $i * $i * $i * $i ) > $i ).
tff('#skF_62',type,
'#skF_62': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_144',type,
'#skF_144': ( $i * $i * $i * $i ) > $i ).
tff('#skF_63',type,
'#skF_63': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(ring_n68954251visors,type,
ring_n68954251visors: $i > $o ).
tff('#skF_105',type,
'#skF_105': $i > $i ).
tff('#skF_129',type,
'#skF_129': ( $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_116',type,
'#skF_116': ( $i * $i * $i * $i * $i ) > $i ).
tff(linord581940658strict,type,
linord581940658strict: $i > $o ).
tff('#skF_85',type,
'#skF_85': ( $i * $i * $i * $i ) > $i ).
tff('#skF_44',type,
'#skF_44': ( $i * $i * $i ) > $i ).
tff(one_one,type,
one_one: $i > $i ).
tff('#skF_165',type,
'#skF_165': ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(ring_1,type,
ring_1: $i > $o ).
tff(a,type,
a: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_54',type,
'#skF_54': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_155',type,
'#skF_155': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(linordered_field,type,
linordered_field: $i > $o ).
tff(combk,type,
combk: ( $i * $i ) > $i ).
tff(combs,type,
combs: ( $i * $i * $i ) > $i ).
tff('#skF_73',type,
'#skF_73': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_66',type,
'#skF_66': ( $i * $i * $i * $i ) > $i ).
tff('#skF_180',type,
'#skF_180': ( $i * $i * $i ) > $i ).
tff(monoid_add,type,
monoid_add: $i > $o ).
tff('#skF_91',type,
'#skF_91': ( $i * $i ) > $i ).
tff('#skF_145',type,
'#skF_145': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(linordered_ring,type,
linordered_ring: $i > $o ).
tff('#skF_109',type,
'#skF_109': $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i * $i ) > $i ).
tff('#skF_48',type,
'#skF_48': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_93',type,
'#skF_93': ( $i * $i ) > $i ).
tff(ord_gr676655987ssThan,type,
ord_gr676655987ssThan: $i > $i ).
tff('#skF_178',type,
'#skF_178': ( $i * $i * $i * $i ) > $i ).
tff(top_top,type,
top_top: $i > $i ).
tff(linordered_semidom,type,
linordered_semidom: $i > $o ).
tff(f,type,
f: $i ).
tff(ab_semigroup_add,type,
ab_semigroup_add: $i > $o ).
tff('#skF_122',type,
'#skF_122': ( $i * $i ) > $i ).
tff('#skF_126',type,
'#skF_126': ( $i * $i ) > $i ).
tff('#skF_177',type,
'#skF_177': ( $i * $i * $i * $i ) > $i ).
tff(member,type,
member: $i > $i ).
tff('#skF_174',type,
'#skF_174': ( $i * $i * $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i * $i ) > $i ).
tff('#skF_88',type,
'#skF_88': ( $i * $i ) > $i ).
tff(combb,type,
combb: ( $i * $i * $i ) > $i ).
tff(finite_fold_image,type,
finite_fold_image: ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i * $i ) > $i ).
tff('#skF_143',type,
'#skF_143': ( $i * $i * $i ) > $i ).
tff('#skF_171',type,
'#skF_171': ( $i * $i ) > $i ).
tff(sum_Plus,type,
sum_Plus: ( $i * $i ) > $i ).
tff('#skF_57',type,
'#skF_57': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': $i > $i ).
tff('#skF_181',type,
'#skF_181': ( $i * $i * $i * $i * $i ) > $i ).
tff(no_zero_divisors,type,
no_zero_divisors: $i > $o ).
tff('#skF_72',type,
'#skF_72': ( $i * $i * $i ) > $i ).
tff(lba,type,
lba: $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i ) > $i ).
tff('#skF_179',type,
'#skF_179': ( $i * $i * $i * $i ) > $i ).
tff('#skF_154',type,
'#skF_154': ( $i * $i * $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_77',type,
'#skF_77': ( $i * $i * $i * $i * $i ) > $i ).
tff(linord626643107strict,type,
linord626643107strict: $i > $o ).
tff('#skF_47',type,
'#skF_47': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_135',type,
'#skF_135': ( $i * $i * $i * $i ) > $i ).
tff('#skF_112',type,
'#skF_112': ( $i * $i * $i * $i ) > $i ).
tff('#skF_151',type,
'#skF_151': ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(bounded_lattice_top,type,
bounded_lattice_top: $i > $o ).
tff('#skF_97',type,
'#skF_97': $i > $i ).
tff('#skF_64',type,
'#skF_64': ( $i * $i ) > $i ).
tff('#skF_87',type,
'#skF_87': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(ord,type,
ord: $i > $o ).
tff(if,type,
if: $i > $i ).
tff(zero_neq_one,type,
zero_neq_one: $i > $o ).
tff(lab,type,
lab: $i ).
tff(fNot,type,
fNot: $i ).
tff('#skF_147',type,
'#skF_147': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(sum_sum,type,
sum_sum: ( $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i * $i ) > $i ).
tff('#skF_121',type,
'#skF_121': ( $i * $i ) > $i ).
tff(nat_size,type,
nat_size: $i ).
tff(bool,type,
bool: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i * $i ) > $i ).
tff(ord_atLeastAtMost,type,
ord_atLeastAtMost: $i > $i ).
tff(collect,type,
collect: $i > $i ).
tff(semilattice_sup,type,
semilattice_sup: $i > $o ).
tff('#skF_37',type,
'#skF_37': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_90',type,
'#skF_90': ( $i * $i ) > $i ).
tff(finite_folding_image,type,
finite_folding_image: ( $i * $i ) > $i ).
tff('#skF_99',type,
'#skF_99': ( $i * $i * $i * $i ) > $i ).
tff('#skF_134',type,
'#skF_134': ( $i * $i * $i * $i ) > $i ).
tff(comm_monoid_mult,type,
comm_monoid_mult: $i > $o ).
tff('#skF_117',type,
'#skF_117': ( $i * $i * $i * $i * $i ) > $i ).
tff(ord_atLeast,type,
ord_atLeast: $i > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff(linord219039673up_add,type,
linord219039673up_add: $i > $o ).
tff('#skF_51',type,
'#skF_51': ( $i * $i * $i * $i ) > $i ).
tff('#skF_162',type,
'#skF_162': $i > $i ).
tff('#skF_142',type,
'#skF_142': ( $i * $i * $i * $i * $i ) > $i ).
tff(nat,type,
nat: $i ).
tff('#skF_156',type,
'#skF_156': $i > $i ).
tff(arrow_1568854078le_Lin,type,
arrow_1568854078le_Lin: $i ).
tff(arrow_1998540521e_indi,type,
arrow_1998540521e_indi: $i ).
tff(big_co1399186613setsum,type,
big_co1399186613setsum: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff(fun,type,
fun: ( $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': $i ).
tff(ordere779506340up_add,type,
ordere779506340up_add: $i > $o ).
tff(b,type,
b: $i ).
tff('#skF_101',type,
'#skF_101': ( $i * $i ) > $i ).
tff('#skF_113',type,
'#skF_113': ( $i * $i * $i * $i * $i ) > $i ).
tff(the_inv_into,type,
the_inv_into: ( $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i * $i * $i ) > $i ).
tff('#skF_78',type,
'#skF_78': ( $i * $i ) > $i ).
tff('#skF_172',type,
'#skF_172': ( $i * $i ) > $i ).
tff(arrow_1541970350le_IIA,type,
arrow_1541970350le_IIA: $i ).
tff('#skF_68',type,
'#skF_68': ( $i * $i * $i ) > $i ).
tff('#skF_56',type,
'#skF_56': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_173',type,
'#skF_173': ( $i * $i ) > $i ).
tff(linordered_semiring,type,
linordered_semiring: $i > $o ).
tff('#skF_45',type,
'#skF_45': ( $i * $i * $i ) > $i ).
tff(ordered_ring,type,
ordered_ring: $i > $o ).
tff(nat_case,type,
nat_case: $i > $i ).
tff('#skF_153',type,
'#skF_153': ( $i * $i * $i * $i * $i ) > $i ).
tff(mlex_prod,type,
mlex_prod: $i > $i ).
tff(ordere1490568538miring,type,
ordere1490568538miring: $i > $o ).
tff('#skF_98',type,
'#skF_98': ( $i * $i * $i * $i ) > $i ).
tff(finite_psubset,type,
finite_psubset: $i > $i ).
tff(finite_folding_idem,type,
finite_folding_idem: ( $i * $i ) > $i ).
tff(ab_sem1668676832m_mult,type,
ab_sem1668676832m_mult: $i > $o ).
tff('#skF_161',type,
'#skF_161': $i > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i ) > $i ).
tff(hilbert_inv_into,type,
hilbert_inv_into: ( $i * $i ) > $i ).
tff(ordere236663937imp_le,type,
ordere236663937imp_le: $i > $o ).
tff('#skF_163',type,
'#skF_163': ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_82',type,
'#skF_82': $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(fequal,type,
fequal: $i > $i ).
tff('#skF_137',type,
'#skF_137': ( $i * $i * $i ) > $i ).
tff('#skF_166',type,
'#skF_166': ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(cancel146912293up_add,type,
cancel146912293up_add: $i > $o ).
tff(product_prod,type,
product_prod: ( $i * $i ) > $i ).
tff('#skF_167',type,
'#skF_167': ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(undefined,type,
undefined: $i > $i ).
tff('#skF_84',type,
'#skF_84': ( $i * $i ) > $i ).
tff('#skF_175',type,
'#skF_175': ( $i * $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_184',type,
'#skF_184': ( $i * $i * $i * $i ) > $i ).
tff(semilattice_inf,type,
semilattice_inf: $i > $o ).
tff(combi,type,
combi: $i > $i ).
tff('#skF_100',type,
'#skF_100': ( $i * $i * $i * $i ) > $i ).
tff('#skF_107',type,
'#skF_107': ( $i * $i ) > $i ).
tff('#skF_92',type,
'#skF_92': $i > $i ).
tff('#skF_80',type,
'#skF_80': $i > $i ).
tff(comm_monoid_add,type,
comm_monoid_add: $i > $o ).
tff(restrict,type,
restrict: ( $i * $i ) > $i ).
tff('#skF_133',type,
'#skF_133': ( $i * $i * $i * $i * $i ) > $i ).
tff(arrow_1066301521nimity,type,
arrow_1066301521nimity: $i ).
tff('#skF_128',type,
'#skF_128': ( $i * $i ) > $i ).
tff(ordere223160158up_add,type,
ordere223160158up_add: $i > $o ).
tff(comm_semiring_1,type,
comm_semiring_1: $i > $o ).
tff('#skF_94',type,
'#skF_94': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_148',type,
'#skF_148': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i * $i ) > $i ).
tff(arrow_2142409994le_alt,type,
arrow_2142409994le_alt: $i ).
tff('#skF_43',type,
'#skF_43': ( $i * $i * $i ) > $i ).
tff(distrib_lattice,type,
distrib_lattice: $i > $o ).
tff(fdisj,type,
fdisj: $i ).
tff('#skF_170',type,
'#skF_170': ( $i * $i ) > $i ).
tff('#skF_52',type,
'#skF_52': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_131',type,
'#skF_131': ( $i * $i ) > $i ).
tff('#skF_41',type,
'#skF_41': ( $i * $i * $i * $i * $i ) > $i ).
tff(bool_size,type,
bool_size: $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(inj_on,type,
inj_on: ( $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i ) > $i ).
tff('#skF_71',type,
'#skF_71': ( $i * $i * $i ) > $i ).
tff('#skF_182',type,
'#skF_182': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i * $i * $i ) > $i ).
tff('#skF_67',type,
'#skF_67': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_141',type,
'#skF_141': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_83',type,
'#skF_83': ( $i * $i ) > $i ).
tff(ti,type,
ti: ( $i * $i ) > $i ).
tff('#skF_103',type,
'#skF_103': ( $i * $i ) > $i ).
tff(semiring_0,type,
semiring_0: $i > $o ).
tff('#skF_76',type,
'#skF_76': ( $i * $i * $i * $i * $i ) > $i ).
tff(ord_gr1471790799AtMost,type,
ord_gr1471790799AtMost: $i > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i * $i ) > $i ).
tff(in_rel,type,
in_rel: ( $i * $i ) > $i ).
tff('#skF_149',type,
'#skF_149': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_102',type,
'#skF_102': ( $i * $i ) > $i ).
tff(n,type,
n: $i ).
tff('#skF_95',type,
'#skF_95': ( $i * $i * $i ) > $i ).
tff(fTrue,type,
fTrue: $i ).
tff('#skF_185',type,
'#skF_185': ( $i * $i * $i ) > $i ).
tff(linord20386208strict,type,
linord20386208strict: $i > $o ).
tff(d,type,
d: $i ).
tff('#skF_60',type,
'#skF_60': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_81',type,
'#skF_81': ( $i * $i ) > $i ).
tff(bounded_lattice,type,
bounded_lattice: $i > $o ).
tff(linordered_idom,type,
linordered_idom: $i > $o ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff(linord1117847801e_zero,type,
linord1117847801e_zero: $i > $o ).
tff(finite_finite,type,
finite_finite: $i > $o ).
tff(arrow_357225482_above,type,
arrow_357225482_above: $i ).
tff(compose,type,
compose: ( $i * $i * $i ) > $i ).
tff(lattice,type,
lattice: $i > $o ).
tff('#skF_61',type,
'#skF_61': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_136',type,
'#skF_136': ( $i * $i * $i * $i ) > $i ).
tff(ord_atLeastLessThan,type,
ord_atLeastLessThan: $i > $i ).
tff('#skF_125',type,
'#skF_125': ( $i * $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(option,type,
option: $i > $i ).
tff(ordere216010020id_add,type,
ordere216010020id_add: $i > $o ).
tff(ordere453448008miring,type,
ordere453448008miring: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff('#skF_157',type,
'#skF_157': ( $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i * $i * $i ) > $i ).
tff(mult_zero,type,
mult_zero: $i > $o ).
tff('#skF_127',type,
'#skF_127': ( $i * $i ) > $i ).
tff('#skF_168',type,
'#skF_168': ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(arrow_708804735ctator,type,
arrow_708804735ctator: $i ).
tff(cancel_semigroup_add,type,
cancel_semigroup_add: $i > $o ).
tff(ring_char_0,type,
ring_char_0: $i > $o ).
tff('#skF_169',type,
'#skF_169': ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(comp,type,
comp: ( $i * $i * $i ) > $i ).
tff('#skF_59',type,
'#skF_59': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_70',type,
'#skF_70': ( $i * $i * $i ) > $i ).
tff(zero_zero,type,
zero_zero: $i > $i ).
tff('#skF_159',type,
'#skF_159': ( $i * $i * $i ) > $i ).
tff('#skF_53',type,
'#skF_53': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(preorder,type,
preorder: $i > $o ).
tff(e,type,
e: $i ).
tff('#skF_106',type,
'#skF_106': ( $i * $i ) > $i ).
tff('#skF_58',type,
'#skF_58': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(monoid_mult,type,
monoid_mult: $i > $o ).
tff('#skF_123',type,
'#skF_123': ( $i * $i ) > $i ).
tff('#skF_138',type,
'#skF_138': ( $i * $i * $i * $i ) > $i ).
tff(dense_linorder,type,
dense_linorder: $i > $o ).
tff(semilattice_inf_inf,type,
semilattice_inf_inf: $i > $i ).
tff(ord_less,type,
ord_less: $i > $i ).
tff(arrow_1665824030_below,type,
arrow_1665824030_below: $i ).
tff('#skF_176',type,
'#skF_176': ( $i * $i * $i * $i ) > $i ).
tff(plus_plus,type,
plus_plus: $i > $i ).
tff('#skF_89',type,
'#skF_89': ( $i * $i ) > $i ).
tff(p,type,
p: $i ).
tff(one,type,
one: $i > $o ).
tff('#skF_119',type,
'#skF_119': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_186',type,
'#skF_186': ( $i * $i * $i * $i ) > $i ).
tff('#skF_115',type,
'#skF_115': ( $i * $i * $i * $i ) > $i ).
tff('#skF_160',type,
'#skF_160': ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(product_Pair,type,
product_Pair: ( $i * $i ) > $i ).
tff('#skF_120',type,
'#skF_120': ( $i * $i ) > $i ).
tff('#skF_124',type,
'#skF_124': ( $i * $i * $i * $i ) > $i ).
tff('#skF_150',type,
'#skF_150': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(semiring,type,
semiring: $i > $o ).
tff('#skF_40',type,
'#skF_40': ( $i * $i * $i * $i ) > $i ).
tff(pi,type,
pi: ( $i * $i ) > $i ).
tff('#skF_96',type,
'#skF_96': ( $i * $i ) > $i ).
tff(fFalse,type,
fFalse: $i ).
tff(order,type,
order: $i > $o ).
tff(extensional,type,
extensional: ( $i * $i ) > $i ).
tff(times_times,type,
times_times: $i > $i ).
tff(ord_greaterThan,type,
ord_greaterThan: $i > $i ).
tff(ring_1_Ints,type,
ring_1_Ints: $i > $i ).
tff(top,type,
top: $i > $o ).
tff('#skF_164',type,
'#skF_164': ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_86',type,
'#skF_86': ( $i * $i * $i * $i ) > $i ).
tff(zero,type,
zero: $i > $o ).
tff(combc,type,
combc: ( $i * $i * $i ) > $i ).
tff(finite_card,type,
finite_card: $i > $i ).
tff(linord893533164strict,type,
linord893533164strict: $i > $o ).
tff('#skF_158',type,
'#skF_158': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_111',type,
'#skF_111': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_79',type,
'#skF_79': ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i * $i * $i ) > $i ).
tff(arrow_1622070166_mkbot,type,
arrow_1622070166_mkbot: $i ).
tff('#skF_152',type,
'#skF_152': ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_74',type,
'#skF_74': $i ).
tff('#skF_104',type,
'#skF_104': $i > $i ).
tff(linorder,type,
linorder: $i > $o ).
tff(c,type,
c: $i ).
tff(f_6846,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_391,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
tff(f_388,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
tff(c_3606,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
inference(cnfTransformation,[status(thm)],[f_6846]) ).
tff(c_320,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(cnfTransformation,[status(thm)],[f_391]) ).
tff(c_3801,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(negUnitSimplification,[status(thm)],[c_3606,c_320]) ).
tff(c_318,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_3802,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3801,c_318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT171+7 : TPTP v9.0.0. Released v5.3.0.
% 0.06/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Apr 8 19:30:29 EDT 2025
% 0.11/0.33 % CPUTime :
% 27.92/9.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.92/9.96
% 27.92/9.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------