%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV526^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:38:48 AM UTC 2026
% Result : Theorem 40.79s 6.05s
% Output : Refutation 40.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 11
% Syntax : Number of formulae : 175 ( 50 unt; 0 typ; 6 def)
% Number of atoms : 8783 ( 386 equ; 0 cnn)
% Maximal formula atoms : 133 ( 50 avg)
% Number of connectives : 44849 ( 152 ~; 335 |; 0 &;42371 @)
% ( 6 <=>; 944 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13646 (13646 >; 0 *; 0 +; 0 <<)
% Number of symbols : 170 ( 165 usr; 17 con; 0-14 aty)
% (1034 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 9687 (3875 sgn 282 !; 2 ?;9687 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c_Eps_i: ( $i > $o ) > $i ).
thf(func_def_1,type,
c_False: $o ).
thf(func_def_2,type,
c_True: $o ).
thf(func_def_3,type,
c_not: $o > $o ).
thf(func_def_4,type,
c_and: $o > $o > $o ).
thf(func_def_5,type,
c_or: $o > $o > $o ).
thf(func_def_6,type,
c_iff: $o > $o > $o ).
thf(func_def_7,type,
c_In: $i > $i > $o ).
thf(func_def_8,type,
c_Subq: $i > $i > $o ).
thf(func_def_10,type,
c_Union: $i > $i ).
thf(func_def_11,type,
c_Power: $i > $i ).
thf(func_def_12,type,
c_Repl: $i > ( $i > $i ) > $i ).
thf(func_def_13,type,
c_TransSet: $i > $o ).
thf(func_def_14,type,
c_atleast2: $i > $o ).
thf(func_def_15,type,
c_atleast3: $i > $o ).
thf(func_def_16,type,
c_atleast4: $i > $o ).
thf(func_def_17,type,
c_atleast5: $i > $o ).
thf(func_def_18,type,
c_atleast6: $i > $o ).
thf(func_def_19,type,
c_exactly2: $i > $o ).
thf(func_def_20,type,
c_exactly3: $i > $o ).
thf(func_def_21,type,
c_exactly4: $i > $o ).
thf(func_def_22,type,
c_exactly5: $i > $o ).
thf(func_def_23,type,
c_exu_i: ( $i > $o ) > $o ).
thf(func_def_24,type,
c_reflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
c_irreflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
c_symmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
c_antisymmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
c_transitive_i: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
c_eqreln_i: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
c_per_i: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
c_linear_i: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
c_partialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_34,type,
c_totalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_37,type,
c_If_i: $o > $i > $i > $i ).
thf(func_def_38,type,
c_exactly1of2: $o > $o > $o ).
thf(func_def_39,type,
c_exactly1of3: $o > $o > $o > $o ).
thf(func_def_40,type,
c_nIn: $i > $i > $o ).
thf(func_def_41,type,
c_nSubq: $i > $i > $o ).
thf(func_def_42,type,
c_UPair: $i > $i > $i ).
thf(func_def_43,type,
c_Sing: $i > $i ).
thf(func_def_44,type,
c_binunion: $i > $i > $i ).
thf(func_def_45,type,
c_SetAdjoin: $i > $i > $i ).
thf(func_def_46,type,
c_famunion: $i > ( $i > $i ) > $i ).
thf(func_def_47,type,
c_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_49,type,
c_binintersect: $i > $i > $i ).
thf(func_def_50,type,
c_setminus: $i > $i > $i ).
thf(func_def_51,type,
c_inj: $i > $i > ( $i > $i ) > $o ).
thf(func_def_52,type,
c_bij: $i > $i > ( $i > $i ) > $o ).
thf(func_def_53,type,
c_atleastp: $i > $i > $o ).
thf(func_def_54,type,
c_equip: $i > $i > $o ).
thf(func_def_55,type,
c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_56,type,
c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_57,type,
c_ordsucc: $i > $i ).
thf(func_def_58,type,
c_nat_p: $i > $o ).
thf(func_def_59,type,
c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
thf(func_def_60,type,
c_add_nat: $i > $i > $i ).
thf(func_def_61,type,
c_mul_nat: $i > $i > $i ).
thf(func_def_62,type,
c_ordinal: $i > $o ).
thf(func_def_63,type,
c_V_: $i > $i ).
thf(func_def_64,type,
c_Inj1: $i > $i ).
thf(func_def_65,type,
c_Inj0: $i > $i ).
thf(func_def_66,type,
c_Unj: $i > $i ).
thf(func_def_67,type,
c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_68,type,
c_setsum: $i > $i > $i ).
thf(func_def_69,type,
c_proj0: $i > $i ).
thf(func_def_70,type,
c_proj1: $i > $i ).
thf(func_def_71,type,
c_binrep: $i > $i > $i ).
thf(func_def_72,type,
c_lam: $i > ( $i > $i ) > $i ).
thf(func_def_73,type,
c_setprod: $i > $i > $i ).
thf(func_def_74,type,
c_ap: $i > $i > $i ).
thf(func_def_75,type,
c_setsum_p: $i > $o ).
thf(func_def_76,type,
c_tuple_p: $i > $i > $o ).
thf(func_def_77,type,
c_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_78,type,
c_setexp: $i > $i > $i ).
thf(func_def_79,type,
c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
c_set_of_pairs: $i > $o ).
thf(func_def_81,type,
c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_82,type,
c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_83,type,
c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_84,type,
c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_85,type,
c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_86,type,
c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_87,type,
c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_88,type,
c_SNoElts_: $i > $i ).
thf(func_def_89,type,
c_SNo_: $i > $i > $o ).
thf(func_def_90,type,
c_PSNo: $i > ( $i > $o ) > $i ).
thf(func_def_91,type,
c_SNo: $i > $o ).
thf(func_def_92,type,
c_SNoLev: $i > $i ).
thf(func_def_93,type,
c_SNoEq_: $i > $i > $i > $o ).
thf(func_def_94,type,
c_SNoLt: $i > $i > $o ).
thf(func_def_95,type,
c_SNoLe: $i > $i > $o ).
thf(func_def_96,type,
c_binop_on: $i > ( $i > $i > $i ) > $o ).
thf(func_def_97,type,
c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
thf(func_def_98,type,
c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_99,type,
c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_100,type,
c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_101,type,
c_combinator: $i > $o ).
thf(func_def_102,type,
c_combinator_equiv: $i > $i > $o ).
thf(func_def_103,type,
c_equip_mod: $i > $i > $i > $o ).
thf(func_def_105,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_106,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_107,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_108,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_109,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_110,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_111,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_112,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_113,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_114,type,
vIMP: $o > $o > $o ).
thf(func_def_117,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_118,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_120,type,
vNOT: $o > $o ).
thf(func_def_121,type,
db13:
!>[X0: $tType] : X0 ).
thf(func_def_122,type,
db12:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
db11:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
db10:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db14:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db15:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db16:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db17:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db18:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
sK0: $o ).
thf(func_def_133,type,
sK1: ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_134,type,
sK2: ( ( $i > $i ) > ( $i > $i ) > $o ) > ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i ).
thf(func_def_135,type,
sK3: ( ( ( $i > $i ) > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i ).
thf(func_def_137,type,
sK5: ( ( ( $i > $i ) > $i ) > $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_138,type,
sK6: ( $i > $i ) > $i ).
thf(func_def_139,type,
sK7: $i > $i ).
thf(func_def_140,type,
sK8: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i ).
thf(func_def_141,type,
sK9: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_142,type,
sK10: ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_143,type,
sK11: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_144,type,
sK12: ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i ).
thf(func_def_145,type,
sK13: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_146,type,
sK14: ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_147,type,
sK15: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_148,type,
sK16: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_149,type,
sK17: ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_150,type,
sK18: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_151,type,
sK19: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_152,type,
sK20: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_153,type,
sK21: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_154,type,
sK22: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_157,type,
sK25: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > $i ).
thf(func_def_158,type,
sK26: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > $i ).
thf(func_def_159,type,
sK27: ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o ) > $i ).
thf(func_def_160,type,
sK28: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i ).
thf(f5,axiom,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(f13,axiom,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(f70,axiom,
( ( ^ [X0: $i] :
( c_Repl @ X0
@ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) )
= c_Inj0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).
thf(f73,axiom,
( ( ^ [X0: $i,X1: $i] :
( c_binunion
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
@ ( c_Repl @ X1
@ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) )
= c_setsum ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
thf(f109,conjecture,
( c_not
@ ! [X0: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( ( $i > $i ) > $i ) > $i > $o,X3: ( $i > $i ) > ( $i > $i ) > $o,X2: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ! [X5: $i,X7: $i,X6: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i,X4: ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ X7
@ ( X6
@ ^ [X8: ( $i > $i ) > $i,X9: $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ X7 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X3
@ ^ [X8: $i] : X8
@ ^ [X8: $i] : ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
=> ( ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( c_In @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ X5 )
=> ( ( X3
@ ^ [X8: $i] : c_Empty
@ ^ [X8: $i] : c_Empty )
=> ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] :
( X9
@ ^ [X11: $i] : c_Empty )
@ ^ [X8: ( $i > $i ) > $i > $i] : X5
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) ) )
=> ( ! [X4: $i,X6: $i,X7: $i,X5: $i] :
( ( c_In @ ( c_Inj1 @ X6 ) @ X7 )
=> ( ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ X7 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [X8: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ X7 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ X6 ) ) )
@ c_Empty )
=> ( X2
@ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : X7
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ X4 ) @ c_Empty ) )
@ ^ [X8: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ X7 @ X6 ) @ X7 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ c_Empty ) ) )
=> ( ! [X7: $i,X5: $i,X6: $i,X4: $i] :
( ( c_In @ ( c_setsum @ c_Empty @ X6 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( X2
@ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ X7 @ X5 )
@ c_Empty
@ ^ [X8: $i] : ( c_Inj0 @ ( c_setsum @ X5 @ c_Empty ) )
@ c_Empty )
=> ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ X7 ) @ X6 ) )
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [X8: ( $i > $i ) > $i > $i] :
( c_setsum
@ ( c_Inj1
@ ( X8
@ ^ [X9: $i] : X6
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ X7 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ X4 ) @ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
=> ( ! [X5: $i,X7: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i,X4: $i,X6: $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Inj0
@ ( c_setsum
@ ( c_Inj0
@ ( X7
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
@ c_Empty
@ ^ [X8: $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) ) )
=> ( ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X8: ( $i > $i ) > $i > $i] :
( X8
@ ^ [X9: $i] :
( c_setsum
@ ( X7
@ ^ [X10: ( $i > $i ) > $i > $i,X11: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ^ [X10: $i] : ( c_Inj0 @ c_Empty )
@ X9 )
@ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
@ c_Empty )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( c_setsum
@ ( X7
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
@ c_Empty
@ ^ [X8: $i] : c_Empty
@ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ c_Empty )
=> ( X1
@ ^ [X8: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ ( X8 @ c_Empty ) ) ) @ ( c_setsum @ ( c_setsum @ ( X8 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ( c_Inj1 @ c_Empty ) ) ) )
=> ( ! [X4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X6: $i > $i,X7: ( $i > $i ) > $i,X5: $i] :
( ( c_In @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_Inj0
@ ( c_setsum @ c_Empty
@ ( X4
@ ^ [X8: $i,X9: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( ( X1
@ ^ [X8: $i > $i] : ( X6 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X7
@ ^ [X8: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( X1
@ ^ [X8: $i > $i] :
( c_Inj1
@ ( c_setsum @ ( X8 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X7
@ ^ [X9: $i] : c_Empty ) ) ) )
@ c_Empty ) ) )
=> ( ! [X7: $i,X5: $i,X6: $i > $i,X4: $i] :
( ( c_In @ X4 @ ( c_Inj0 @ c_Empty ) )
=> ( ( X2
@ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ X5 )
@ ( c_Inj0 @ X7 )
@ ^ [X8: $i] : ( c_setsum @ c_Empty @ X8 )
@ c_Empty )
=> ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : c_Empty
@ ^ [X8: ( $i > $i ) > $i > $i] : ( c_setsum @ ( c_Inj1 @ c_Empty ) @ X5 )
@ ( c_Inj0 @ c_Empty )
@ X7 ) ) )
=> ( ! [X4: $i,X5: $i,X7: $i,X6: ( $i > $i ) > $i] :
( ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] :
( X9
@ ( c_setsum
@ ( X8
@ ^ [X10: $i > $i > $i] : ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [X10: $i] :
( X9
@ ( X8
@ ^ [X11: $i > $i > $i] : c_Empty )
@ ^ [X11: $i] :
( X9
@ ( X9 @ c_Empty
@ ^ [X12: $i] : c_Empty )
@ ^ [X12: $i] : c_Empty ) ) )
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ X10 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
@ ^ [X8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ X5 )
@ ( c_Inj0 @ X7 )
@ ( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( X6
@ ^ [X8: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ X5 ) ) ) )
=> ( c_In @ X4 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f110,negated_conjecture,
~ ( c_not
@ ! [X0: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( ( $i > $i ) > $i ) > $i > $o,X3: ( $i > $i ) > ( $i > $i ) > $o,X2: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ! [X5: $i,X7: $i,X6: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i,X4: ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ X7
@ ( X6
@ ^ [X8: ( $i > $i ) > $i,X9: $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ X7 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X3
@ ^ [X8: $i] : X8
@ ^ [X8: $i] : ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
=> ( ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( c_In @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ X5 )
=> ( ( X3
@ ^ [X8: $i] : c_Empty
@ ^ [X8: $i] : c_Empty )
=> ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] :
( X9
@ ^ [X11: $i] : c_Empty )
@ ^ [X8: ( $i > $i ) > $i > $i] : X5
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) ) )
=> ( ! [X4: $i,X6: $i,X7: $i,X5: $i] :
( ( c_In @ ( c_Inj1 @ X6 ) @ X7 )
=> ( ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ X7 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [X8: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ X7 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ X6 ) ) )
@ c_Empty )
=> ( X2
@ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : X7
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ X4 ) @ c_Empty ) )
@ ^ [X8: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ X7 @ X6 ) @ X7 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ c_Empty ) ) )
=> ( ! [X7: $i,X5: $i,X6: $i,X4: $i] :
( ( c_In @ ( c_setsum @ c_Empty @ X6 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( X2
@ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ X7 @ X5 )
@ c_Empty
@ ^ [X8: $i] : ( c_Inj0 @ ( c_setsum @ X5 @ c_Empty ) )
@ c_Empty )
=> ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ X7 ) @ X6 ) )
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [X8: ( $i > $i ) > $i > $i] :
( c_setsum
@ ( c_Inj1
@ ( X8
@ ^ [X9: $i] : X6
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ X7 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ X4 ) @ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
=> ( ! [X5: $i,X7: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i,X4: $i,X6: $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Inj0
@ ( c_setsum
@ ( c_Inj0
@ ( X7
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
@ c_Empty
@ ^ [X8: $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) ) )
=> ( ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X8: ( $i > $i ) > $i > $i] :
( X8
@ ^ [X9: $i] :
( c_setsum
@ ( X7
@ ^ [X10: ( $i > $i ) > $i > $i,X11: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ^ [X10: $i] : ( c_Inj0 @ c_Empty )
@ X9 )
@ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
@ c_Empty )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( c_setsum
@ ( X7
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
@ c_Empty
@ ^ [X8: $i] : c_Empty
@ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ c_Empty )
=> ( X1
@ ^ [X8: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ ( X8 @ c_Empty ) ) ) @ ( c_setsum @ ( c_setsum @ ( X8 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ( c_Inj1 @ c_Empty ) ) ) )
=> ( ! [X4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X6: $i > $i,X7: ( $i > $i ) > $i,X5: $i] :
( ( c_In @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_Inj0
@ ( c_setsum @ c_Empty
@ ( X4
@ ^ [X8: $i,X9: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( ( X1
@ ^ [X8: $i > $i] : ( X6 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X7
@ ^ [X8: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( X1
@ ^ [X8: $i > $i] :
( c_Inj1
@ ( c_setsum @ ( X8 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X7
@ ^ [X9: $i] : c_Empty ) ) ) )
@ c_Empty ) ) )
=> ( ! [X7: $i,X5: $i,X6: $i > $i,X4: $i] :
( ( c_In @ X4 @ ( c_Inj0 @ c_Empty ) )
=> ( ( X2
@ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ X5 )
@ ( c_Inj0 @ X7 )
@ ^ [X8: $i] : ( c_setsum @ c_Empty @ X8 )
@ c_Empty )
=> ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : c_Empty
@ ^ [X8: ( $i > $i ) > $i > $i] : ( c_setsum @ ( c_Inj1 @ c_Empty ) @ X5 )
@ ( c_Inj0 @ c_Empty )
@ X7 ) ) )
=> ( ! [X4: $i,X5: $i,X7: $i,X6: ( $i > $i ) > $i] :
( ( X0
@ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] :
( X9
@ ( c_setsum
@ ( X8
@ ^ [X10: $i > $i > $i] : ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [X10: $i] :
( X9
@ ( X8
@ ^ [X11: $i > $i > $i] : c_Empty )
@ ^ [X11: $i] :
( X9
@ ( X9 @ c_Empty
@ ^ [X12: $i] : c_Empty )
@ ^ [X12: $i] : c_Empty ) ) )
@ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ X10 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
@ ^ [X8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ X5 )
@ ( c_Inj0 @ X7 )
@ ( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( X6
@ ^ [X8: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ X5 ) ) ) )
=> ( c_In @ X4 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
thf(f123,plain,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
inference(rectify,[],[f13]) ).
thf(f124,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(fool_elimination,[],[f123]) ).
thf(f141,plain,
( ( ^ [X0: $i] :
( c_Repl @ X0
@ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) )
= c_Inj0 ),
inference(rectify,[],[f70]) ).
thf(f142,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f141]) ).
thf(f193,plain,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
inference(rectify,[],[f5]) ).
thf(f194,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(fool_elimination,[],[f193]) ).
thf(f217,plain,
( ( ^ [X0: $i,X1: $i] :
( c_binunion
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
@ ( c_Repl @ X1
@ ^ [X3: $i] : ( c_Inj1 @ X3 ) ) ) )
= c_setsum ),
inference(rectify,[],[f73]) ).
thf(f218,plain,
( c_setsum
= ( ^ [Y0: $i,Y1: $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Inj0 @ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Inj1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f217]) ).
thf(f262,plain,
~ ( c_not
@ ! [X0: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( ( $i > $i ) > $i ) > $i > $o,X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ! [X5: $i,X6: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( ( c_In @ X5
@ ( X6
@ ^ [X8: ( $i > $i ) > $i,X9: $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ X5 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X2
@ ^ [X11: $i] : X11
@ ^ [X12: $i] : ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
=> ( ! [X13: $i] :
( ( c_In @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ X13 )
=> ( ( X2
@ ^ [X17: $i] : c_Empty
@ ^ [X18: $i] : c_Empty )
=> ( X0
@ ^ [X19: ( ( $i > $i > $i ) > $i ) > $i,X20: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [X21: $i,X22: ( $i > $i ) > $i,X23: $i] :
( X22
@ ^ [X24: $i] : c_Empty )
@ ^ [X25: ( $i > $i ) > $i > $i] : X13
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) ) )
=> ( ! [X26: $i,X27: $i,X28: $i] :
( ( c_In @ ( c_Inj1 @ X27 ) @ X28 )
=> ( ( X0
@ ^ [X30: ( ( $i > $i > $i ) > $i ) > $i,X31: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X32: $i,X33: ( $i > $i ) > $i,X34: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ X28 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [X35: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ X28 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ X27 ) ) )
@ c_Empty )
=> ( X3
@ ^ [X36: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : X28
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ X26 ) @ c_Empty ) )
@ ^ [X37: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ X28 @ X27 ) @ X28 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ c_Empty ) ) )
=> ( ! [X38: $i,X39: $i,X40: $i,X41: $i] :
( ( c_In @ ( c_setsum @ c_Empty @ X40 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( X3
@ ^ [X42: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ X38 @ X39 )
@ c_Empty
@ ^ [X43: $i] : ( c_Inj0 @ ( c_setsum @ X39 @ c_Empty ) )
@ c_Empty )
=> ( X0
@ ^ [X44: ( ( $i > $i > $i ) > $i ) > $i,X45: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ X38 ) @ X40 ) )
@ ^ [X46: $i,X47: ( $i > $i ) > $i,X48: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [X49: ( $i > $i ) > $i > $i] :
( c_setsum
@ ( c_Inj1
@ ( X49
@ ^ [X50: $i] : X40
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ X38 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ X41 ) @ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
=> ( ! [X52: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Inj0
@ ( c_setsum
@ ( c_Inj0
@ ( X52
@ ^ [X55: ( $i > $i ) > $i > $i,X56: $i > $i] : c_Empty
@ c_Empty
@ ^ [X57: $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) ) )
=> ( ( X0
@ ^ [X58: ( ( $i > $i > $i ) > $i ) > $i,X59: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X60: $i,X61: ( $i > $i ) > $i,X62: $i] : ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X63: ( $i > $i ) > $i > $i] :
( X63
@ ^ [X64: $i] :
( c_setsum
@ ( X52
@ ^ [X65: ( $i > $i ) > $i > $i,X66: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ^ [X67: $i] : ( c_Inj0 @ c_Empty )
@ X64 )
@ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
@ c_Empty )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( c_setsum
@ ( X52
@ ^ [X68: ( $i > $i ) > $i > $i,X69: $i > $i] : c_Empty
@ c_Empty
@ ^ [X70: $i] : c_Empty
@ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ c_Empty )
=> ( X1
@ ^ [X71: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ ( X71 @ c_Empty ) ) ) @ ( c_setsum @ ( c_setsum @ ( X71 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ( c_Inj1 @ c_Empty ) ) ) )
=> ( ! [X72: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X73: $i > $i,X74: ( $i > $i ) > $i] :
( ( c_In @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_Inj0
@ ( c_setsum @ c_Empty
@ ( X72
@ ^ [X76: $i,X77: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( ( X1
@ ^ [X78: $i > $i] : ( X73 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X74
@ ^ [X79: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( X1
@ ^ [X80: $i > $i] :
( c_Inj1
@ ( c_setsum @ ( X80 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X74
@ ^ [X81: $i] : c_Empty ) ) ) )
@ c_Empty ) ) )
=> ( ! [X82: $i,X83: $i,X85: $i] :
( ( c_In @ X85 @ ( c_Inj0 @ c_Empty ) )
=> ( ( X3
@ ^ [X86: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ X83 )
@ ( c_Inj0 @ X82 )
@ ^ [X87: $i] : ( c_setsum @ c_Empty @ X87 )
@ c_Empty )
=> ( X0
@ ^ [X88: ( ( $i > $i > $i ) > $i ) > $i,X89: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [X90: $i,X91: ( $i > $i ) > $i,X92: $i] : c_Empty
@ ^ [X93: ( $i > $i ) > $i > $i] : ( c_setsum @ ( c_Inj1 @ c_Empty ) @ X83 )
@ ( c_Inj0 @ c_Empty )
@ X82 ) ) )
=> ( ! [X94: $i,X95: $i,X96: $i,X97: ( $i > $i ) > $i] :
( ( X0
@ ^ [X98: ( ( $i > $i > $i ) > $i ) > $i,X99: $i > ( $i > $i ) > $i] :
( X99
@ ( c_setsum
@ ( X98
@ ^ [X100: $i > $i > $i] : ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [X101: $i] :
( X99
@ ( X98
@ ^ [X102: $i > $i > $i] : c_Empty )
@ ^ [X103: $i] :
( X99
@ ( X99 @ c_Empty
@ ^ [X104: $i] : c_Empty )
@ ^ [X105: $i] : c_Empty ) ) )
@ ^ [X106: $i,X107: ( $i > $i ) > $i,X108: $i] : ( c_Inj0 @ ( c_setsum @ X108 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
@ ^ [X109: ( $i > $i ) > $i > $i] : ( c_Inj1 @ X95 )
@ ( c_Inj0 @ X96 )
@ ( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( X97
@ ^ [X110: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ X95 ) ) ) )
=> ( c_In @ X94 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f263,plain,
( $true
= ( ~ ( c_not
@ ( !! @ ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o )
@ ^ [Y0: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y5
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i,Y7: $i,Y8: $i] : ( c_Inj1 @ ( c_setsum @ Y5 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( Y1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: $i] : ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ Y4 )
=> ( ( Y1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: $i] : c_Empty )
=> ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( Y6
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y4
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Inj1 @ Y5 ) @ Y4 )
=> ( ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ Y4 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ Y4 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ Y5 ) ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y4
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ Y6 ) @ c_Empty ) )
@ ^ [Y7: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ Y4 @ Y5 ) @ Y4 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_setsum @ c_Empty @ Y5 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ Y7 @ Y6 )
@ c_Empty
@ ^ [Y8: $i] : ( c_Inj0 @ ( c_setsum @ Y6 @ c_Empty ) )
@ c_Empty )
=> ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ Y7 ) @ Y5 ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] :
( c_setsum
@ ( c_Inj1
@ ( Y8
@ ^ [Y9: $i] : Y5
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ Y7 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ Y4 ) @ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Inj0
@ ( c_setsum
@ ( c_Inj0
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) ) )
=> ( ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] : ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( Y5
@ ^ [Y6: $i] :
( c_setsum
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ^ [Y7: $i] : ( c_Inj0 @ c_Empty )
@ Y6 )
@ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
@ c_Empty )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( c_setsum
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ c_Empty )
=> ( Y2
@ ^ [Y5: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ ( Y5 @ c_Empty ) ) ) @ ( c_setsum @ ( c_setsum @ ( Y5 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y6: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_Inj0
@ ( c_setsum @ c_Empty
@ ( Y6
@ ^ [Y7: $i,Y8: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( ( Y2
@ ^ [Y7: $i > $i] : ( Y5 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_setsum
@ ( Y4
@ ^ [Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( Y2
@ ^ [Y7: $i > $i] :
( c_Inj1
@ ( c_setsum @ ( Y7 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( Y4
@ ^ [Y8: $i] : c_Empty ) ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y4 @ ( c_Inj0 @ c_Empty ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ Y5 )
@ ( c_Inj0 @ Y6 )
@ ^ [Y7: $i] : ( c_setsum @ c_Empty @ Y7 )
@ c_Empty )
=> ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : c_Empty
@ ^ [Y7: ( $i > $i ) > $i > $i] : ( c_setsum @ ( c_Inj1 @ c_Empty ) @ Y5 )
@ ( c_Inj0 @ c_Empty )
@ Y6 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( Y9
@ ( c_setsum
@ ( Y8
@ ^ [Y10: $i > $i > $i] : ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [Y10: $i] :
( Y9
@ ( Y8
@ ^ [Y11: $i > $i > $i] : c_Empty )
@ ^ [Y11: $i] :
( Y9
@ ( Y9 @ c_Empty
@ ^ [Y12: $i] : c_Empty )
@ ^ [Y12: $i] : c_Empty ) ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj0 @ ( c_setsum @ Y10 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y6 )
@ ( c_Inj0 @ Y5 )
@ ( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ Y6 ) ) ) )
=> ( c_In @ Y7 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f262]) ).
thf(f308,plain,
( $true
= ( ~ ( c_not
@ ( !! @ ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o )
@ ^ [Y0: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y5
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i,Y7: $i,Y8: $i] : ( c_Inj1 @ ( c_setsum @ Y5 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( Y1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: $i] : ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ Y4 )
=> ( ( Y1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: $i] : c_Empty )
=> ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( Y6
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y4
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Inj1 @ Y5 ) @ Y4 )
=> ( ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ Y4 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ Y4 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ Y5 ) ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y4
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ Y6 ) @ c_Empty ) )
@ ^ [Y7: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ Y4 @ Y5 ) @ Y4 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_setsum @ c_Empty @ Y5 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ Y7 @ Y6 )
@ c_Empty
@ ^ [Y8: $i] : ( c_Inj0 @ ( c_setsum @ Y6 @ c_Empty ) )
@ c_Empty )
=> ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ Y7 ) @ Y5 ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] :
( c_setsum
@ ( c_Inj1
@ ( Y8
@ ^ [Y9: $i] : Y5
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ Y7 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ Y4 ) @ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Inj0
@ ( c_setsum
@ ( c_Inj0
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) ) )
=> ( ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] : ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( Y5
@ ^ [Y6: $i] :
( c_setsum
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ^ [Y7: $i] : ( c_Inj0 @ c_Empty )
@ Y6 )
@ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
@ c_Empty )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( c_setsum
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ c_Empty )
=> ( Y2
@ ^ [Y5: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ ( Y5 @ c_Empty ) ) ) @ ( c_setsum @ ( c_setsum @ ( Y5 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y6: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_Inj0
@ ( c_setsum @ c_Empty
@ ( Y6
@ ^ [Y7: $i,Y8: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( ( Y2
@ ^ [Y7: $i > $i] : ( Y5 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_setsum
@ ( Y4
@ ^ [Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( Y2
@ ^ [Y7: $i > $i] :
( c_Inj1
@ ( c_setsum @ ( Y7 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( Y4
@ ^ [Y8: $i] : c_Empty ) ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y4 @ ( c_Inj0 @ c_Empty ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ Y5 )
@ ( c_Inj0 @ Y6 )
@ ^ [Y7: $i] : ( c_setsum @ c_Empty @ Y7 )
@ c_Empty )
=> ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : c_Empty
@ ^ [Y7: ( $i > $i ) > $i > $i] : ( c_setsum @ ( c_Inj1 @ c_Empty ) @ Y5 )
@ ( c_Inj0 @ c_Empty )
@ Y6 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( Y9
@ ( c_setsum
@ ( Y8
@ ^ [Y10: $i > $i > $i] : ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [Y10: $i] :
( Y9
@ ( Y8
@ ^ [Y11: $i > $i > $i] : c_Empty )
@ ^ [Y11: $i] :
( Y9
@ ( Y9 @ c_Empty
@ ^ [Y12: $i] : c_Empty )
@ ^ [Y12: $i] : c_Empty ) ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj0 @ ( c_setsum @ Y10 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y6 )
@ ( c_Inj0 @ Y5 )
@ ( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ Y6 ) ) ) )
=> ( c_In @ Y7 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f263]) ).
thf(f312,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f314,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f142]) ).
thf(f318,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(cnf_transformation,[],[f194]) ).
thf(f319,plain,
( c_setsum
= ( ^ [Y0: $i,Y1: $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Inj0 @ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Inj1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f218]) ).
thf(f322,plain,
( c_setsum
= ( ^ [Y0: $i,Y1: $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Inj1 @ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Inj1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f319,f314]) ).
thf(f323,plain,
( $true
= ( ~ ( ^ [Y0: $o] :
( Y0
=> c_False )
@ ( !! @ ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o )
@ ^ [Y0: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y5
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( c_Inj1
@ ( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ Y5
@ ( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ c_Empty
@ c_Empty ) ) ) ) )
=> ( Y1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: $i] :
( c_Inj1
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( c_In
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ ( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Inj1 @ Y6 ) )
@ ( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Inj1 @ Y6 ) )
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ c_Empty
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ Y4 )
=> ( ( Y1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: $i] : c_Empty )
=> ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( Y6
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y4
@ c_Empty
@ ( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Inj1 @ Y6 ) )
@ c_Empty ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Inj1 @ Y5 ) @ Y4 )
=> ( ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] :
( c_Inj1
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ Y4
@ ( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ c_Empty ) )
@ c_Empty ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ Y4
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty )
@ Y5 ) ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y4
@ ( c_Inj1
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ Y6 )
@ c_Empty ) )
@ ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ Y4
@ Y5 )
@ Y4 )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ c_Empty ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ Y5 )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ c_Empty ) ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ Y7
@ Y6 )
@ c_Empty
@ ^ [Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ ( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ Y6
@ c_Empty ) )
@ c_Empty )
=> ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ c_Empty
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ c_Empty
@ c_Empty )
@ Y7 )
@ Y5 ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] :
( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ ( c_Inj1
@ ( Y8
@ ^ [Y9: $i] : Y5
@ ( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ Y7 )
@ c_Empty
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ c_Empty ) )
@ Y4 )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( c_Inj1 @ c_Empty )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ c_Empty ) ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Inj1 @ Y6 ) )
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ ( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Inj1 @ Y6 ) )
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) ) )
=> ( ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ ( c_Inj1
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ c_Empty ) ) ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( Y5
@ ^ [Y6: $i] :
( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i] :
( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ c_Empty
@ c_Empty )
@ c_Empty
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ c_Empty )
@ Y6 )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( c_Inj1 @ c_Empty ) ) )
@ c_Empty )
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ c_Empty
@ ( c_Inj1
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ ( ^ [Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y7 ) )
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) ) )
@ c_Empty
@ c_Empty ) ) ) )
@ c_Empty )
=> ( Y2
@ ^ [Y5: $i > $i] :
( ^ [Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ Y8 ) )
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) ) )
@ ( c_Inj1
@ ( ^ [Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ Y8 ) )
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) ) )
@ c_Empty
@ ( Y5 @ c_Empty ) ) )
@ ( ^ [Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ Y8 ) )
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) ) )
@ ( ^ [Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ Y8 ) )
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) ) )
@ ( Y5 @ c_Empty )
@ ( ^ [Y6: $i] :
( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) )
@ c_Empty ) )
@ c_Empty ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y6: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( c_Inj1 @ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) ) ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( Y6
@ ^ [Y7: $i,Y8: $i > $i] :
( ^ [Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y11: $i] :
( ^ [Y12: $i] :
( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) )
@ Y11 ) )
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) ) )
@ c_Empty
@ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty ) ) ) ) )
=> ( ( Y2
@ ^ [Y7: $i > $i] :
( Y5
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ ( c_Inj1
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ c_Empty ) ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( Y4
@ ^ [Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ ( c_Inj1
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty ) ) ) ) )
=> ( Y2
@ ^ [Y7: $i > $i] :
( c_Inj1
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( Y7
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ c_Empty ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( c_Inj1 @ c_Empty )
@ ( Y4
@ ^ [Y8: $i] : c_Empty ) ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y4
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ Y5 )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ Y6 )
@ ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ Y7 )
@ c_Empty )
=> ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : c_Empty
@ ^ [Y7: ( $i > $i ) > $i > $i] :
( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( c_Inj1 @ c_Empty )
@ Y5 )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty )
@ Y6 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( Y9
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ ( Y8
@ ^ [Y10: $i > $i > $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ c_Empty ) )
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ ( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ c_Empty )
@ c_Empty ) )
@ ^ [Y10: $i] :
( Y9
@ ( Y8
@ ^ [Y11: $i > $i > $i] : c_Empty )
@ ^ [Y11: $i] :
( Y9
@ ( Y9 @ c_Empty
@ ^ [Y12: $i] : c_Empty )
@ ^ [Y12: $i] : c_Empty ) ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ ( ^ [Y11: $i,Y12: $i] :
( c_binunion
@ ( c_Repl @ Y11
@ ^ [Y13: $i] :
( ^ [Y14: $i] :
( c_Repl @ Y14
@ ^ [Y15: $i] : ( c_Inj1 @ Y15 ) )
@ Y13 ) )
@ ( c_Repl @ Y12
@ ^ [Y13: $i] : ( c_Inj1 @ Y13 ) ) )
@ Y10
@ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y6 )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y5 )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ c_Empty )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ Y6 ) ) ) )
=> ( c_In @ Y7
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ c_Empty )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ c_Empty ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ c_Empty ) ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f308,f312,f322,f322,f322,f322,f322,f322,f314,f314,f322,f322,f322,f322,f314,f322,f322,f314,f322,f322,f322,f314,f322,f314,f322,f322,f322,f322,f322,f314,f314,f322,f314,f322,f322,f322,f322,f322,f322,f322,f322,f322,f314,f314,f314,f322,f322,f314,f322,f314,f322,f314,f314,f322,f322,f322,f314,f322,f322,f322,f322,f322,f322,f322,f322,f314,f322,f322,f322,f322,f322,f314,f322,f322,f322,f314,f314,f314,f322,f322,f314,f314,f322,f322,f322,f314,f322,f314,f322,f322,f314,f322,f314,f322,f314,f314,f322,f314,f322,f322,f322,f322,f322,f322,f322,f314,f322,f314]) ).
thf(f326,plain,
( $true
= ( ^ [Y0: $o] :
( Y0
=> c_False )
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(definition_unfolding,[],[f318,f312]) ).
thf(f330,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
=> c_False ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f331,plain,
( $true
= ( ~ ( ( !! @ ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o )
@ ^ [Y0: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y5
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( Y1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y4 )
=> ( ( Y1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: $i] : c_Empty )
=> ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( Y6
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y4
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Inj1 @ Y5 ) @ Y4 )
=> ( ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y4
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y8
@ ^ [Y9: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [Y5: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( Y5 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y5 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y6: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y2
@ ^ [Y7: $i > $i] :
( Y5
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y2
@ ^ [Y7: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y7
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y4 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : c_Empty
@ ^ [Y7: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y8
@ ^ [Y10: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y10: $i] :
( Y9
@ ( Y8
@ ^ [Y11: $i > $i > $i] : c_Empty )
@ ^ [Y11: $i] :
( Y9
@ ( Y9 @ c_Empty
@ ^ [Y12: $i] : c_Empty )
@ ^ [Y12: $i] : c_Empty ) ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Repl @ Y11 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y6 )
@ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y7
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) )
=> c_False ) ) ),
inference(beta-eta_normalization,[],[f323]) ).
thf(f332,plain,
( $false
= ( ( !! @ ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o )
@ ^ [Y0: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y5
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( Y1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y4 )
=> ( ( Y1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: $i] : c_Empty )
=> ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( Y6
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y4
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Inj1 @ Y5 ) @ Y4 )
=> ( ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y4
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y8
@ ^ [Y9: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [Y5: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( Y5 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y5 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y6: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y2
@ ^ [Y7: $i > $i] :
( Y5
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y2
@ ^ [Y7: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y7
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y4 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : c_Empty
@ ^ [Y7: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y8
@ ^ [Y10: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y10: $i] :
( Y9
@ ( Y8
@ ^ [Y11: $i > $i > $i] : c_Empty )
@ ^ [Y11: $i] :
( Y9
@ ( Y9 @ c_Empty
@ ^ [Y12: $i] : c_Empty )
@ ^ [Y12: $i] : c_Empty ) ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Repl @ Y11 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y6 )
@ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y7
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) )
=> c_False ) ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f333,plain,
c_False = $false,
inference(imp_proxy_clausification,[],[f332]) ).
thf(f334,plain,
( $true
= ( !! @ ( ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o )
@ ^ [Y0: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y5
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( Y1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y4 )
=> ( ( Y1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: $i] : c_Empty )
=> ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( Y6
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y4
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Inj1 @ Y5 ) @ Y4 )
=> ( ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y4
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y8
@ ^ [Y9: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [Y5: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( Y5 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y5 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y6: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y2
@ ^ [Y7: $i > $i] :
( Y5
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y2
@ ^ [Y7: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y7
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y4 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : c_Empty
@ ^ [Y7: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y8
@ ^ [Y10: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y10: $i] :
( Y9
@ ( Y8
@ ^ [Y11: $i > $i > $i] : c_Empty )
@ ^ [Y11: $i] :
( Y9
@ ( Y9 @ c_Empty
@ ^ [Y12: $i] : c_Empty )
@ ^ [Y12: $i] : c_Empty ) ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Repl @ Y11 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y6 )
@ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y7
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f332]) ).
thf(f336,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
=> $false ) ),
inference(backward_demodulation,[],[f330,f333]) ).
thf(f338,plain,
( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(boolean_simplification,[],[f336]) ).
thf(f340,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ),
inference(not_proxy_clausification,[],[f338]) ).
thf(f347,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f349,plain,
! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
= $false ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f353,plain,
! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( $true
= ( ^ [Y0: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y5
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( Y1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y4 )
=> ( ( Y1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: $i] : c_Empty )
=> ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( Y6
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y4
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Inj1 @ Y5 ) @ Y4 )
=> ( ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y4
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y8
@ ^ [Y9: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y3
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y5: $i] : c_Empty
@ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [Y5: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( Y5 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y5 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y6: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i,Y8: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y2
@ ^ [Y7: $i > $i] :
( Y5
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y2
@ ^ [Y7: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y7
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y4 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y3
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : c_Empty
@ ^ [Y7: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y6 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3
@ ^ [Y8: ( ( $i > $i > $i ) > $i ) > $i,Y9: $i > ( $i > $i ) > $i] :
( Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y8
@ ^ [Y10: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y10: $i] :
( Y9
@ ( Y8
@ ^ [Y11: $i > $i > $i] : c_Empty )
@ ^ [Y11: $i] :
( Y9
@ ( Y9 @ c_Empty
@ ^ [Y12: $i] : c_Empty )
@ ^ [Y12: $i] : c_Empty ) ) )
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i,Y10: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Repl @ Y11 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y6 )
@ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y7
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f334]) ).
thf(f354,plain,
! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( $true
= ( !! @ ( ( $i > $i ) > ( $i > $i ) > $o )
@ ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ Y4
@ ( Y3
@ ^ [Y5: ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( Y0
@ ^ [Y5: $i] : Y5
@ ^ [Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y3 )
=> ( ( Y0
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: $i] : c_Empty )
=> ( Y2
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( Y5
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y4: ( $i > $i ) > $i > $i] : Y3
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ Y4 ) @ Y3 )
=> ( ( Y2
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y3
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y5 @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y2
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y7
@ ^ [Y8: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y3
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y4: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y2
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( Y4
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y6: ( $i > $i ) > $i > $i,Y7: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y5 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y4: $i] : c_Empty
@ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y1
@ ^ [Y4: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( Y4 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y4 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y5: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y5
@ ^ [Y6: $i,Y7: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y1
@ ^ [Y6: $i > $i] :
( Y4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y6: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ^ [Y7: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y3 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 )
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] : c_Empty
@ ^ [Y6: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y5 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] :
( Y8
@ ( c_binunion
@ ( c_Repl
@ ( Y7
@ ^ [Y9: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y9: $i] :
( Y8
@ ( Y7
@ ^ [Y10: $i > $i > $i] : c_Empty )
@ ^ [Y10: $i] :
( Y8
@ ( Y8 @ c_Empty
@ ^ [Y11: $i] : c_Empty )
@ ^ [Y11: $i] : c_Empty ) ) )
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y7: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y5 )
@ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y6
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f355,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( $true
= ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ Y4
@ ( Y3
@ ^ [Y5: ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( Y0
@ ^ [Y5: $i] : Y5
@ ^ [Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y3 )
=> ( ( Y0
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: $i] : c_Empty )
=> ( Y2
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( Y5
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y4: ( $i > $i ) > $i > $i] : Y3
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ Y4 ) @ Y3 )
=> ( ( Y2
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y3
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y5 @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y2
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y7
@ ^ [Y8: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y3
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y4: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y2
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( Y4
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y6: ( $i > $i ) > $i > $i,Y7: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y5 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y4: $i] : c_Empty
@ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y1
@ ^ [Y4: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( Y4 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y4 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y5: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y5
@ ^ [Y6: $i,Y7: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y1
@ ^ [Y6: $i > $i] :
( Y4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y6: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ^ [Y7: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ Y3 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 )
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] : c_Empty
@ ^ [Y6: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y5 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2
@ ^ [Y7: ( ( $i > $i > $i ) > $i ) > $i,Y8: $i > ( $i > $i ) > $i] :
( Y8
@ ( c_binunion
@ ( c_Repl
@ ( Y7
@ ^ [Y9: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y9: $i] :
( Y8
@ ( Y7
@ ^ [Y10: $i > $i > $i] : c_Empty )
@ ^ [Y10: $i] :
( Y8
@ ( Y8 @ c_Empty
@ ^ [Y11: $i] : c_Empty )
@ ^ [Y11: $i] : c_Empty ) ) )
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i,Y9: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y7: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y5 )
@ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y6
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( $true
= ( !! @ ( ( ( $i > $i ) > $i ) > $i > $o )
@ ^ [Y0: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ Y3
@ ( Y2
@ ^ [Y4: ( $i > $i ) > $i,Y5: $i,Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y4: $i] : Y4
@ ^ [Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y2 )
=> ( ( X2
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: $i] : c_Empty )
=> ( Y1
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( Y4
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y2
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_Inj1 @ Y3 ) @ Y2 )
=> ( ( Y1
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y4 @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y1
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y6: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y6
@ ^ [Y7: $i] : Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y3: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y1
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( Y3
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y3: $i] : c_Empty
@ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y3: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( Y3 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y3 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y2: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y5: $i,Y6: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y5: $i > $i] :
( Y3
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y5: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y6: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ Y2 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 )
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty )
=> ( Y1
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] : c_Empty
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y2: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y1
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] :
( Y7
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y8: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] :
( Y7
@ ( Y6
@ ^ [Y9: $i > $i > $i] : c_Empty )
@ ^ [Y9: $i] :
( Y7
@ ( Y7 @ c_Empty
@ ^ [Y10: $i] : c_Empty )
@ ^ [Y10: $i] : c_Empty ) ) )
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y6: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y4 )
@ ( c_Repl @ Y3 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f355]) ).
thf(f357,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( ^ [Y0: ( ( $i > $i ) > $i ) > $i > $o] :
( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ Y3
@ ( Y2
@ ^ [Y4: ( $i > $i ) > $i,Y5: $i,Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y4: $i] : Y4
@ ^ [Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y2 )
=> ( ( X2
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: $i] : c_Empty )
=> ( Y1
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( Y4
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y2
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_Inj1 @ Y3 ) @ Y2 )
=> ( ( Y1
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y4 @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y1
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y6: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y6
@ ^ [Y7: $i] : Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y3: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y1
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( Y3
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y3: $i] : c_Empty
@ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y3: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( Y3 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y3 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y2: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y5: $i,Y6: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y5: $i > $i] :
( Y3
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y5: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y6: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ Y2 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 )
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty )
=> ( Y1
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] : c_Empty
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y2: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y1
@ ^ [Y6: ( ( $i > $i > $i ) > $i ) > $i,Y7: $i > ( $i > $i ) > $i] :
( Y7
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y8: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] :
( Y7
@ ( Y6
@ ^ [Y9: $i > $i > $i] : c_Empty )
@ ^ [Y9: $i] :
( Y7
@ ( Y7 @ c_Empty
@ ^ [Y10: $i] : c_Empty )
@ ^ [Y10: $i] : c_Empty ) ) )
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i,Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y6: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y4 )
@ ( c_Repl @ Y3 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( $true
= ( !! @ ( ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y0: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2
@ ( Y1
@ ^ [Y3: ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y3: $i] : Y3
@ ^ [Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y1 )
=> ( ( X2
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: $i] : c_Empty )
=> ( Y0
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( Y3
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y2: ( $i > $i ) > $i > $i] : Y1
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Inj1 @ Y2 ) @ Y1 )
=> ( ( Y0
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y1
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y3 @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y0
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y5
@ ^ [Y6: $i] : Y2
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y2: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( Y2
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y3 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y2: $i] : c_Empty
@ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y2: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y2 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y1: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y3: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ^ [Y4: $i,Y5: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y4: $i > $i] :
( Y2
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y4: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ^ [Y5: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ Y1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 )
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : c_Empty
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y3 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y1: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( Y6
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ^ [Y7: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] :
( Y6
@ ( Y5
@ ^ [Y8: $i > $i > $i] : c_Empty )
@ ^ [Y8: $i] :
( Y6
@ ( Y6 @ c_Empty
@ ^ [Y9: $i] : c_Empty )
@ ^ [Y9: $i] : c_Empty ) ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y5: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y3 )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f357]) ).
thf(f359,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( $true
= ( ^ [Y0: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2
@ ( Y1
@ ^ [Y3: ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y3: $i] : Y3
@ ^ [Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y1 )
=> ( ( X2
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: $i] : c_Empty )
=> ( Y0
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( Y3
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y2: ( $i > $i ) > $i > $i] : Y1
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Inj1 @ Y2 ) @ Y1 )
=> ( ( Y0
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y1
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y3 @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y0
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y5: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y5
@ ^ [Y6: $i] : Y2
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y2: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( Y0
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( Y2
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y3 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y2: $i] : c_Empty
@ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y2: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y2 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y1: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y3: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ^ [Y4: $i,Y5: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y4: $i > $i] :
( Y2
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y4: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ^ [Y5: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ Y1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 )
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : c_Empty
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y3 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y1: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0
@ ^ [Y5: ( ( $i > $i > $i ) > $i ) > $i,Y6: $i > ( $i > $i ) > $i] :
( Y6
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ^ [Y7: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] :
( Y6
@ ( Y5
@ ^ [Y8: $i > $i > $i] : c_Empty )
@ ^ [Y8: $i] :
( Y6
@ ( Y6 @ c_Empty
@ ^ [Y9: $i] : c_Empty )
@ ^ [Y9: $i] : c_Empty ) ) )
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i,Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y5: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y3 )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( $true
= ( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> c_False ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f361,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( $true
= ( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
=> $false ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f360,f333]) ).
thf(f362,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( $true
= ( ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f361]) ).
thf(f363,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $true
= ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $true
= ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) )
=> ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f367]) ).
thf(f369,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: ( $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y6: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] :
( Y5
@ ( Y4
@ ^ [Y7: $i > $i > $i] : c_Empty )
@ ^ [Y7: $i] :
( Y5
@ ( Y5 @ c_Empty
@ ^ [Y8: $i] : c_Empty )
@ ^ [Y8: $i] : c_Empty ) ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y2 )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
@ ( sK1 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f370]) ).
thf(f373,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f371]) ).
thf(f375,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ Y1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i,Y3: $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y2: $i] : Y2
@ ^ [Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
@ ( sK2 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f373]) ).
thf(f377,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f375]) ).
thf(f379,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y1: $i] : c_Empty
@ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y1: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) )
@ ( sK3 @ X3 @ X4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f377]) ).
thf(f381,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( sK3 @ X3 @ X4
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y0: $i] : c_Empty
@ c_Empty )
@ c_Inj1 )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y0: ( ( $i > $i > $i ) > $i ) > $i,Y1: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y0: ( $i > $i ) > $i > $i] :
( Y0
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl
@ ( sK3 @ X3 @ X4
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X3 @ X4
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y0: $i] : c_Empty
@ c_Empty )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y0: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( Y0 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y0 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f383,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( ( X4
@ ^ [Y0: ( ( $i > $i > $i ) > $i ) > $i,Y1: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ ^ [Y0: ( $i > $i ) > $i > $i] :
( Y0
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl
@ ( sK3 @ X3 @ X4
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X3 @ X4
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i] : c_Empty
@ c_Empty
@ ^ [Y0: $i] : c_Empty
@ c_Empty )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [Y0: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( Y0 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y0 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) ) ) ),
inference(imp_proxy_clausification,[],[f381]) ).
thf(f385,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( ( X3
@ ^ [Y0: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( Y0 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y0 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f383]) ).
thf(f388,definition,
( spl4_1
<=> ! [X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f389,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f388]) ).
thf(f391,definition,
( spl4_2
<=> ! [X3: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( ( X3
@ ^ [Y0: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( Y0 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y0 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f392,plain,
( ! [X3: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( X3
@ ^ [Y0: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( Y0 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y0 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) )
= $false )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X3
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X3
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f391]) ).
thf(f393,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f385,f391,f388]) ).
thf(f395,plain,
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( ^ [Y3: ( $i > $i ) > $i,Y4: $i] : $true
@ ^ [Y3: $i > $i] :
( Y1
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( ^ [Y3: ( $i > $i ) > $i,Y4: $i] : $true
@ ^ [Y3: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y4: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: ( $i > $i ) > $i,Y1: $i] : $true
@ ^ [Y0: $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( Y0 @ c_Empty ) @ c_Inj1 ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( Y0 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ( c_Inj1 @ c_Empty ) ) )
| ~ spl4_2 ),
inference(primitive_instantiation,[],[f392]) ).
thf(f401,plain,
( ( $true = $false )
| ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( $true
=> $true ) ) ) ) ) )
| ~ spl4_2 ),
inference(beta-eta_normalization,[],[f395]) ).
thf(f402,plain,
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( $true
=> $true ) ) ) ) ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f403,plain,
( ( ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i,Y4: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> $true ) ) ) )
= $false )
| ~ spl4_2 ),
inference(boolean_simplification,[],[f402]) ).
thf(f404,plain,
( ( $false
= ( !! @ ( ( $i > $i ) > $i )
@ ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] : $true ) ) ) )
| ~ spl4_2 ),
inference(boolean_simplification,[],[f403]) ).
thf(f408,plain,
( ( ( ^ [Y0: ( $i > $i ) > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y2: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] : $true ) )
@ sK6 )
= $false )
| ~ spl4_2 ),
inference(sigma_proxy_clausification,[],[f404]) ).
thf(f410,plain,
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y1: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] : $true ) )
= $false )
| ~ spl4_2 ),
inference(beta-eta_normalization,[],[f408]) ).
thf(f412,plain,
( ( ( ^ [Y0: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y1: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] : $true )
@ sK7 )
= $false )
| ~ spl4_2 ),
inference(sigma_proxy_clausification,[],[f410]) ).
thf(f415,plain,
( ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] : $true )
= $false )
| ~ spl4_2 ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f416,plain,
( ( ( ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] : $true
@ sK8 )
= $false )
| ~ spl4_2 ),
inference(sigma_proxy_clausification,[],[f415]) ).
thf(f418,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(beta-eta_normalization,[],[f416]) ).
thf(f419,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f420,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f419]) ).
thf(f422,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y4: ( ( $i > $i > $i ) > $i ) > $i,Y5: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i,Y6: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y4: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y4
@ ^ [Y5: $i] : Y1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
@ ( sK9 @ X1 @ X4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ~ spl4_1 ),
inference(sigma_proxy_clausification,[],[f389]) ).
thf(f424,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f422]) ).
thf(f426,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y5: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] :
( Y4
@ ( Y3
@ ^ [Y6: $i > $i > $i] : c_Empty )
@ ^ [Y6: $i] :
( Y4
@ ( Y4 @ c_Empty
@ ^ [Y7: $i] : c_Empty )
@ ^ [Y7: $i] : c_Empty ) ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y1 )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
@ ( sK10 @ X4 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false ) )
| ~ spl4_1 ),
inference(sigma_proxy_clausification,[],[f424]) ).
thf(f428,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f426]) ).
thf(f430,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y0 )
=> ( ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y0
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) )
@ ( sK11 @ X1 @ X4 ) ) ) )
| ~ spl4_1 ),
inference(sigma_proxy_clausification,[],[f428]) ).
thf(f432,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f430]) ).
thf(f434,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ Y0 )
=> ( ( X2
@ ^ [Y1: $i] : c_Empty
@ ^ [Y1: $i] : c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( Y2
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y1: ( $i > $i ) > $i > $i] : Y0
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ( sK12 @ X4 @ X2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) ) )
| ~ spl4_1 ),
inference(sigma_proxy_clausification,[],[f432]) ).
thf(f436,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( ( c_In
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ( sK12 @ X4 @ X2 ) )
=> ( ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty )
=> ( X4
@ ^ [Y0: ( ( $i > $i > $i ) > $i ) > $i,Y1: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] :
( Y1
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y0: ( $i > $i ) > $i > $i] : ( sK12 @ X4 @ X2 )
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f434]) ).
thf(f438,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty )
=> ( X4
@ ^ [Y0: ( ( $i > $i > $i ) > $i ) > $i,Y1: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] :
( Y1
@ ^ [Y3: $i] : c_Empty )
@ ^ [Y0: ( $i > $i ) > $i > $i] : ( sK12 @ X4 @ X2 )
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false ) )
| ~ spl4_1 ),
inference(imp_proxy_clausification,[],[f436]) ).
thf(f441,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ~ spl4_1 ),
inference(imp_proxy_clausification,[],[f438]) ).
thf(f443,definition,
( spl4_3
<=> ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f444,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f443]) ).
thf(f446,definition,
( spl4_4
<=> ! [X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f447,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f446]) ).
thf(f448,plain,
( spl4_3
| spl4_4
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f441,f388,f446,f443]) ).
thf(f449,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y0 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : c_Empty
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y2 ) ) ) ) )
@ ( sK13 @ X1 @ X4 ) ) ) )
| ~ spl4_4 ),
inference(sigma_proxy_clausification,[],[f447]) ).
thf(f451,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : c_Empty
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f449]) ).
thf(f453,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : c_Empty
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y4: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] :
( Y3
@ ( Y2
@ ^ [Y5: $i > $i > $i] : c_Empty )
@ ^ [Y5: $i] :
( Y3
@ ( Y3 @ c_Empty
@ ^ [Y6: $i] : c_Empty )
@ ^ [Y6: $i] : c_Empty ) ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: ( $i > $i ) > $i > $i] : ( c_Inj1 @ Y0 )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y2: $i] : c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
@ ( sK14 @ X4 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false ) )
| ~ spl4_4 ),
inference(sigma_proxy_clausification,[],[f451]) ).
thf(f455,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y3: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] :
( Y2
@ ( Y1
@ ^ [Y4: $i > $i > $i] : c_Empty )
@ ^ [Y4: $i] :
( Y2
@ ( Y2 @ c_Empty
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : c_Empty ) ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y1: $i] : c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : c_Empty
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 ) ) ) ) )
= $false ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f453]) ).
thf(f457,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y3: ( ( $i > $i > $i ) > $i ) > $i,Y4: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i,Y5: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y3: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y3
@ ^ [Y4: $i] : Y0
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) )
@ ( sK15 @ X1 @ X4 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : c_Empty
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y3: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] :
( Y2
@ ( Y1
@ ^ [Y4: $i > $i > $i] : c_Empty )
@ ^ [Y4: $i] :
( Y2
@ ( Y2 @ c_Empty
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : c_Empty ) ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y1: $i] : c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(sigma_proxy_clausification,[],[f455]) ).
thf(f459,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : c_Empty
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y3: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] :
( Y2
@ ( Y1
@ ^ [Y4: $i > $i > $i] : c_Empty )
@ ^ [Y4: $i] :
( Y2
@ ( Y2 @ c_Empty
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : c_Empty ) ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y1: $i] : c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y2
@ ^ [Y3: $i] : ( sK15 @ X1 @ X4 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f457]) ).
thf(f461,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : c_Empty
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y1 ) ) ) )
@ ( sK16 @ X1 @ X4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y2
@ ^ [Y3: $i] : ( sK15 @ X1 @ X4 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y3: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] :
( Y2
@ ( Y1
@ ^ [Y4: $i > $i > $i] : c_Empty )
@ ^ [Y4: $i] :
( Y2
@ ( Y2 @ c_Empty
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : c_Empty ) ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y1: $i] : c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(sigma_proxy_clausification,[],[f459]) ).
thf(f464,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y3: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] :
( Y2
@ ( Y1
@ ^ [Y4: $i > $i > $i] : c_Empty )
@ ^ [Y4: $i] :
( Y2
@ ( Y2 @ c_Empty
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : c_Empty ) ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y1: $i] : c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y2
@ ^ [Y3: $i] : ( sK15 @ X1 @ X4 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] : c_Empty
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y0 ) ) ) ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f461]) ).
thf(f465,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] :
( Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y3: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] :
( Y2
@ ( Y1
@ ^ [Y4: $i > $i > $i] : c_Empty )
@ ^ [Y4: $i] :
( Y2
@ ( Y2 @ c_Empty
@ ^ [Y5: $i] : c_Empty )
@ ^ [Y5: $i] : c_Empty ) ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y1: $i] : c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) )
@ ( sK17 @ X4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y2
@ ^ [Y3: $i] : ( sK15 @ X1 @ X4 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] : c_Empty
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y0 ) ) ) ) ) )
| ~ spl4_4 ),
inference(sigma_proxy_clausification,[],[f464]) ).
thf(f468,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y2
@ ^ [Y3: $i] : ( sK15 @ X1 @ X4 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] : c_Empty
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y0 ) ) ) ) )
| ( ( ( X4
@ ^ [Y0: ( ( $i > $i > $i ) > $i ) > $i,Y1: $i > ( $i > $i ) > $i] :
( Y1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y2: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] :
( Y1
@ ( Y0
@ ^ [Y3: $i > $i > $i] : c_Empty )
@ ^ [Y3: $i] :
( Y1
@ ( Y1 @ c_Empty
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : c_Empty ) ) )
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y0: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y0: $i] : c_Empty )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ ( sK17 @ X4 )
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f465]) ).
thf(f470,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X4: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $true
= ( X4
@ ^ [Y0: ( ( $i > $i > $i ) > $i ) > $i,Y1: $i > ( $i > $i ) > $i] :
( Y1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y2: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] :
( Y1
@ ( Y0
@ ^ [Y3: $i > $i > $i] : c_Empty )
@ ^ [Y3: $i] :
( Y1
@ ( Y1 @ c_Empty
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : c_Empty ) ) )
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y0: ( $i > $i ) > $i > $i] : ( c_Inj1 @ ( sK14 @ X4 ) )
@ ( c_Repl @ ( sK10 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1 @ X4
@ ^ [Y0: $i] : c_Empty )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK15 @ X1 @ X4 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y2
@ ^ [Y3: $i] : ( sK15 @ X1 @ X4 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK9 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( sK13 @ X1 @ X4 ) @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> ( X4
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] : c_Empty
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK16 @ X1 @ X4 ) @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 ) @ ( sK11 @ X1 @ X4 ) )
=> ( ( X4
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( sK11 @ X1 @ X4 )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK11 @ X1 @ X4 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(imp_proxy_clausification,[],[f468]) ).
thf(f513,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> ( ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false
@ ^ [Y1: ( ( $i > $i > $i ) > $i ) > $i,Y2: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] : c_Empty
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y1: $i > ( ( $i > $i ) > $i ) > $i > $i,Y2: ( ( $i > $i ) > $i > $i ) > $i,Y3: $i,Y4: $i] : $false
@ ^ [Y0: ( ( $i > $i > $i ) > $i ) > $i,Y1: $i > ( $i > $i ) > $i] :
( Y1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y2: $i > $i > $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] :
( Y1
@ ( Y0
@ ^ [Y3: $i > $i > $i] : c_Empty )
@ ^ [Y3: $i] :
( Y1
@ ( Y1 @ c_Empty
@ ^ [Y4: $i] : c_Empty )
@ ^ [Y4: $i] : c_Empty ) ) )
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y0: ( $i > $i ) > $i > $i] :
( c_Inj1
@ ( sK14
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false ) )
@ ( c_Repl
@ ( sK10
@ ^ [Y0: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y1: $i > ( ( $i > $i ) > $i ) > $i > $i,Y2: ( ( $i > $i ) > $i > $i ) > $i,Y3: $i,Y4: $i] : $false )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK1
@ ^ [Y0: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y1: $i > ( ( $i > $i ) > $i ) > $i > $i,Y2: ( ( $i > $i ) > $i > $i ) > $i,Y3: $i,Y4: $i] : $false
@ ^ [Y0: $i] : c_Empty )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK14
@ ^ [Y0: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y1: $i > ( ( $i > $i ) > $i ) > $i > $i,Y2: ( ( $i > $i ) > $i > $i ) > $i,Y3: $i,Y4: $i] : $false )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 )
@ ( sK11 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false ) )
=> ( ( ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] : c_Empty
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y5: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y6: $i > ( ( $i > $i ) > $i ) > $i > $i,Y7: ( ( $i > $i ) > $i > $i ) > $i,Y8: $i,Y9: $i] : $false )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty )
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false
@ ^ [Y2: ( ( $i > $i > $i ) > $i ) > $i,Y3: $i > ( $i > $i ) > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y4: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y5: $i > ( ( $i > $i ) > $i ) > $i > $i,Y6: ( ( $i > $i ) > $i > $i ) > $i,Y7: $i,Y8: $i] : $false )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i,Y4: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y2: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y2
@ ^ [Y3: $i] :
( sK15 @ X1
@ ^ [Y4: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y5: $i > ( ( $i > $i ) > $i ) > $i > $i,Y6: ( ( $i > $i ) > $i > $i ) > $i,Y7: $i,Y8: $i] : $false )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK9 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(primitive_instantiation,[],[f470]) ).
thf(f516,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $true = $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> $false ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> $false ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 )
@ ( sK11 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false ) )
=> ( $false
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f513]) ).
thf(f517,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> $false ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 )
@ ( sK11 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false ) )
=> ( $false
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> $false ) ) )
= $false ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f516]) ).
thf(f518,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 )
@ ( sK11 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false ) )
=> ( $false
=> ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK11 @ X1
@ ^ [Y3: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y4: $i > ( ( $i > $i ) > $i ) > $i > $i,Y5: ( ( $i > $i ) > $i > $i ) > $i,Y6: $i,Y7: $i] : $false )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> $false ) ) )
= $false ) )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f517]) ).
thf(f519,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ Y0 )
@ ( sK11 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false ) )
=> $true ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> $false ) ) )
= $false ) )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f518]) ).
thf(f520,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty )
=> $false ) ) )
= $false ) )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f519]) ).
thf(f521,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ) )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f520]) ).
thf(f527,definition,
( spl4_5
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f528,plain,
( ( $false
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
| spl4_5 ),
inference(avatar_component_clause,[],[f527]) ).
thf(f529,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f527]) ).
thf(f531,definition,
( spl4_6
<=> ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f532,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty ) ) ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f531]) ).
thf(f533,plain,
( spl4_5
| spl4_6
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f521,f446,f531,f527]) ).
thf(f554,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true )
@ sK23 )
= $false )
| ~ spl4_5 ),
inference(sigma_proxy_clausification,[],[f529]) ).
thf(f556,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f554]) ).
thf(f558,plain,
( ( $false
= ( ^ [Y0: $i] : $true
@ sK24 ) )
| ~ spl4_5 ),
inference(sigma_proxy_clausification,[],[f556]) ).
thf(f560,plain,
( ( $true = $false )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f558]) ).
thf(f561,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f560]) ).
thf(f562,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f561]) ).
thf(f564,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true )
@ X1 ) )
| spl4_5 ),
inference(pi_proxy_clausification,[],[f528]) ).
thf(f566,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $true )
| spl4_5 ),
inference(beta-eta_normalization,[],[f564]) ).
thf(f572,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) )
@ ( sK25 @ X1 ) ) ) )
| ~ spl4_6 ),
inference(sigma_proxy_clausification,[],[f532]) ).
thf(f574,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK25 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK25 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f572]) ).
thf(f576,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( ( ^ [Y0: $i] :
( ( c_In
@ ( sK13 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y2: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y3: $i > ( ( $i > $i ) > $i ) > $i > $i,Y4: ( ( $i > $i ) > $i > $i ) > $i,Y5: $i,Y6: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 )
@ ^ [Y1: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty ) )
@ ( sK26 @ X1 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK25 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK25 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ~ spl4_6 ),
inference(sigma_proxy_clausification,[],[f574]) ).
thf(f578,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK25 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK25 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) )
| ( $false
= ( ( c_In
@ ( sK13 @ X1
@ ^ [Y0: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y1: $i > ( ( $i > $i ) > $i ) > $i > $i,Y2: ( ( $i > $i ) > $i > $i ) > $i,Y3: $i,Y4: $i] : $false )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( sK26 @ X1 ) @ c_Inj1 )
@ ^ [Y0: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f576]) ).
thf(f580,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK25 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK25 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) )
| ( ( ~ ( X1
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( sK26 @ X1 ) @ c_Inj1 )
@ ^ [Y0: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty ) )
= $false ) )
| ~ spl4_6 ),
inference(imp_proxy_clausification,[],[f578]) ).
thf(f582,plain,
( ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( $true
= ( X1
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( sK26 @ X1 ) @ c_Inj1 )
@ ^ [Y0: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15 @ X1
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( X1
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK25 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK25 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) ) )
| ~ spl4_6 ),
inference(not_proxy_clausification,[],[f580]) ).
thf(f622,plain,
( ( $true
= ( ^ [Y0: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i > $i,Y3: $i] : $false
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK16
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl
@ ( sK26
@ ^ [Y0: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i > $i,Y3: $i] : $false )
@ c_Inj1 )
@ ^ [Y0: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ ( ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK25
@ ^ [Y2: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y3: $i,Y4: $i > $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK25
@ ^ [Y2: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y3: $i,Y4: $i > $i,Y5: $i] : $false )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) ) ) )
| ~ spl4_6 ),
inference(primitive_instantiation,[],[f582]) ).
thf(f636,plain,
( ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ $false ) )
= $false )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f622]) ).
thf(f637,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ~ $false ) )
= $false )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f636]) ).
thf(f638,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK15
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false
@ ^ [Y1: ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i,Y2: $i > ( ( $i > $i ) > $i ) > $i > $i,Y3: ( ( $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i] : $false )
@ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> $true ) ) )
| ~ spl4_6 ),
inference(boolean_simplification,[],[f637]) ).
thf(f639,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false )
| ~ spl4_6 ),
inference(boolean_simplification,[],[f638]) ).
thf(f646,plain,
( ( $true = $false )
| spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f639,f566]) ).
thf(f647,plain,
( $false
| spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f646]) ).
thf(f648,plain,
( spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f647]) ).
thf(f661,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( ( ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2 @ X2
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
@ ( sK28 @ X2 ) )
= $false )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl4_3 ),
inference(sigma_proxy_clausification,[],[f444]) ).
thf(f665,plain,
( ( $true
= ( ^ [Y0: $i > $i,Y1: $i > $i] : $false
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2
@ ^ [Y1: $i > $i,Y2: $i > $i] : $false
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( ^ [Y1: $i > $i,Y2: $i > $i] : $false
@ ^ [Y1: $i] : Y1
@ ^ [Y1: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ~ spl4_3 ),
inference(primitive_instantiation,[],[f444]) ).
thf(f673,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $false
= ( ( c_In @ ( sK28 @ X2 )
@ ( sK2 @ X2
@ ^ [Y0: ( $i > $i ) > $i,Y1: $i,Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( sK28 @ X2 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> ( X2
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f661]) ).
thf(f676,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2
@ ^ [Y1: $i > $i,Y2: $i > $i] : $false
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> $false ) ) )
| ( $true = $false )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f665]) ).
thf(f677,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK2
@ ^ [Y1: $i > $i,Y2: $i > $i] : $false
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
=> $false ) ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f676]) ).
thf(f678,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( c_In @ Y0
@ ( sK2
@ ^ [Y1: $i > $i,Y2: $i > $i] : $false
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) ) )
| ~ spl4_3 ),
inference(boolean_simplification,[],[f677]) ).
thf(f680,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) )
= $false )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl4_3 ),
inference(imp_proxy_clausification,[],[f673]) ).
thf(f682,plain,
( ( $false
= ( ^ [Y0: $i] :
~ ( c_In @ Y0
@ ( sK2
@ ^ [Y1: $i > $i,Y2: $i > $i] : $false
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i,Y3: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
@ sK29 ) )
| ~ spl4_3 ),
inference(sigma_proxy_clausification,[],[f678]) ).
thf(f684,plain,
( ( ( ~ ( c_In @ sK29
@ ( sK2
@ ^ [Y0: $i > $i,Y1: $i > $i] : $false
@ ^ [Y0: ( $i > $i ) > $i,Y1: $i,Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ sK29
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f682]) ).
thf(f686,plain,
( ( $true
= ( c_In @ sK29
@ ( sK2
@ ^ [Y0: $i > $i,Y1: $i > $i] : $false
@ ^ [Y0: ( $i > $i ) > $i,Y1: $i,Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ sK29
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
| ~ spl4_3 ),
inference(not_proxy_clausification,[],[f684]) ).
thf(f688,plain,
( ( $true
= ( ^ [Y0: $i > $i,Y1: $i > $i] : ( Y0 != Y1 )
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ( $false
= ( ^ [Y0: $i > $i,Y1: $i > $i] : ( Y0 != Y1 )
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
| ~ spl4_3 ),
inference(primitive_instantiation,[],[f680]) ).
thf(f699,plain,
( ( $true
= ( ( ^ [Y0: $i] : c_Empty )
!= ( ^ [Y0: $i] : c_Empty ) ) )
| ( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
= $false )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f688]) ).
thf(f700,plain,
( ( $true = ( ~ $true ) )
| ( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
= $false )
| ~ spl4_3 ),
inference(boolean_simplification,[],[f699]) ).
thf(f701,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
= $false )
| ( $true = $false )
| ~ spl4_3 ),
inference(boolean_simplification,[],[f700]) ).
thf(f702,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
= $false )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f701]) ).
thf(f704,plain,
( ( $true
= ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) ) )
| ~ spl4_3 ),
inference(not_proxy_clausification,[],[f702]) ).
thf(f706,plain,
( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) ) ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[],[f704]) ).
thf(f712,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : Y0
@ X1 )
= ( ^ [Y0: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ X1 ) )
| ~ spl4_3 ),
inference(argument_congruence,[],[f706]) ).
thf(f713,plain,
( ! [X1: $i] :
( ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) ) )
= X1 )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f712]) ).
thf(f756,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl4_3 ),
inference(superposition,[],[f713,f713]) ).
thf(f813,plain,
( ! [X0: $i,X1: $i] :
( ( c_In @ X1 @ X0 )
= $false )
| ~ spl4_3 ),
inference(superposition,[],[f349,f756]) ).
thf(f871,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(backward_demodulation,[],[f686,f813]) ).
thf(f876,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f871]) ).
thf(f877,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f876]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f393]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f420]) ).
cnf(s3,plain,
( ~ spl4_1
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f448]) ).
cnf(s4,plain,
( ~ spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f533]) ).
cnf(s7,plain,
~ spl4_5,
inference(sat_conversion,[],[f562]) ).
cnf(s8,plain,
( spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f648]) ).
cnf(s20,plain,
~ spl4_3,
inference(sat_conversion,[],[f877]) ).
cnf(s22,plain,
~ spl4_6,
inference(rat,[],[s8,s7]) ).
cnf(s23,plain,
~ spl4_4,
inference(rat,[],[s4,s22,s7]) ).
cnf(s24,plain,
~ spl4_1,
inference(rat,[],[s3,s23,s20]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s1,s2,s24]) ).
thf(f882,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV526^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:55:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.40 % (903875)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.40 % (903884)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2531009996:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.40 % (903886)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.40 % (903886)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.40 % (903884)Instruction limit reached!
% 0.68/0.40 % (903884)------------------------------
% 0.68/0.40 % (903884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (903884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (903884)CaDiCaL version: 2.1.3
% 0.68/0.40 % (903884)Termination reason: Instruction limit
% 0.68/0.40 % (903884)Termination phase: Property scanning
% 0.68/0.40 % (903884)Time elapsed: 0.006 s
% 0.68/0.40 % (903884)Peak memory usage: 10 MB
% 0.68/0.40 % (903884)Instructions burned: 26 (million)
% 0.68/0.40 % (903880)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1265916601:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.40 % (903881)lrs+10_16_si=on:nwc=1.5:random_seed=2263227098:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.40 % (903882)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3185675199:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.40 % (903883)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=140701329:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.68/0.40 % (903885)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=912672456:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.40 % (903886)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=431595510:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.40 % (903882)Instruction limit reached!
% 0.68/0.40 % (903882)------------------------------
% 0.68/0.40 % (903882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (903882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (903882)CaDiCaL version: 2.1.3
% 0.68/0.40 % (903882)Termination reason: Instruction limit
% 0.68/0.40 % (903882)Termination phase: shuffling
% 0.68/0.40 % (903882)Time elapsed: 0.002 s
% 0.68/0.40 % (903882)Peak memory usage: 10 MB
% 0.68/0.40 % (903882)Instructions burned: 4 (million)
% 0.68/0.40 % (903881)Instruction limit reached!
% 0.68/0.40 % (903881)------------------------------
% 0.68/0.40 % (903881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (903881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (903881)CaDiCaL version: 2.1.3
% 0.68/0.40 % (903881)Termination reason: Instruction limit
% 0.68/0.40 % (903881)Termination phase: Property scanning
% 0.68/0.40 % (903881)Time elapsed: 0.009 s
% 0.68/0.40 % (903881)Peak memory usage: 10 MB
% 0.68/0.40 % (903881)Instructions burned: 19 (million)
% 0.68/0.40 % (903888)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=861051670:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.40 % (903888)Instruction limit reached!
% 0.68/0.40 % (903888)------------------------------
% 0.68/0.40 % (903888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (903888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (903888)CaDiCaL version: 2.1.3
% 0.68/0.40 % (903888)Termination reason: Instruction limit
% 0.68/0.40 % (903888)Termination phase: shuffling
% 0.68/0.40 % (903888)Time elapsed: 0.001 s
% 0.68/0.40 % (903888)Peak memory usage: 10 MB
% 0.68/0.40 % (903888)Instructions burned: 4 (million)
% 0.68/0.40 % (903895)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=630113971:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.40 % (903898)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1657635636:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.43 % (903896)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.43 % (903895)Instruction limit reached!
% 0.68/0.43 % (903895)------------------------------
% 0.68/0.43 % (903895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (903895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (903895)CaDiCaL version: 2.1.3
% 0.68/0.43 % (903895)Termination reason: Instruction limit
% 0.68/0.43 % (903895)Termination phase: shuffling
% 0.68/0.43 % (903895)Time elapsed: 0.003 s
% 0.68/0.43 % (903895)Peak memory usage: 10 MB
% 0.68/0.43 % (903895)Instructions burned: 5 (million)
% 0.68/0.43 % (903898)Instruction limit reached!
% 0.68/0.43 % (903898)------------------------------
% 0.68/0.43 % (903898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (903898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (903898)CaDiCaL version: 2.1.3
% 0.68/0.43 % (903898)Termination reason: Instruction limit
% 0.68/0.43 % (903898)Termination phase: shuffling
% 0.68/0.43 % (903898)Time elapsed: 0.004 s
% 0.68/0.43 % (903898)Peak memory usage: 10 MB
% 0.68/0.43 % (903898)Instructions burned: 16 (million)
% 0.68/0.43 % (903896)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=812988508:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.43 % (903885)Instruction limit reached!
% 0.68/0.43 % (903885)------------------------------
% 0.68/0.43 % (903885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (903885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (903885)CaDiCaL version: 2.1.3
% 0.68/0.43 % (903885)Termination reason: Instruction limit
% 0.68/0.43 % (903885)Termination phase: Function definition elimination
% 0.68/0.43 % (903885)Time elapsed: 0.033 s
% 0.68/0.43 % (903885)Peak memory usage: 11 MB
% 0.68/0.43 % (903885)Instructions burned: 79 (million)
% 0.68/0.43 % (903896)Instruction limit reached!
% 0.68/0.43 % (903896)------------------------------
% 0.68/0.43 % (903896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (903896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (903896)CaDiCaL version: 2.1.3
% 0.68/0.43 % (903896)Termination reason: Instruction limit
% 0.68/0.43 % (903896)Termination phase: shuffling
% 0.68/0.43 % (903896)Time elapsed: 0.005 s
% 0.68/0.43 % (903896)Peak memory usage: 10 MB
% 0.68/0.43 % (903896)Instructions burned: 12 (million)
% 0.68/0.43 % (903903)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1061514877:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.68/0.43 % (903901)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.43 % (903901)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.43 % (903901)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3145757690:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.43 % (903905)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.68/0.43 % (903904)lrs+10_1_si=on:cs=on:random_seed=1036685126:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.68/0.43 % (903905)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1951184723:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.43 % (903905)Instruction limit reached!
% 0.68/0.43 % (903905)------------------------------
% 0.68/0.43 % (903905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (903905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (903905)CaDiCaL version: 2.1.3
% 0.68/0.46 % (903905)Termination reason: Instruction limit
% 0.68/0.46 % (903905)Termination phase: shuffling
% 0.68/0.46 % (903905)Time elapsed: 0.002 s
% 0.68/0.46 % (903905)Peak memory usage: 10 MB
% 0.68/0.46 % (903904)Instruction limit reached!
% 0.68/0.46 % (903904)------------------------------
% 0.68/0.46 % (903904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (903904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (903904)CaDiCaL version: 2.1.3
% 0.68/0.46 % (903904)Termination reason: Instruction limit
% 0.68/0.46 % (903904)Termination phase: shuffling
% 0.68/0.46 % (903904)Time elapsed: 0.004 s
% 0.68/0.46 % (903904)Peak memory usage: 10 MB
% 0.68/0.46 % (903904)Instructions burned: 9 (million)
% 0.68/0.46 % (903880)Instruction limit reached!
% 0.68/0.46 % (903880)------------------------------
% 0.68/0.46 % (903880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (903880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (903880)CaDiCaL version: 2.1.3
% 0.68/0.46 % (903880)Termination reason: Instruction limit
% 0.68/0.46 % (903880)Termination phase: Function definition elimination
% 0.68/0.46 % (903880)Time elapsed: 0.058 s
% 0.68/0.46 % (903880)Peak memory usage: 11 MB
% 0.68/0.46 % (903880)Instructions burned: 88 (million)
% 0.68/0.46 % (903905)Instructions burned: 6 (million)
% 0.68/0.46 % (903901)Instruction limit reached!
% 0.68/0.46 % (903901)------------------------------
% 0.68/0.46 % (903901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (903901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (903901)CaDiCaL version: 2.1.3
% 0.68/0.46 % (903901)Termination reason: Instruction limit
% 0.68/0.46 % (903901)Termination phase: Property scanning
% 0.68/0.46 % (903901)Time elapsed: 0.013 s
% 0.68/0.46 % (903901)Peak memory usage: 10 MB
% 0.68/0.46 % (903901)Instructions burned: 29 (million)
% 0.68/0.46 % (903886)Instruction limit reached!
% 0.68/0.46 % (903886)------------------------------
% 0.68/0.46 % (903886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (903886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (903886)CaDiCaL version: 2.1.3
% 0.68/0.46 % (903886)Termination reason: Instruction limit
% 0.68/0.46 % (903886)Termination phase: Twee Goal Transformation
% 0.68/0.46 % (903886)Time elapsed: 0.062 s
% 0.68/0.46 % (903886)Peak memory usage: 11 MB
% 0.68/0.46 % (903886)Instructions burned: 159 (million)
% 0.68/0.46 % (903903)Instruction limit reached!
% 0.68/0.46 % (903903)------------------------------
% 0.68/0.46 % (903903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (903903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (903903)CaDiCaL version: 2.1.3
% 0.68/0.46 % (903903)Termination reason: Instruction limit
% 0.68/0.46 % (903903)Termination phase: Property scanning
% 0.68/0.46 % (903903)Time elapsed: 0.022 s
% 0.68/0.46 % (903903)Peak memory usage: 11 MB
% 0.68/0.46 % (903903)Instructions burned: 104 (million)
% 0.68/0.46 % (903915)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2025970344:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.68/0.46 % (903911)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1512363081:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.68/0.47 % (903910)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2319220456:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.68/0.47 % (903915)Instruction limit reached!
% 0.68/0.47 % (903915)------------------------------
% 0.68/0.47 % (903915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.47 % (903915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.47 % (903915)CaDiCaL version: 2.1.3
% 0.68/0.47 % (903915)Termination reason: Instruction limit
% 0.68/0.47 % (903915)Termination phase: shuffling
% 0.68/0.47 % (903915)Time elapsed: 0.004 s
% 0.68/0.47 % (903915)Peak memory usage: 10 MB
% 0.68/0.47 % (903915)Instructions burned: 18 (million)
% 0.68/0.47 % (903914)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=112046676:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.68/0.47 % (903913)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1424763292:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.43/0.52 % (903912)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3878789363:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.43/0.52 % (903919)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4075007493:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.43/0.52 % (903919)Instruction limit reached!
% 1.43/0.52 % (903919)------------------------------
% 1.43/0.52 % (903919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.52 % (903919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.52 % (903919)CaDiCaL version: 2.1.3
% 1.43/0.52 % (903919)Termination reason: Instruction limit
% 1.43/0.52 % (903919)Termination phase: shuffling
% 1.43/0.52 % (903919)Time elapsed: 0.001 s
% 1.43/0.52 % (903919)Peak memory usage: 10 MB
% 1.43/0.52 % (903919)Instructions burned: 6 (million)
% 1.43/0.52 % (903913)Instruction limit reached!
% 1.43/0.52 % (903913)------------------------------
% 1.43/0.52 % (903913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.52 % (903913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.52 % (903913)CaDiCaL version: 2.1.3
% 1.43/0.52 % (903913)Termination reason: Instruction limit
% 1.43/0.52 % (903913)Termination phase: shuffling
% 1.43/0.52 % (903913)Time elapsed: 0.007 s
% 1.43/0.52 % (903913)Peak memory usage: 10 MB
% 1.43/0.52 % (903913)Instructions burned: 15 (million)
% 1.43/0.52 % (903910)Instruction limit reached!
% 1.43/0.52 % (903910)------------------------------
% 1.43/0.52 % (903910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.52 % (903910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.52 % (903910)CaDiCaL version: 2.1.3
% 1.43/0.52 % (903910)Termination reason: Instruction limit
% 1.43/0.52 % (903910)Termination phase: Function definition elimination
% 1.43/0.52 % (903910)Time elapsed: 0.017 s
% 1.43/0.52 % (903910)Peak memory usage: 11 MB
% 1.43/0.52 % (903910)Instructions burned: 39 (million)
% 1.43/0.52 % (903912)Instruction limit reached!
% 1.43/0.52 % (903912)------------------------------
% 1.43/0.52 % (903912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.52 % (903912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.52 % (903912)CaDiCaL version: 2.1.3
% 1.43/0.52 % (903912)Termination reason: Instruction limit
% 1.43/0.52 % (903912)Termination phase: Property scanning
% 1.43/0.52 % (903912)Time elapsed: 0.011 s
% 1.43/0.52 % (903912)Peak memory usage: 10 MB
% 1.43/0.52 % (903912)Instructions burned: 27 (million)
% 1.43/0.52 % (903924)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3390371613:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.43/0.52 % (903924)Instruction limit reached!
% 1.43/0.52 % (903924)------------------------------
% 1.43/0.52 % (903924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.52 % (903924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.52 % (903924)CaDiCaL version: 2.1.3
% 1.43/0.52 % (903924)Termination reason: Instruction limit
% 1.43/0.52 % (903924)Termination phase: Property scanning
% 1.43/0.52 % (903924)Time elapsed: 0.006 s
% 1.43/0.52 % (903924)Peak memory usage: 10 MB
% 1.43/0.52 % (903924)Instructions burned: 28 (million)
% 1.43/0.52 % (903925)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3726974430:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.43/0.52 % (903927)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.43/0.52 % (903927)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.43/0.52 % (903926)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3577110106:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.43/0.52 % (903929)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.02/0.57 % (903927)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=188980244:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.02/0.57 % (903929)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=339357598:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.02/0.57 % (903929)Instruction limit reached!
% 2.02/0.57 % (903929)------------------------------
% 2.02/0.57 % (903929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.57 % (903929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.57 % (903929)CaDiCaL version: 2.1.3
% 2.02/0.57 % (903929)Termination reason: Instruction limit
% 2.02/0.57 % (903929)Termination phase: shuffling
% 2.02/0.57 % (903929)Time elapsed: 0.002 s
% 2.02/0.57 % (903929)Peak memory usage: 10 MB
% 2.02/0.57 % (903929)Instructions burned: 11 (million)
% 2.02/0.57 % (903925)Instruction limit reached!
% 2.02/0.57 % (903925)------------------------------
% 2.02/0.57 % (903925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.57 % (903925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.57 % (903925)CaDiCaL version: 2.1.3
% 2.02/0.57 % (903925)Termination reason: Instruction limit
% 2.02/0.57 % (903925)Termination phase: Property scanning
% 2.02/0.57 % (903925)Time elapsed: 0.010 s
% 2.02/0.57 % (903925)Peak memory usage: 10 MB
% 2.02/0.57 % (903925)Instructions burned: 24 (million)
% 2.02/0.57 % (903927)Instruction limit reached!
% 2.02/0.57 % (903927)------------------------------
% 2.02/0.57 % (903927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.57 % (903927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.57 % (903927)CaDiCaL version: 2.1.3
% 2.02/0.57 % (903927)Termination reason: Instruction limit
% 2.02/0.57 % (903927)Termination phase: shuffling
% 2.02/0.57 % (903927)Time elapsed: 0.006 s
% 2.02/0.57 % (903927)Peak memory usage: 10 MB
% 2.02/0.57 % (903927)Instructions burned: 15 (million)
% 2.02/0.57 % (903934)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=157883995:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.02/0.57 % (903934)Instruction limit reached!
% 2.02/0.57 % (903934)------------------------------
% 2.02/0.57 % (903934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.57 % (903934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.57 % (903934)CaDiCaL version: 2.1.3
% 2.02/0.57 % (903934)Termination reason: Instruction limit
% 2.02/0.57 % (903934)Termination phase: Property scanning
% 2.02/0.57 % (903934)Time elapsed: 0.007 s
% 2.02/0.57 % (903934)Peak memory usage: 10 MB
% 2.02/0.57 % (903934)Instructions burned: 31 (million)
% 2.02/0.57 % (903935)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2434783014:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.02/0.57 % (903926)Instruction limit reached!
% 2.02/0.57 % (903926)------------------------------
% 2.02/0.57 % (903926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.57 % (903926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.57 % (903926)CaDiCaL version: 2.1.3
% 2.02/0.57 % (903926)Termination reason: Instruction limit
% 2.02/0.57 % (903926)Termination phase: Saturation
% 2.02/0.57 % (903926)Time elapsed: 0.026 s
% 2.02/0.57 % (903926)Peak memory usage: 12 MB
% 2.02/0.57 % (903926)Instructions burned: 61 (million)
% 2.02/0.57 % (903936)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3011030503:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.02/0.57 % (903936)Instruction limit reached!
% 2.02/0.57 % (903936)------------------------------
% 2.02/0.57 % (903936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.57 % (903936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.57 % (903935)Instruction limit reached!
% 2.02/0.57 % (903935)------------------------------
% 2.02/0.57 % (903935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.57 % (903936)CaDiCaL version: 2.1.3
% 2.31/0.65 % (903936)Termination reason: Instruction limit
% 2.31/0.65 % (903936)Termination phase: Property scanning
% 2.31/0.65 % (903935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.65 % (903936)Time elapsed: 0.006 s
% 2.31/0.65 % (903936)Peak memory usage: 10 MB
% 2.31/0.65 % (903935)CaDiCaL version: 2.1.3
% 2.31/0.65 % (903936)Instructions burned: 27 (million)
% 2.31/0.65 % (903935)Termination reason: Instruction limit
% 2.31/0.65 % (903935)Termination phase: shuffling
% 2.31/0.65 % (903935)Time elapsed: 0.008 s
% 2.31/0.65 % (903935)Peak memory usage: 10 MB
% 2.31/0.65 % (903935)Instructions burned: 7 (million)
% 2.31/0.65 % (903938)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2431696078:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.31/0.65 % (903940)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=580180447:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.31/0.65 % (903942)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2169275570:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.31/0.65 % (903938)Instruction limit reached!
% 2.31/0.65 % (903938)------------------------------
% 2.31/0.65 % (903938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.65 % (903938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.65 % (903938)CaDiCaL version: 2.1.3
% 2.31/0.65 % (903938)Termination reason: Instruction limit
% 2.31/0.65 % (903938)Termination phase: Property scanning
% 2.31/0.65 % (903938)Time elapsed: 0.010 s
% 2.31/0.65 % (903938)Peak memory usage: 10 MB
% 2.31/0.65 % (903938)Instructions burned: 24 (million)
% 2.31/0.65 % (903911)Instruction limit reached!
% 2.31/0.65 % (903911)------------------------------
% 2.31/0.65 % (903911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.65 % (903911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.65 % (903911)CaDiCaL version: 2.1.3
% 2.31/0.65 % (903911)Termination reason: Instruction limit
% 2.31/0.65 % (903911)Termination phase: Saturation
% 2.31/0.65 % (903911)Time elapsed: 0.097 s
% 2.31/0.65 % (903911)Peak memory usage: 12 MB
% 2.31/0.65 % (903911)Instructions burned: 252 (million)
% 2.31/0.65 % (903943)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2353906886:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.31/0.65 % (903947)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1595216952:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.31/0.65 % (903948)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.31/0.65 % (903948)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4147048057:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.31/0.65 % (903942)Instruction limit reached!
% 2.31/0.65 % (903942)------------------------------
% 2.31/0.65 % (903942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.65 % (903942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.65 % (903942)CaDiCaL version: 2.1.3
% 2.31/0.65 % (903942)Termination reason: Instruction limit
% 2.31/0.65 % (903942)Termination phase: Twee Goal Transformation
% 2.31/0.65 % (903942)Time elapsed: 0.031 s
% 2.31/0.65 % (903942)Peak memory usage: 11 MB
% 2.31/0.65 % (903942)Instructions burned: 148 (million)
% 2.31/0.65 % (903948)Instruction limit reached!
% 2.31/0.65 % (903948)------------------------------
% 2.31/0.65 % (903948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.65 % (903948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.65 % (903948)CaDiCaL version: 2.1.3
% 2.31/0.65 % (903948)Termination reason: Instruction limit
% 2.31/0.65 % (903948)Termination phase: shuffling
% 2.31/0.65 % (903948)Time elapsed: 0.004 s
% 2.31/0.65 % (903948)Peak memory usage: 10 MB
% 2.31/0.65 % (903948)Instructions burned: 9 (million)
% 2.31/0.65 % (903952)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=883004284:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.31/0.65 % (903947)Instruction limit reached!
% 2.31/0.65 % (903947)------------------------------
% 2.31/0.65 % (903947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.73 % (903947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.73 % (903947)CaDiCaL version: 2.1.3
% 2.47/0.73 % (903947)Termination reason: Instruction limit
% 2.47/0.73 % (903947)Termination phase: Property scanning
% 2.47/0.73 % (903947)Time elapsed: 0.018 s
% 2.47/0.73 % (903947)Peak memory usage: 11 MB
% 2.47/0.73 % (903947)Instructions burned: 42 (million)
% 2.47/0.73 % (903914)Instruction limit reached!
% 2.47/0.73 % (903914)------------------------------
% 2.47/0.73 % (903914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.73 % (903914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.73 % (903914)CaDiCaL version: 2.1.3
% 2.47/0.73 % (903914)Termination reason: Instruction limit
% 2.47/0.73 % (903914)Termination phase: Saturation
% 2.47/0.73 % (903914)Time elapsed: 0.129 s
% 2.47/0.73 % (903914)Peak memory usage: 12 MB
% 2.47/0.73 % (903914)Instructions burned: 329 (million)
% 2.47/0.73 % (903953)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3116520152:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.47/0.73 % (903955)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.47/0.73 % (903955)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2305125370:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.47/0.73 % (903956)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3465243570:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.47/0.73 % (903955)Instruction limit reached!
% 2.47/0.73 % (903955)------------------------------
% 2.47/0.73 % (903955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.73 % (903955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.73 % (903955)CaDiCaL version: 2.1.3
% 2.47/0.73 % (903955)Termination reason: Instruction limit
% 2.47/0.73 % (903955)Termination phase: shuffling
% 2.47/0.73 % (903955)Time elapsed: 0.003 s
% 2.47/0.73 % (903955)Peak memory usage: 10 MB
% 2.47/0.73 % (903955)Instructions burned: 7 (million)
% 2.47/0.73 % (903956)Instruction limit reached!
% 2.47/0.73 % (903956)------------------------------
% 2.47/0.73 % (903956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.73 % (903956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.73 % (903956)CaDiCaL version: 2.1.3
% 2.47/0.73 % (903956)Termination reason: Instruction limit
% 2.47/0.73 % (903956)Termination phase: Property scanning
% 2.47/0.73 % (903956)Time elapsed: 0.010 s
% 2.47/0.73 % (903956)Peak memory usage: 10 MB
% 2.47/0.73 % (903956)Instructions burned: 22 (million)
% 2.47/0.73 % (903952)Instruction limit reached!
% 2.47/0.73 % (903952)------------------------------
% 2.47/0.73 % (903952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.73 % (903952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.73 % (903952)CaDiCaL version: 2.1.3
% 2.47/0.73 % (903952)Termination reason: Instruction limit
% 2.47/0.73 % (903952)Termination phase: Saturation
% 2.47/0.73 % (903952)Time elapsed: 0.038 s
% 2.47/0.73 % (903952)Peak memory usage: 12 MB
% 2.47/0.73 % (903952)Instructions burned: 185 (million)
% 2.47/0.73 % (903960)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2365835357:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.47/0.73 % (903962)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1634663559:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.47/0.73 % (903883)Instruction limit reached!
% 2.47/0.73 % (903883)------------------------------
% 2.47/0.73 % (903883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.73 % (903883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.73 % (903883)CaDiCaL version: 2.1.3
% 2.47/0.73 % (903883)Termination reason: Instruction limit
% 2.47/0.73 % (903883)Termination phase: Saturation
% 2.47/0.79 % (903883)Time elapsed: 0.257 s
% 2.47/0.79 % (903883)Peak memory usage: 16 MB
% 2.47/0.79 % (903883)Instructions burned: 635 (million)
% 2.47/0.79 % (903960)Instruction limit reached!
% 2.47/0.79 % (903960)------------------------------
% 2.47/0.79 % (903960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.79 % (903960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.79 % (903960)CaDiCaL version: 2.1.3
% 2.47/0.79 % (903960)Termination reason: Instruction limit
% 2.47/0.79 % (903960)Termination phase: Property scanning
% 2.47/0.79 % (903960)Time elapsed: 0.009 s
% 2.47/0.79 % (903960)Peak memory usage: 10 MB
% 2.47/0.79 % (903960)Instructions burned: 21 (million)
% 2.47/0.79 % (903961)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3999459880:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.47/0.79 % (903965)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1005668632:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.47/0.79 % (903967)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2943290027:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.47/0.79 % (903953)Instruction limit reached!
% 2.47/0.79 % (903953)------------------------------
% 2.47/0.79 % (903953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.79 % (903953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.79 % (903953)CaDiCaL version: 2.1.3
% 2.47/0.79 % (903953)Termination reason: Instruction limit
% 2.47/0.79 % (903953)Termination phase: Property scanning
% 2.47/0.79 % (903953)Time elapsed: 0.067 s
% 2.47/0.79 % (903953)Peak memory usage: 11 MB
% 2.47/0.79 % (903953)Instructions burned: 170 (million)
% 2.47/0.79 % (903965)Instruction limit reached!
% 2.47/0.79 % (903965)------------------------------
% 2.47/0.79 % (903965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.79 % (903965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.79 % (903965)CaDiCaL version: 2.1.3
% 2.47/0.79 % (903965)Termination reason: Instruction limit
% 2.47/0.79 % (903965)Termination phase: Property scanning
% 2.47/0.79 % (903965)Time elapsed: 0.020 s
% 2.47/0.79 % (903965)Peak memory usage: 11 MB
% 2.47/0.79 % (903965)Instructions burned: 47 (million)
% 2.47/0.79 % (903970)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2555702354:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.47/0.79 % (903971)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.47/0.79 % (903943)Instruction limit reached!
% 2.47/0.79 % (903943)------------------------------
% 2.47/0.79 % (903943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.79 % (903943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.79 % (903943)CaDiCaL version: 2.1.3
% 2.47/0.79 % (903943)Termination reason: Instruction limit
% 2.47/0.79 % (903943)Termination phase: Saturation
% 2.47/0.79 % (903943)Time elapsed: 0.136 s
% 2.47/0.79 % (903943)Peak memory usage: 12 MB
% 2.47/0.79 % (903943)Instructions burned: 193 (million)
% 2.47/0.79 % (903970)Instruction limit reached!
% 2.47/0.79 % (903970)------------------------------
% 2.47/0.79 % (903970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.79 % (903970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.79 % (903970)CaDiCaL version: 2.1.3
% 2.47/0.79 % (903970)Termination reason: Instruction limit
% 2.47/0.79 % (903970)Termination phase: Property scanning
% 2.47/0.79 % (903970)Time elapsed: 0.009 s
% 2.47/0.79 % (903970)Peak memory usage: 10 MB
% 2.47/0.79 % (903970)Instructions burned: 21 (million)
% 2.47/0.79 % (903971)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2666055174:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.47/0.79 % (903973)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3550655210:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.47/0.79 % (903975)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=287859832:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.93/0.93 % (903973)Instruction limit reached!
% 3.93/0.93 % (903973)------------------------------
% 3.93/0.93 % (903973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.93 % (903973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.93 % (903973)CaDiCaL version: 2.1.3
% 3.93/0.93 % (903973)Termination reason: Instruction limit
% 3.93/0.93 % (903973)Termination phase: shuffling
% 3.93/0.93 % (903973)Time elapsed: 0.006 s
% 3.93/0.93 % (903973)Peak memory usage: 10 MB
% 3.93/0.93 % (903973)Instructions burned: 13 (million)
% 3.93/0.93 % (903978)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=762047035:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.93/0.93 % (903975)Instruction limit reached!
% 3.93/0.93 % (903975)------------------------------
% 3.93/0.93 % (903975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.93 % (903975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.93 % (903975)CaDiCaL version: 2.1.3
% 3.93/0.93 % (903975)Termination reason: Instruction limit
% 3.93/0.93 % (903975)Termination phase: Function definition elimination
% 3.93/0.93 % (903975)Time elapsed: 0.028 s
% 3.93/0.93 % (903975)Peak memory usage: 11 MB
% 3.93/0.93 % (903975)Instructions burned: 67 (million)
% 3.93/0.93 % (903961)Instruction limit reached!
% 3.93/0.93 % (903961)------------------------------
% 3.93/0.93 % (903961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.93 % (903961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.93 % (903961)CaDiCaL version: 2.1.3
% 3.93/0.93 % (903961)Termination reason: Instruction limit
% 3.93/0.93 % (903961)Termination phase: Saturation
% 3.93/0.93 % (903961)Time elapsed: 0.121 s
% 3.93/0.93 % (903961)Peak memory usage: 11 MB
% 3.93/0.93 % (903961)Instructions burned: 317 (million)
% 3.93/0.93 % (903978)Instruction limit reached!
% 3.93/0.93 % (903978)------------------------------
% 3.93/0.93 % (903978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.93 % (903978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.93 % (903978)CaDiCaL version: 2.1.3
% 3.93/0.93 % (903978)Termination reason: Instruction limit
% 3.93/0.93 % (903978)Termination phase: Function definition elimination
% 3.93/0.93 % (903978)Time elapsed: 0.022 s
% 3.93/0.93 % (903978)Peak memory usage: 11 MB
% 3.93/0.93 % (903978)Instructions burned: 53 (million)
% 3.93/0.93 % (903980)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2606655844:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.93/0.93 % (903971)Instruction limit reached!
% 3.93/0.93 % (903971)------------------------------
% 3.93/0.93 % (903971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.93 % (903971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.93 % (903971)CaDiCaL version: 2.1.3
% 3.93/0.93 % (903971)Termination reason: Instruction limit
% 3.93/0.93 % (903971)Termination phase: Property scanning
% 3.93/0.93 % (903971)Time elapsed: 0.078 s
% 3.93/0.93 % (903971)Peak memory usage: 11 MB
% 3.93/0.93 % (903971)Instructions burned: 201 (million)
% 3.93/0.93 % (903980)Instruction limit reached!
% 3.93/0.93 % (903980)------------------------------
% 3.93/0.93 % (903980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.93 % (903980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.93 % (903980)CaDiCaL version: 2.1.3
% 3.93/0.93 % (903980)Termination reason: Instruction limit
% 3.93/0.93 % (903980)Termination phase: Property scanning
% 3.93/0.93 % (903980)Time elapsed: 0.014 s
% 3.93/0.93 % (903980)Peak memory usage: 10 MB
% 3.93/0.93 % (903980)Instructions burned: 32 (million)
% 3.93/0.93 % (903981)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=190834171:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.93/0.93 % (903983)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2431950460:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.93/0.93 % (903985)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.35/1.04 % (903984)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=210535461:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.35/1.04 % (903985)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3762444758:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.35/1.04 % (903983)Instruction limit reached!
% 5.35/1.04 % (903983)------------------------------
% 5.35/1.04 % (903983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.04 % (903983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.04 % (903983)CaDiCaL version: 2.1.3
% 5.35/1.04 % (903983)Termination reason: Instruction limit
% 5.35/1.04 % (903983)Termination phase: Property scanning
% 5.35/1.04 % (903983)Time elapsed: 0.015 s
% 5.35/1.04 % (903983)Peak memory usage: 10 MB
% 5.35/1.04 % (903983)Instructions burned: 36 (million)
% 5.35/1.04 % (903990)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=4166116147:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 5.35/1.04 % (903962)Instruction limit reached!
% 5.35/1.04 % (903962)------------------------------
% 5.35/1.04 % (903962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.04 % (903962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.04 % (903962)CaDiCaL version: 2.1.3
% 5.35/1.04 % (903962)Termination reason: Instruction limit
% 5.35/1.04 % (903962)Termination phase: Saturation
% 5.35/1.04 % (903962)Time elapsed: 0.179 s
% 5.35/1.04 % (903962)Peak memory usage: 15 MB
% 5.35/1.04 % (903962)Instructions burned: 857 (million)
% 5.35/1.04 % (903984)Instruction limit reached!
% 5.35/1.04 % (903984)------------------------------
% 5.35/1.04 % (903984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.04 % (903984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.04 % (903984)CaDiCaL version: 2.1.3
% 5.35/1.04 % (903984)Termination reason: Instruction limit
% 5.35/1.04 % (903984)Termination phase: Function definition elimination
% 5.35/1.04 % (903984)Time elapsed: 0.028 s
% 5.35/1.04 % (903984)Peak memory usage: 11 MB
% 5.35/1.04 % (903984)Instructions burned: 68 (million)
% 5.35/1.04 % (903992)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2822651241:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 5.35/1.04 % (903981)Instruction limit reached!
% 5.35/1.04 % (903981)------------------------------
% 5.35/1.04 % (903981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.04 % (903981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.04 % (903981)CaDiCaL version: 2.1.3
% 5.35/1.04 % (903981)Termination reason: Instruction limit
% 5.35/1.04 % (903981)Termination phase: Saturation
% 5.35/1.04 % (903981)Time elapsed: 0.057 s
% 5.35/1.04 % (903981)Peak memory usage: 12 MB
% 5.35/1.04 % (903981)Instructions burned: 138 (million)
% 5.35/1.04 % (903993)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2849172994:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 5.35/1.04 % (903992)Instruction limit reached!
% 5.35/1.04 % (903992)------------------------------
% 5.35/1.04 % (903992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.05 % (903992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.05 % (903992)CaDiCaL version: 2.1.3
% 5.35/1.05 % (903992)Termination reason: Instruction limit
% 5.35/1.05 % (903992)Termination phase: Function definition elimination
% 5.35/1.05 % (903992)Time elapsed: 0.021 s
% 5.35/1.05 % (903992)Peak memory usage: 11 MB
% 5.35/1.05 % (903992)Instructions burned: 99 (million)
% 5.35/1.05 % (903967)Instruction limit reached!
% 5.35/1.05 % (903967)------------------------------
% 5.35/1.05 % (903967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.05 % (903967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.05 % (903967)CaDiCaL version: 2.1.3
% 5.35/1.05 % (903967)Termination reason: Instruction limit
% 5.35/1.05 % (903967)Termination phase: Saturation
% 5.35/1.05 % (903967)Time elapsed: 0.193 s
% 5.35/1.05 % (903967)Peak memory usage: 14 MB
% 5.35/1.05 % (903967)Instructions burned: 481 (million)
% 5.35/1.05 % (903995)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=166321286:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.35/1.13 % (903997)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=951240925:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.35/1.13 % (903985)Instruction limit reached!
% 5.35/1.13 % (903985)------------------------------
% 5.35/1.13 % (903985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.13 % (903985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.13 % (903985)CaDiCaL version: 2.1.3
% 5.35/1.13 % (903985)Termination reason: Instruction limit
% 5.35/1.13 % (903985)Termination phase: Property scanning
% 5.35/1.13 % (903985)Time elapsed: 0.070 s
% 5.35/1.13 % (903985)Peak memory usage: 10 MB
% 5.35/1.13 % (903985)Instructions burned: 180 (million)
% 5.35/1.13 % (903998)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1449531265:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.35/1.13 % (904001)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1028908899:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.35/1.13 % (904001)Instruction limit reached!
% 5.35/1.13 % (904001)------------------------------
% 5.35/1.13 % (904001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.13 % (904001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.13 % (904001)CaDiCaL version: 2.1.3
% 5.35/1.13 % (904001)Termination reason: Instruction limit
% 5.35/1.13 % (904001)Termination phase: Function definition elimination
% 5.35/1.13 % (904001)Time elapsed: 0.019 s
% 5.35/1.13 % (904001)Peak memory usage: 10 MB
% 5.35/1.13 % (904001)Instructions burned: 45 (million)
% 5.35/1.13 % (903990)Instruction limit reached!
% 5.35/1.13 % (903990)------------------------------
% 5.35/1.13 % (903990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.13 % (903990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.13 % (903990)CaDiCaL version: 2.1.3
% 5.35/1.13 % (903990)Termination reason: Instruction limit
% 5.35/1.13 % (903990)Termination phase: Saturation
% 5.35/1.13 % (903990)Time elapsed: 0.097 s
% 5.35/1.13 % (903990)Peak memory usage: 12 MB
% 5.35/1.13 % (903990)Instructions burned: 246 (million)
% 5.35/1.13 % (904004)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4029545260:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 5.35/1.13 % (904005)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=2314177571:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 5.35/1.13 % (903998)Instruction limit reached!
% 5.35/1.13 % (903998)------------------------------
% 5.35/1.13 % (903998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.13 % (903998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.13 % (903998)CaDiCaL version: 2.1.3
% 5.35/1.13 % (903998)Termination reason: Instruction limit
% 5.35/1.13 % (903998)Termination phase: Saturation
% 5.35/1.13 % (903998)Time elapsed: 0.060 s
% 5.35/1.13 % (903998)Peak memory usage: 14 MB
% 5.35/1.13 % (903998)Instructions burned: 131 (million)
% 5.35/1.13 % (904008)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1310046671:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 5.35/1.13 % (903997)Instruction limit reached!
% 5.35/1.13 % (903997)------------------------------
% 5.35/1.13 % (903997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.13 % (903997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.13 % (903997)CaDiCaL version: 2.1.3
% 5.35/1.13 % (903997)Termination reason: Instruction limit
% 5.35/1.13 % (903997)Termination phase: Saturation
% 5.35/1.13 % (903997)Time elapsed: 0.108 s
% 5.35/1.13 % (903997)Peak memory usage: 13 MB
% 5.35/1.13 % (903997)Instructions burned: 518 (million)
% 5.35/1.13 % (904010)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=1172079706:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 5.35/1.13 % (904008)Instruction limit reached!
% 5.35/1.13 % (904008)------------------------------
% 5.35/1.13 % (904008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.13 % (904008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.25 % (904008)CaDiCaL version: 2.1.3
% 6.26/1.25 % (904008)Termination reason: Instruction limit
% 6.26/1.25 % (904008)Termination phase: Function definition elimination
% 6.26/1.25 % (904008)Time elapsed: 0.040 s
% 6.26/1.25 % (904008)Peak memory usage: 11 MB
% 6.26/1.25 % (904008)Instructions burned: 97 (million)
% 6.26/1.25 % (904010)Instruction limit reached!
% 6.26/1.25 % (904010)------------------------------
% 6.26/1.25 % (904010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.25 % (904010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.25 % (904010)CaDiCaL version: 2.1.3
% 6.26/1.25 % (904010)Termination reason: Instruction limit
% 6.26/1.25 % (904010)Termination phase: Function definition elimination
% 6.26/1.25 % (904010)Time elapsed: 0.015 s
% 6.26/1.25 % (904010)Peak memory usage: 11 MB
% 6.26/1.25 % (904010)Instructions burned: 70 (million)
% 6.26/1.25 % (903993)Instruction limit reached!
% 6.26/1.25 % (903993)------------------------------
% 6.26/1.25 % (903993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.25 % (903993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.25 % (903993)CaDiCaL version: 2.1.3
% 6.26/1.25 % (903993)Termination reason: Instruction limit
% 6.26/1.25 % (903993)Termination phase: Saturation
% 6.26/1.25 % (903993)Time elapsed: 0.161 s
% 6.26/1.25 % (903993)Peak memory usage: 13 MB
% 6.26/1.25 % (903993)Instructions burned: 430 (million)
% 6.26/1.25 % (904013)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=2535418737:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 6.26/1.25 % (904012)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=3401574642:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 6.26/1.25 % (904015)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2282348106:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/375Mi)
% 6.26/1.25 % (903940)Instruction limit reached!
% 6.26/1.25 % (903940)------------------------------
% 6.26/1.25 % (903940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.25 % (903940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.25 % (903940)CaDiCaL version: 2.1.3
% 6.26/1.25 % (903940)Termination reason: Instruction limit
% 6.26/1.25 % (903940)Termination phase: Saturation
% 6.26/1.25 % (903940)Time elapsed: 0.489 s
% 6.26/1.25 % (903940)Peak memory usage: 13 MB
% 6.26/1.25 % (903940)Instructions burned: 1241 (million)
% 6.26/1.25 % (904018)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2503782700:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2993 on theBenchmark for (2993ds/495Mi)
% 6.26/1.25 % (904012)Instruction limit reached!
% 6.26/1.25 % (904012)------------------------------
% 6.26/1.25 % (904012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.25 % (904012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.25 % (904012)CaDiCaL version: 2.1.3
% 6.26/1.25 % (904012)Termination reason: Instruction limit
% 6.26/1.25 % (904012)Termination phase: Function definition elimination
% 6.26/1.25 % (904012)Time elapsed: 0.042 s
% 6.26/1.25 % (904012)Peak memory usage: 11 MB
% 6.26/1.25 % (904012)Instructions burned: 106 (million)
% 6.26/1.25 % (904020)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1330078265:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 6.26/1.25 % (904005)Instruction limit reached!
% 6.26/1.25 % (904005)------------------------------
% 6.26/1.25 % (904005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.25 % (904005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.25 % (904005)CaDiCaL version: 2.1.3
% 6.26/1.25 % (904005)Termination reason: Instruction limit
% 6.26/1.25 % (904005)Termination phase: Saturation
% 6.26/1.25 % (904005)Time elapsed: 0.178 s
% 6.26/1.25 % (904005)Peak memory usage: 13 MB
% 6.26/1.25 % (904005)Instructions burned: 451 (million)
% 6.85/1.37 % (904020)Instruction limit reached!
% 6.85/1.37 % (904020)------------------------------
% 6.85/1.37 % (904020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.85/1.37 % (904020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.37 % (904020)CaDiCaL version: 2.1.3
% 6.85/1.37 % (904020)Termination reason: Instruction limit
% 6.85/1.37 % (904020)Termination phase: Property scanning
% 6.85/1.37 % (904020)Time elapsed: 0.028 s
% 6.85/1.37 % (904020)Peak memory usage: 10 MB
% 6.85/1.37 % (904020)Instructions burned: 35 (million)
% 6.85/1.37 % (904022)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2517835717:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 6.85/1.37 % (904023)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=1248989052:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2992 on theBenchmark for (2992ds/66Mi)
% 6.85/1.37 % (904023)Instruction limit reached!
% 6.85/1.37 % (904023)------------------------------
% 6.85/1.37 % (904023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.85/1.37 % (904023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.37 % (904023)CaDiCaL version: 2.1.3
% 6.85/1.37 % (904023)Termination reason: Instruction limit
% 6.85/1.37 % (904023)Termination phase: Saturation
% 6.85/1.37 % (904023)Time elapsed: 0.029 s
% 6.85/1.37 % (904023)Peak memory usage: 13 MB
% 6.85/1.37 % (904023)Instructions burned: 67 (million)
% 6.85/1.37 % (904015)Instruction limit reached!
% 6.85/1.37 % (904015)------------------------------
% 6.85/1.37 % (904015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.85/1.37 % (904015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.37 % (904015)CaDiCaL version: 2.1.3
% 6.85/1.37 % (904015)Termination reason: Instruction limit
% 6.85/1.37 % (904015)Termination phase: Saturation
% 6.85/1.37 % (904015)Time elapsed: 0.139 s
% 6.85/1.37 % (904015)Peak memory usage: 12 MB
% 6.85/1.37 % (904015)Instructions burned: 375 (million)
% 6.85/1.37 % (904022)Instruction limit reached!
% 6.85/1.37 % (904022)------------------------------
% 6.85/1.37 % (904022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.85/1.37 % (904022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.37 % (904022)CaDiCaL version: 2.1.3
% 6.85/1.37 % (904022)Termination reason: Instruction limit
% 6.85/1.37 % (904022)Termination phase: Function definition elimination
% 6.85/1.37 % (904022)Time elapsed: 0.038 s
% 6.85/1.37 % (904022)Peak memory usage: 11 MB
% 6.85/1.37 % (904022)Instructions burned: 93 (million)
% 6.85/1.37 % (904026)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1836156931:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2991 on theBenchmark for (2991ds/22Mi)
% 6.85/1.37 % (904027)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=171065936:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 6.85/1.37 % (904028)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3803702893:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 6.85/1.37 % (904004)Instruction limit reached!
% 6.85/1.37 % (904004)------------------------------
% 6.85/1.37 % (904004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.85/1.37 % (904004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.37 % (904004)CaDiCaL version: 2.1.3
% 6.85/1.37 % (904004)Termination reason: Instruction limit
% 6.85/1.37 % (904004)Termination phase: Saturation
% 6.85/1.37 % (904004)Time elapsed: 0.262 s
% 6.85/1.37 % (904004)Peak memory usage: 17 MB
% 6.85/1.37 % (904004)Instructions burned: 571 (million)
% 6.85/1.37 % (904026)Instruction limit reached!
% 6.85/1.37 % (904026)------------------------------
% 6.85/1.37 % (904026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.85/1.37 % (904026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.37 % (904026)CaDiCaL version: 2.1.3
% 6.85/1.37 % (904026)Termination reason: Instruction limit
% 6.85/1.37 % (904026)Termination phase: Property scanning
% 6.85/1.37 % (904026)Time elapsed: 0.010 s
% 6.85/1.37 % (904026)Peak memory usage: 10 MB
% 6.85/1.37 % (904026)Instructions burned: 23 (million)
% 6.85/1.37 % (904028)Instruction limit reached!
% 6.85/1.37 % (904028)------------------------------
% 7.28/1.50 % (904028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.28/1.50 % (904028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.50 % (904028)CaDiCaL version: 2.1.3
% 7.28/1.50 % (904028)Termination reason: Instruction limit
% 7.28/1.50 % (904028)Termination phase: Property scanning
% 7.28/1.50 % (904028)Time elapsed: 0.013 s
% 7.28/1.50 % (904028)Peak memory usage: 10 MB
% 7.28/1.50 % (904028)Instructions burned: 28 (million)
% 7.28/1.50 % (904032)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 7.28/1.50 % (903995)Instruction limit reached!
% 7.28/1.50 % (903995)------------------------------
% 7.28/1.50 % (903995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.28/1.50 % (903995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.50 % (903995)CaDiCaL version: 2.1.3
% 7.28/1.50 % (903995)Termination reason: Instruction limit
% 7.28/1.50 % (903995)Termination phase: Saturation
% 7.28/1.50 % (903995)Time elapsed: 0.348 s
% 7.28/1.50 % (903995)Peak memory usage: 13 MB
% 7.28/1.50 % (903995)Instructions burned: 876 (million)
% 7.28/1.50 % (904033)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=1863058083:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/340Mi)
% 7.28/1.50 % (904032)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=1662822295:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/137Mi)
% 7.28/1.50 % (904034)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=2017088855:i=227:sd=1:bd=all:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/227Mi)
% 7.28/1.50 % (904035)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 7.28/1.50 % (904035)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=716449638:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/373Mi)
% 7.28/1.50 % (904018)Instruction limit reached!
% 7.28/1.50 % (904018)------------------------------
% 7.28/1.50 % (904018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.28/1.50 % (904018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.50 % (904018)CaDiCaL version: 2.1.3
% 7.28/1.50 % (904018)Termination reason: Instruction limit
% 7.28/1.50 % (904018)Termination phase: Saturation
% 7.28/1.50 % (904018)Time elapsed: 0.196 s
% 7.28/1.50 % (904018)Peak memory usage: 12 MB
% 7.28/1.50 % (904018)Instructions burned: 495 (million)
% 7.28/1.50 % (904032)Instruction limit reached!
% 7.28/1.50 % (904032)------------------------------
% 7.28/1.50 % (904032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.28/1.50 % (904032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.50 % (904032)CaDiCaL version: 2.1.3
% 7.28/1.50 % (904032)Termination reason: Instruction limit
% 7.28/1.50 % (904032)Termination phase: Property scanning
% 7.28/1.50 % (904032)Time elapsed: 0.053 s
% 7.28/1.50 % (904032)Peak memory usage: 11 MB
% 7.28/1.50 % (904032)Instructions burned: 137 (million)
% 7.28/1.50 % (904040)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=497706922:i=116:ep=RSTC:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/116Mi)
% 7.28/1.50 % (904041)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3217887501:i=575:rtra=on_2990 on theBenchmark for (2990ds/575Mi)
% 7.28/1.50 % (904034)Instruction limit reached!
% 7.28/1.50 % (904034)------------------------------
% 7.28/1.50 % (904034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.28/1.50 % (904034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.50 % (904034)CaDiCaL version: 2.1.3
% 7.28/1.50 % (904034)Termination reason: Instruction limit
% 7.28/1.50 % (904034)Termination phase: Saturation
% 7.28/1.50 % (904034)Time elapsed: 0.090 s
% 7.28/1.50 % (904034)Peak memory usage: 13 MB
% 7.28/1.50 % (904034)Instructions burned: 229 (million)
% 7.28/1.50 % (904027)Instruction limit reached!
% 7.28/1.50 % (904027)------------------------------
% 7.28/1.50 % (904027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.79/1.77 % (904027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/1.77 % (904027)CaDiCaL version: 2.1.3
% 8.79/1.77 % (904027)Termination reason: Instruction limit
% 8.79/1.77 % (904027)Termination phase: Saturation
% 8.79/1.77 % (904027)Time elapsed: 0.131 s
% 8.79/1.77 % (904027)Peak memory usage: 12 MB
% 8.79/1.77 % (904027)Instructions burned: 340 (million)
% 8.79/1.77 % (904040)Instruction limit reached!
% 8.79/1.77 % (904040)------------------------------
% 8.79/1.77 % (904040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.79/1.77 % (904040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/1.77 % (904040)CaDiCaL version: 2.1.3
% 8.79/1.77 % (904040)Termination reason: Instruction limit
% 8.79/1.77 % (904040)Termination phase: Property scanning
% 8.79/1.77 % (904040)Time elapsed: 0.049 s
% 8.79/1.77 % (904040)Peak memory usage: 11 MB
% 8.79/1.77 % (904040)Instructions burned: 124 (million)
% 8.79/1.77 % (904044)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2839551459:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2990 on theBenchmark for (2990ds/270Mi)
% 8.79/1.77 % (904045)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1994034673:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2990 on theBenchmark for (2990ds/9840Mi)
% 8.79/1.77 % (904046)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=1251842413:i=421:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/421Mi)
% 8.79/1.77 % (904033)Instruction limit reached!
% 8.79/1.77 % (904033)------------------------------
% 8.79/1.77 % (904033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.79/1.77 % (904033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/1.77 % (904033)CaDiCaL version: 2.1.3
% 8.79/1.77 % (904033)Termination reason: Instruction limit
% 8.79/1.77 % (904033)Termination phase: Saturation
% 8.79/1.77 % (904033)Time elapsed: 0.130 s
% 8.79/1.77 % (904033)Peak memory usage: 12 MB
% 8.79/1.77 % (904033)Instructions burned: 340 (million)
% 8.79/1.77 % (904050)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.79/1.77 % (904050)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=261671038:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/270Mi)
% 8.79/1.77 % (904035)Instruction limit reached!
% 8.79/1.77 % (904035)------------------------------
% 8.79/1.77 % (904035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.79/1.77 % (904035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/1.77 % (904035)CaDiCaL version: 2.1.3
% 8.79/1.77 % (904035)Termination reason: Instruction limit
% 8.79/1.77 % (904035)Termination phase: Saturation
% 8.79/1.77 % (904035)Time elapsed: 0.145 s
% 8.79/1.77 % (904035)Peak memory usage: 12 MB
% 8.79/1.77 % (904035)Instructions burned: 375 (million)
% 8.79/1.77 % (904053)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2393945174:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/31Mi)
% 8.79/1.77 % (904053)Instruction limit reached!
% 8.79/1.77 % (904053)------------------------------
% 8.79/1.77 % (904053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.79/1.77 % (904053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/1.77 % (904053)CaDiCaL version: 2.1.3
% 8.79/1.77 % (904053)Termination reason: Instruction limit
% 8.79/1.77 % (904053)Termination phase: Property scanning
% 8.79/1.77 % (904053)Time elapsed: 0.015 s
% 8.79/1.77 % (904053)Peak memory usage: 10 MB
% 8.79/1.77 % (904053)Instructions burned: 32 (million)
% 8.79/1.77 % (904055)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 8.79/1.77 % (904055)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.79/1.77 % (904055)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2982079328:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2989 on theBenchmark for (2989ds/1440Mi)
% 9.43/1.98 % (904050)Instruction limit reached!
% 9.43/1.98 % (904050)------------------------------
% 9.43/1.98 % (904050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.43/1.98 % (904050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/1.98 % (904050)CaDiCaL version: 2.1.3
% 9.43/1.98 % (904050)Termination reason: Instruction limit
% 9.43/1.98 % (904050)Termination phase: Property scanning
% 9.43/1.98 % (904050)Time elapsed: 0.103 s
% 9.43/1.98 % (904050)Peak memory usage: 11 MB
% 9.43/1.98 % (904050)Instructions burned: 270 (million)
% 9.43/1.98 % (904044)Instruction limit reached!
% 9.43/1.98 % (904044)------------------------------
% 9.43/1.98 % (904044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.43/1.98 % (904044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/1.98 % (904044)CaDiCaL version: 2.1.3
% 9.43/1.98 % (904044)Termination reason: Instruction limit
% 9.43/1.98 % (904044)Termination phase: Property scanning
% 9.43/1.98 % (904044)Time elapsed: 0.132 s
% 9.43/1.98 % (904044)Peak memory usage: 10 MB
% 9.43/1.98 % (904044)Instructions burned: 272 (million)
% 9.43/1.98 % (904057)dis+10_2_sil=128000:si=on:random_seed=2189157278:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2988 on theBenchmark for (2988ds/339Mi)
% 9.43/1.98 % (904058)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=4006732020:i=111:add=on:fgj=on:rtra=on:fdi=1024_2988 on theBenchmark for (2988ds/111Mi)
% 9.43/1.98 % (904046)Instruction limit reached!
% 9.43/1.98 % (904046)------------------------------
% 9.43/1.98 % (904046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.43/1.98 % (904046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/1.98 % (904046)CaDiCaL version: 2.1.3
% 9.43/1.98 % (904046)Termination reason: Instruction limit
% 9.43/1.98 % (904046)Termination phase: Saturation
% 9.43/1.98 % (904046)Time elapsed: 0.159 s
% 9.43/1.98 % (904046)Peak memory usage: 13 MB
% 9.43/1.98 % (904046)Instructions burned: 423 (million)
% 9.43/1.98 % (904041)Instruction limit reached!
% 9.43/1.98 % (904041)------------------------------
% 9.43/1.98 % (904041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.43/1.98 % (904041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/1.98 % (904041)CaDiCaL version: 2.1.3
% 9.43/1.98 % (904041)Termination reason: Instruction limit
% 9.43/1.98 % (904041)Termination phase: Saturation
% 9.43/1.98 % (904041)Time elapsed: 0.227 s
% 9.43/1.98 % (904041)Peak memory usage: 13 MB
% 9.43/1.98 % (904041)Instructions burned: 575 (million)
% 9.43/1.98 % (904061)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3375393874:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/122Mi)
% 9.43/1.98 % (904058)Instruction limit reached!
% 9.43/1.98 % (904058)------------------------------
% 9.43/1.98 % (904058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.43/1.98 % (904058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/1.98 % (904058)CaDiCaL version: 2.1.3
% 9.43/1.98 % (904058)Termination reason: Instruction limit
% 9.43/1.98 % (904058)Termination phase: Property scanning
% 9.43/1.98 % (904058)Time elapsed: 0.045 s
% 9.43/1.98 % (904058)Peak memory usage: 11 MB
% 9.43/1.98 % (904058)Instructions burned: 112 (million)
% 9.43/1.98 % (904062)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=3630345927:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/136Mi)
% 9.43/1.98 % (904065)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1169711984:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/232Mi)
% 9.43/1.98 % (904061)Instruction limit reached!
% 9.43/1.98 % (904061)------------------------------
% 9.43/1.98 % (904061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.43/1.98 % (904061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/1.98 % (904061)CaDiCaL version: 2.1.3
% 12.57/2.13 % (904061)Termination reason: Instruction limit
% 12.57/2.13 % (904061)Termination phase: Property scanning
% 12.57/2.13 % (904061)Time elapsed: 0.049 s
% 12.57/2.13 % (904061)Peak memory usage: 11 MB
% 12.57/2.13 % (904061)Instructions burned: 123 (million)
% 12.57/2.13 % (904062)Instruction limit reached!
% 12.57/2.13 % (904062)------------------------------
% 12.57/2.13 % (904062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.13 % (904062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.13 % (904062)CaDiCaL version: 2.1.3
% 12.57/2.13 % (904062)Termination reason: Instruction limit
% 12.57/2.13 % (904062)Termination phase: Property scanning
% 12.57/2.13 % (904062)Time elapsed: 0.054 s
% 12.57/2.13 % (904062)Peak memory usage: 11 MB
% 12.57/2.13 % (904062)Instructions burned: 138 (million)
% 12.57/2.13 % (904067)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=493600937:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2987 on theBenchmark for (2987ds/1254Mi)
% 12.57/2.13 % (904069)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 12.57/2.13 % (904069)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=2973352580:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2987 on theBenchmark for (2987ds/281Mi)
% 12.57/2.13 % (904057)Instruction limit reached!
% 12.57/2.13 % (904057)------------------------------
% 12.57/2.13 % (904057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.13 % (904057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.13 % (904057)CaDiCaL version: 2.1.3
% 12.57/2.13 % (904057)Termination reason: Instruction limit
% 12.57/2.13 % (904057)Termination phase: Saturation
% 12.57/2.13 % (904057)Time elapsed: 0.130 s
% 12.57/2.13 % (904057)Peak memory usage: 12 MB
% 12.57/2.13 % (904057)Instructions burned: 341 (million)
% 12.57/2.13 % (904071)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=4273868263:i=619:add=on:rtra=on_2987 on theBenchmark for (2987ds/619Mi)
% 12.57/2.13 % (904065)Instruction limit reached!
% 12.57/2.13 % (904065)------------------------------
% 12.57/2.13 % (904065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.13 % (904065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.13 % (904065)CaDiCaL version: 2.1.3
% 12.57/2.13 % (904065)Termination reason: Instruction limit
% 12.57/2.13 % (904065)Termination phase: Saturation
% 12.57/2.13 % (904065)Time elapsed: 0.106 s
% 12.57/2.13 % (904065)Peak memory usage: 14 MB
% 12.57/2.13 % (904065)Instructions burned: 233 (million)
% 12.57/2.13 % (904073)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4112228387:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/865Mi)
% 12.57/2.13 % (904069)Instruction limit reached!
% 12.57/2.13 % (904069)------------------------------
% 12.57/2.13 % (904069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.13 % (904069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.13 % (904069)CaDiCaL version: 2.1.3
% 12.57/2.13 % (904069)Termination reason: Instruction limit
% 12.57/2.13 % (904069)Termination phase: Property scanning
% 12.57/2.13 % (904069)Time elapsed: 0.109 s
% 12.57/2.13 % (904069)Peak memory usage: 11 MB
% 12.57/2.13 % (904069)Instructions burned: 284 (million)
% 12.57/2.13 % (904075)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3713291165:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/212Mi)
% 12.57/2.13 % (904075)Instruction limit reached!
% 12.57/2.13 % (904075)------------------------------
% 12.57/2.13 % (904075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.13 % (904075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.13 % (904075)CaDiCaL version: 2.1.3
% 12.57/2.13 % (904075)Termination reason: Instruction limit
% 12.57/2.13 % (904075)Termination phase: Saturation
% 12.57/2.13 % (904075)Time elapsed: 0.086 s
% 12.57/2.13 % (904075)Peak memory usage: 12 MB
% 12.57/2.13 % (904075)Instructions burned: 214 (million)
% 12.57/2.13 % (904077)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=852296130:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/130Mi)
% 13.78/2.30 % (904071)Instruction limit reached!
% 13.78/2.30 % (904071)------------------------------
% 13.78/2.30 % (904071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.78/2.30 % (904071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.30 % (904071)CaDiCaL version: 2.1.3
% 13.78/2.30 % (904071)Termination reason: Instruction limit
% 13.78/2.30 % (904071)Termination phase: Saturation
% 13.78/2.30 % (904071)Time elapsed: 0.245 s
% 13.78/2.30 % (904071)Peak memory usage: 13 MB
% 13.78/2.30 % (904071)Instructions burned: 621 (million)
% 13.78/2.30 % (904077)Instruction limit reached!
% 13.78/2.30 % (904077)------------------------------
% 13.78/2.30 % (904077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.78/2.30 % (904077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.30 % (904077)CaDiCaL version: 2.1.3
% 13.78/2.30 % (904077)Termination reason: Instruction limit
% 13.78/2.30 % (904077)Termination phase: Saturation
% 13.78/2.30 % (904077)Time elapsed: 0.053 s
% 13.78/2.30 % (904077)Peak memory usage: 13 MB
% 13.78/2.30 % (904077)Instructions burned: 132 (million)
% 13.78/2.30 % (904079)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=4054483938:st=1.5:i=346:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/346Mi)
% 13.78/2.30 % (904080)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=2449014568:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2984 on theBenchmark for (2984ds/152Mi)
% 13.78/2.30 % (904080)Instruction limit reached!
% 13.78/2.30 % (904080)------------------------------
% 13.78/2.30 % (904080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.78/2.30 % (904080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.30 % (904080)CaDiCaL version: 2.1.3
% 13.78/2.30 % (904080)Termination reason: Instruction limit
% 13.78/2.30 % (904080)Termination phase: Property scanning
% 13.78/2.30 % (904080)Time elapsed: 0.060 s
% 13.78/2.30 % (904080)Peak memory usage: 11 MB
% 13.78/2.30 % (904080)Instructions burned: 153 (million)
% 13.78/2.30 % (904083)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3222614829:i=75:ep=R:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/75Mi)
% 13.78/2.30 % (904083)Instruction limit reached!
% 13.78/2.30 % (904083)------------------------------
% 13.78/2.30 % (904083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.78/2.30 % (904083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.30 % (904083)CaDiCaL version: 2.1.3
% 13.78/2.30 % (904083)Termination reason: Instruction limit
% 13.78/2.30 % (904083)Termination phase: Function definition elimination
% 13.78/2.30 % (904083)Time elapsed: 0.031 s
% 13.78/2.30 % (904083)Peak memory usage: 10 MB
% 13.78/2.30 % (904083)Instructions burned: 75 (million)
% 13.78/2.30 % (904085)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=3260117365:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/387Mi)
% 13.78/2.30 % (904055)Instruction limit reached!
% 13.78/2.30 % (904055)------------------------------
% 13.78/2.30 % (904055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.78/2.30 % (904055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.30 % (904055)CaDiCaL version: 2.1.3
% 13.78/2.30 % (904055)Termination reason: Instruction limit
% 13.78/2.30 % (904055)Termination phase: Saturation
% 13.78/2.30 % (904055)Time elapsed: 0.611 s
% 13.78/2.30 % (904055)Peak memory usage: 13 MB
% 13.78/2.30 % (904055)Instructions burned: 1441 (million)
% 13.78/2.30 % (904079)Instruction limit reached!
% 13.78/2.30 % (904079)------------------------------
% 13.78/2.30 % (904079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.78/2.30 % (904079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.30 % (904079)CaDiCaL version: 2.1.3
% 13.78/2.30 % (904079)Termination reason: Instruction limit
% 13.78/2.30 % (904079)Termination phase: Saturation
% 13.78/2.30 % (904079)Time elapsed: 0.153 s
% 13.78/2.30 % (904079)Peak memory usage: 18 MB
% 13.78/2.30 % (904079)Instructions burned: 346 (million)
% 13.78/2.30 % (904073)Instruction limit reached!
% 13.78/2.30 % (904073)------------------------------
% 13.78/2.30 % (904073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.78/2.30 % (904073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.30 % (904073)CaDiCaL version: 2.1.3
% 13.78/2.30 % (904073)Termination reason: Instruction limit
% 14.34/2.46 % (904073)Termination phase: Saturation
% 14.34/2.46 % (904073)Time elapsed: 0.376 s
% 14.34/2.46 % (904073)Peak memory usage: 13 MB
% 14.34/2.46 % (904073)Instructions burned: 867 (million)
% 14.34/2.46 % (904087)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=210928:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2982 on theBenchmark for (2982ds/148Mi)
% 14.34/2.46 % (904088)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=2198858577:i=161:piset=and:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/161Mi)
% 14.34/2.46 % (904089)lrs+10_1_sil=128000:si=on:random_seed=3812940364:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/888Mi)
% 14.34/2.46 % (904067)Instruction limit reached!
% 14.34/2.46 % (904067)------------------------------
% 14.34/2.46 % (904067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.34/2.46 % (904067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.34/2.46 % (904067)CaDiCaL version: 2.1.3
% 14.34/2.46 % (904067)Termination reason: Instruction limit
% 14.34/2.46 % (904067)Termination phase: Saturation
% 14.34/2.46 % (904067)Time elapsed: 0.526 s
% 14.34/2.46 % (904067)Peak memory usage: 25 MB
% 14.34/2.46 % (904067)Instructions burned: 1255 (million)
% 14.34/2.46 % (904093)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=923190789:i=136:add=on:ins=4:rtra=on:sup=off_2982 on theBenchmark for (2982ds/136Mi)
% 14.34/2.46 % (904088)Instruction limit reached!
% 14.34/2.46 % (904088)------------------------------
% 14.34/2.46 % (904088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.34/2.46 % (904088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.34/2.46 % (904088)CaDiCaL version: 2.1.3
% 14.34/2.46 % (904088)Termination reason: Instruction limit
% 14.34/2.46 % (904088)Termination phase: Property scanning
% 14.34/2.46 % (904088)Time elapsed: 0.065 s
% 14.34/2.46 % (904088)Peak memory usage: 11 MB
% 14.34/2.46 % (904088)Instructions burned: 162 (million)
% 14.34/2.46 % (904087)Instruction limit reached!
% 14.34/2.46 % (904087)------------------------------
% 14.34/2.46 % (904087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.34/2.46 % (904087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.34/2.46 % (904087)CaDiCaL version: 2.1.3
% 14.34/2.46 % (904087)Termination reason: Instruction limit
% 14.34/2.46 % (904087)Termination phase: Saturation
% 14.34/2.46 % (904087)Time elapsed: 0.073 s
% 14.34/2.46 % (904087)Peak memory usage: 13 MB
% 14.34/2.46 % (904087)Instructions burned: 149 (million)
% 14.34/2.46 % (904095)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=783825216:i=88:s2at=3:nm=2:rtra=on:rawr=on_2982 on theBenchmark for (2982ds/88Mi)
% 14.34/2.46 % (904096)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1989766302:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2981 on theBenchmark for (2981ds/93Mi)
% 14.34/2.46 % (904093)Instruction limit reached!
% 14.34/2.46 % (904093)------------------------------
% 14.34/2.46 % (904093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.34/2.46 % (904093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.34/2.46 % (904093)CaDiCaL version: 2.1.3
% 14.34/2.46 % (904093)Termination reason: Instruction limit
% 14.34/2.46 % (904093)Termination phase: Property scanning
% 14.34/2.46 % (904093)Time elapsed: 0.054 s
% 14.34/2.46 % (904093)Peak memory usage: 11 MB
% 14.34/2.46 % (904093)Instructions burned: 138 (million)
% 14.34/2.46 % (904095)Instruction limit reached!
% 14.34/2.46 % (904095)------------------------------
% 14.34/2.46 % (904095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.34/2.46 % (904095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.34/2.46 % (904095)CaDiCaL version: 2.1.3
% 14.34/2.46 % (904095)Termination reason: Instruction limit
% 14.34/2.46 % (904095)Termination phase: Function definition elimination
% 14.34/2.46 % (904095)Time elapsed: 0.036 s
% 14.34/2.46 % (904095)Peak memory usage: 11 MB
% 14.34/2.46 % (904095)Instructions burned: 90 (million)
% 14.34/2.46 % (904096)Instruction limit reached!
% 14.34/2.46 % (904096)------------------------------
% 14.34/2.46 % (904096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.63 % (904096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.63 % (904096)CaDiCaL version: 2.1.3
% 15.22/2.63 % (904096)Termination reason: Instruction limit
% 15.22/2.63 % (904096)Termination phase: Function definition elimination
% 15.22/2.63 % (904096)Time elapsed: 0.039 s
% 15.22/2.63 % (904096)Peak memory usage: 11 MB
% 15.22/2.63 % (904096)Instructions burned: 96 (million)
% 15.22/2.63 % (904085)Instruction limit reached!
% 15.22/2.63 % (904085)------------------------------
% 15.22/2.63 % (904085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.63 % (904085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.63 % (904085)CaDiCaL version: 2.1.3
% 15.22/2.63 % (904085)Termination reason: Instruction limit
% 15.22/2.63 % (904085)Termination phase: Saturation
% 15.22/2.63 % (904085)Time elapsed: 0.154 s
% 15.22/2.63 % (904085)Peak memory usage: 12 MB
% 15.22/2.63 % (904085)Instructions burned: 388 (million)
% 15.22/2.63 % (904099)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1805662067:i=2186:rtra=on:ixr=off_2981 on theBenchmark for (2981ds/2186Mi)
% 15.22/2.63 % (904100)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1406460189:s2a=on:i=240:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/240Mi)
% 15.22/2.63 % (904102)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 15.22/2.63 % (904101)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=61250714:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2981 on theBenchmark for (2981ds/805Mi)
% 15.22/2.63 % (904102)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=1124753067:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2981 on theBenchmark for (2981ds/391Mi)
% 15.22/2.63 % (904013)Instruction limit reached!
% 15.22/2.63 % (904013)------------------------------
% 15.22/2.63 % (904013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.63 % (904013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.63 % (904013)CaDiCaL version: 2.1.3
% 15.22/2.63 % (904013)Termination reason: Instruction limit
% 15.22/2.63 % (904013)Termination phase: Saturation
% 15.22/2.63 % (904013)Time elapsed: 1.263 s
% 15.22/2.63 % (904013)Peak memory usage: 18 MB
% 15.22/2.63 % (904013)Instructions burned: 5759 (million)
% 15.22/2.63 % (904107)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=2931328093:i=355:av=off:fsr=off:rtra=on:ixr=off_2980 on theBenchmark for (2980ds/355Mi)
% 15.22/2.63 % (904100)Instruction limit reached!
% 15.22/2.63 % (904100)------------------------------
% 15.22/2.63 % (904100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.63 % (904100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.63 % (904100)CaDiCaL version: 2.1.3
% 15.22/2.63 % (904100)Termination reason: Instruction limit
% 15.22/2.63 % (904100)Termination phase: Property scanning
% 15.22/2.63 % (904100)Time elapsed: 0.095 s
% 15.22/2.63 % (904100)Peak memory usage: 11 MB
% 15.22/2.63 % (904100)Instructions burned: 241 (million)
% 15.22/2.63 % (904109)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=4119376851:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2980 on theBenchmark for (2980ds/314Mi)
% 15.22/2.63 % (904107)Instruction limit reached!
% 15.22/2.63 % (904107)------------------------------
% 15.22/2.63 % (904107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.63 % (904107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.63 % (904107)CaDiCaL version: 2.1.3
% 15.22/2.63 % (904107)Termination reason: Instruction limit
% 15.22/2.63 % (904107)Termination phase: Saturation
% 15.22/2.63 % (904107)Time elapsed: 0.072 s
% 15.22/2.63 % (904107)Peak memory usage: 12 MB
% 15.22/2.63 % (904107)Instructions burned: 355 (million)
% 15.22/2.63 % (904111)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=162393619:s2a=on:i=251:fsr=off:rtra=on_2979 on theBenchmark for (2979ds/251Mi)
% 15.22/2.63 % (904102)Instruction limit reached!
% 15.22/2.63 % (904102)------------------------------
% 15.22/2.63 % (904102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.63 % (904102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.35/2.85 % (904102)CaDiCaL version: 2.1.3
% 16.35/2.85 % (904102)Termination reason: Instruction limit
% 16.35/2.85 % (904102)Termination phase: Saturation
% 16.35/2.85 % (904102)Time elapsed: 0.153 s
% 16.35/2.85 % (904102)Peak memory usage: 12 MB
% 16.35/2.85 % (904102)Instructions burned: 391 (million)
% 16.35/2.85 % (904113)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=536374778:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2979 on theBenchmark for (2979ds/2470Mi)
% 16.35/2.85 % (904111)Instruction limit reached!
% 16.35/2.85 % (904111)------------------------------
% 16.35/2.85 % (904111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.35/2.85 % (904111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.35/2.85 % (904111)CaDiCaL version: 2.1.3
% 16.35/2.85 % (904111)Termination reason: Instruction limit
% 16.35/2.85 % (904111)Termination phase: Property scanning
% 16.35/2.85 % (904111)Time elapsed: 0.052 s
% 16.35/2.85 % (904111)Peak memory usage: 11 MB
% 16.35/2.85 % (904111)Instructions burned: 256 (million)
% 16.35/2.85 % (904089)Instruction limit reached!
% 16.35/2.85 % (904089)------------------------------
% 16.35/2.85 % (904089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.35/2.85 % (904089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.35/2.85 % (904089)CaDiCaL version: 2.1.3
% 16.35/2.85 % (904089)Termination reason: Instruction limit
% 16.35/2.85 % (904089)Termination phase: Saturation
% 16.35/2.85 % (904089)Time elapsed: 0.354 s
% 16.35/2.85 % (904089)Peak memory usage: 13 MB
% 16.35/2.85 % (904089)Instructions burned: 889 (million)
% 16.35/2.85 % (904116)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1745865571:i=116:ep=RSTC:rtra=on:ntd=on_2979 on theBenchmark for (2979ds/116Mi)
% 16.35/2.85 % (904109)Instruction limit reached!
% 16.35/2.85 % (904109)------------------------------
% 16.35/2.85 % (904109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.35/2.85 % (904109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.35/2.85 % (904109)CaDiCaL version: 2.1.3
% 16.35/2.85 % (904109)Termination reason: Instruction limit
% 16.35/2.85 % (904109)Termination phase: Saturation
% 16.35/2.85 % (904109)Time elapsed: 0.121 s
% 16.35/2.85 % (904109)Peak memory usage: 12 MB
% 16.35/2.85 % (904109)Instructions burned: 317 (million)
% 16.35/2.85 % (904115)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=4243124054:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2979 on theBenchmark for (2979ds/673Mi)
% 16.35/2.85 % (904118)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1153598047:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2978 on theBenchmark for (2978ds/270Mi)
% 16.35/2.85 % (904116)Instruction limit reached!
% 16.35/2.85 % (904116)------------------------------
% 16.35/2.85 % (904116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.35/2.85 % (904116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.35/2.85 % (904116)CaDiCaL version: 2.1.3
% 16.35/2.85 % (904116)Termination reason: Instruction limit
% 16.35/2.85 % (904116)Termination phase: Property scanning
% 16.35/2.85 % (904116)Time elapsed: 0.046 s
% 16.35/2.85 % (904116)Peak memory usage: 11 MB
% 16.35/2.85 % (904116)Instructions burned: 117 (million)
% 16.35/2.85 % (904121)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2738611121:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2978 on theBenchmark for (2978ds/30Mi)
% 16.35/2.85 % (904121)Instruction limit reached!
% 16.35/2.85 % (904121)------------------------------
% 16.35/2.85 % (904121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.35/2.85 % (904121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.35/2.85 % (904121)CaDiCaL version: 2.1.3
% 16.35/2.85 % (904121)Termination reason: Instruction limit
% 16.35/2.85 % (904121)Termination phase: Property scanning
% 16.35/2.85 % (904121)Time elapsed: 0.013 s
% 16.35/2.85 % (904121)Peak memory usage: 10 MB
% 17.35/3.02 % (904121)Instructions burned: 30 (million)
% 17.35/3.02 % (904101)Instruction limit reached!
% 17.35/3.02 % (904101)------------------------------
% 17.35/3.02 % (904101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.35/3.02 % (904101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.35/3.02 % (904101)CaDiCaL version: 2.1.3
% 17.35/3.02 % (904101)Termination reason: Instruction limit
% 17.35/3.02 % (904101)Termination phase: Saturation
% 17.35/3.02 % (904101)Time elapsed: 0.315 s
% 17.35/3.02 % (904101)Peak memory usage: 13 MB
% 17.35/3.02 % (904101)Instructions burned: 805 (million)
% 17.35/3.02 % (904123)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 17.35/3.02 % (904123)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3177430073:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2978 on theBenchmark for (2978ds/39Mi)
% 17.35/3.02 % (904124)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3523970731:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2978 on theBenchmark for (2978ds/365Mi)
% 17.35/3.02 % (904123)Instruction limit reached!
% 17.35/3.02 % (904123)------------------------------
% 17.35/3.02 % (904123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.35/3.02 % (904123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.35/3.02 % (904123)CaDiCaL version: 2.1.3
% 17.35/3.02 % (904123)Termination reason: Instruction limit
% 17.35/3.02 % (904123)Termination phase: Property scanning
% 17.35/3.02 % (904123)Time elapsed: 0.016 s
% 17.35/3.02 % (904123)Peak memory usage: 10 MB
% 17.35/3.02 % (904123)Instructions burned: 39 (million)
% 17.35/3.02 % (904118)Instruction limit reached!
% 17.35/3.02 % (904118)------------------------------
% 17.35/3.02 % (904118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.35/3.02 % (904118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.35/3.02 % (904118)CaDiCaL version: 2.1.3
% 17.35/3.02 % (904118)Termination reason: Instruction limit
% 17.35/3.02 % (904118)Termination phase: Property scanning
% 17.35/3.02 % (904118)Time elapsed: 0.106 s
% 17.35/3.02 % (904118)Peak memory usage: 10 MB
% 17.35/3.02 % (904118)Instructions burned: 270 (million)
% 17.35/3.02 % (904127)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2981593318:i=158:av=off:rtra=on_2977 on theBenchmark for (2977ds/158Mi)
% 17.35/3.02 % (904128)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 17.35/3.02 % (904128)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=455428062:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2977 on theBenchmark for (2977ds/252Mi)
% 17.35/3.02 % (904127)Instruction limit reached!
% 17.35/3.02 % (904127)------------------------------
% 17.35/3.02 % (904127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.35/3.02 % (904127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.35/3.02 % (904127)CaDiCaL version: 2.1.3
% 17.35/3.02 % (904127)Termination reason: Instruction limit
% 17.35/3.02 % (904127)Termination phase: Saturation
% 17.35/3.02 % (904127)Time elapsed: 0.077 s
% 17.35/3.02 % (904127)Peak memory usage: 13 MB
% 17.35/3.02 % (904127)Instructions burned: 159 (million)
% 17.35/3.02 % (904131)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=434242998:i=213:rtra=on:ss=axioms_2976 on theBenchmark for (2976ds/213Mi)
% 17.35/3.02 % (904128)Instruction limit reached!
% 17.35/3.02 % (904128)------------------------------
% 17.35/3.02 % (904128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.35/3.02 % (904128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.35/3.02 % (904128)CaDiCaL version: 2.1.3
% 17.35/3.02 % (904128)Termination reason: Instruction limit
% 17.35/3.02 % (904128)Termination phase: Property scanning
% 17.35/3.02 % (904128)Time elapsed: 0.104 s
% 17.35/3.02 % (904128)Peak memory usage: 11 MB
% 17.35/3.02 % (904128)Instructions burned: 252 (million)
% 17.35/3.02 % (904124)Instruction limit reached!
% 17.35/3.02 % (904124)------------------------------
% 17.35/3.02 % (904124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.35/3.02 % (904124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.54/3.08 % (904124)CaDiCaL version: 2.1.3
% 19.54/3.08 % (904124)Termination reason: Instruction limit
% 19.54/3.08 % (904124)Termination phase: Saturation
% 19.54/3.08 % (904124)Time elapsed: 0.150 s
% 19.54/3.08 % (904124)Peak memory usage: 12 MB
% 19.54/3.08 % (904124)Instructions burned: 367 (million)
% 19.54/3.08 % (904133)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=944226248:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2976 on theBenchmark for (2976ds/160Mi)
% 19.54/3.08 % (904134)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=2963345954:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2976 on theBenchmark for (2976ds/763Mi)
% 19.54/3.08 % (904115)Instruction limit reached!
% 19.54/3.08 % (904115)------------------------------
% 19.54/3.08 % (904115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.54/3.08 % (904115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.54/3.08 % (904115)CaDiCaL version: 2.1.3
% 19.54/3.08 % (904115)Termination reason: Instruction limit
% 19.54/3.08 % (904115)Termination phase: Saturation
% 19.54/3.08 % (904115)Time elapsed: 0.282 s
% 19.54/3.08 % (904115)Peak memory usage: 13 MB
% 19.54/3.08 % (904115)Instructions burned: 675 (million)
% 19.54/3.08 % (904131)Refutation not found, incomplete strategy
% 19.54/3.08 % (904131)------------------------------
% 19.54/3.08 % (904131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.54/3.08 % (904131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.54/3.08 % (904131)CaDiCaL version: 2.1.3
% 19.54/3.08 % (904131)Termination reason: Refutation not found, incomplete strategy
% 19.54/3.08 % (904131)Time elapsed: 0.069 s
% 19.54/3.08 % (904131)Peak memory usage: 14 MB
% 19.54/3.08 % (904131)Instructions burned: 119 (million)
% 19.54/3.08 % (904131)------------------------------
% 19.54/3.08 % (904131)------------------------------
% 19.54/3.08 % (904137)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 19.54/3.08 % (904137)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2862470546:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2976 on theBenchmark for (2976ds/237Mi)
% 19.54/3.08 % (904138)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=3328931357:s2a=on:i=386:rtra=on:ntd=on_2975 on theBenchmark for (2975ds/386Mi)
% 19.54/3.08 % (904133)Instruction limit reached!
% 19.54/3.08 % (904133)------------------------------
% 19.54/3.08 % (904133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.54/3.08 % (904133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.54/3.08 % (904133)CaDiCaL version: 2.1.3
% 19.54/3.08 % (904133)Termination reason: Instruction limit
% 19.54/3.08 % (904133)Termination phase: Twee Goal Transformation
% 19.54/3.08 % (904133)Time elapsed: 0.064 s
% 19.54/3.08 % (904133)Peak memory usage: 11 MB
% 19.54/3.08 % (904133)Instructions burned: 160 (million)
% 19.54/3.08 % (904141)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=428236174:i=300:piset=and:nm=32:rtra=on_2975 on theBenchmark for (2975ds/300Mi)
% 19.54/3.08 % (904137)Instruction limit reached!
% 19.54/3.08 % (904137)------------------------------
% 19.54/3.08 % (904137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.54/3.08 % (904137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.54/3.08 % (904137)CaDiCaL version: 2.1.3
% 19.54/3.08 % (904137)Termination reason: Instruction limit
% 19.54/3.08 % (904137)Termination phase: Saturation
% 19.54/3.08 % (904137)Time elapsed: 0.094 s
% 19.54/3.08 % (904137)Peak memory usage: 13 MB
% 19.54/3.08 % (904137)Instructions burned: 238 (million)
% 19.54/3.08 % (904143)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=2208430588:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2974 on theBenchmark for (2974ds/567Mi)
% 19.54/3.08 % (904138)Instruction limit reached!
% 19.54/3.08 % (904138)------------------------------
% 19.54/3.08 % (904138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.54/3.08 % (904138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.54/3.08 % (904138)CaDiCaL version: 2.1.3
% 19.54/3.08 % (904138)Termination reason: Instruction limit
% 20.03/3.17 % (904138)Termination phase: Saturation
% 20.03/3.17 % (904138)Time elapsed: 0.150 s
% 20.03/3.17 % (904138)Peak memory usage: 12 MB
% 20.03/3.17 % (904138)Instructions burned: 387 (million)
% 20.03/3.17 % (904141)Instruction limit reached!
% 20.03/3.17 % (904141)------------------------------
% 20.03/3.17 % (904141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.03/3.17 % (904141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.03/3.17 % (904141)CaDiCaL version: 2.1.3
% 20.03/3.17 % (904141)Termination reason: Instruction limit
% 20.03/3.17 % (904141)Termination phase: Property scanning
% 20.03/3.17 % (904141)Time elapsed: 0.117 s
% 20.03/3.17 % (904141)Peak memory usage: 11 MB
% 20.03/3.17 % (904141)Instructions burned: 301 (million)
% 20.03/3.17 % (904145)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=3786375154:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2974 on theBenchmark for (2974ds/379Mi)
% 20.03/3.17 % (904146)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=1351427975:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2974 on theBenchmark for (2974ds/429Mi)
% 20.03/3.17 % (904113)Instruction limit reached!
% 20.03/3.17 % (904113)------------------------------
% 20.03/3.17 % (904113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.03/3.17 % (904113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.03/3.17 % (904113)CaDiCaL version: 2.1.3
% 20.03/3.17 % (904113)Termination reason: Instruction limit
% 20.03/3.17 % (904113)Termination phase: Saturation
% 20.03/3.17 % (904113)Time elapsed: 0.574 s
% 20.03/3.17 % (904113)Peak memory usage: 27 MB
% 20.03/3.17 % (904113)Instructions burned: 2475 (million)
% 20.03/3.17 % (904149)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=4219745771:i=478:bd=all:rtra=on_2973 on theBenchmark for (2973ds/478Mi)
% 20.03/3.17 % (904134)Instruction limit reached!
% 20.03/3.17 % (904134)------------------------------
% 20.03/3.17 % (904134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.03/3.17 % (904134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.03/3.17 % (904134)CaDiCaL version: 2.1.3
% 20.03/3.17 % (904134)Termination reason: Instruction limit
% 20.03/3.17 % (904134)Termination phase: Saturation
% 20.03/3.17 % (904134)Time elapsed: 0.303 s
% 20.03/3.17 % (904134)Peak memory usage: 12 MB
% 20.03/3.17 % (904134)Instructions burned: 763 (million)
% 20.03/3.17 % (904151)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=933208423:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2973 on theBenchmark for (2973ds/445Mi)
% 20.03/3.17 % (904149)Instruction limit reached!
% 20.03/3.17 % (904149)------------------------------
% 20.03/3.17 % (904149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.03/3.17 % (904149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.03/3.17 % (904149)CaDiCaL version: 2.1.3
% 20.03/3.17 % (904149)Termination reason: Instruction limit
% 20.03/3.17 % (904149)Termination phase: Saturation
% 20.03/3.17 % (904149)Time elapsed: 0.099 s
% 20.03/3.17 % (904149)Peak memory usage: 13 MB
% 20.03/3.17 % (904149)Instructions burned: 479 (million)
% 20.03/3.17 % (904153)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3033389342:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2972 on theBenchmark for (2972ds/71Mi)
% 20.03/3.17 % (904145)Instruction limit reached!
% 20.03/3.17 % (904145)------------------------------
% 20.03/3.17 % (904145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.03/3.17 % (904145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.03/3.17 % (904145)CaDiCaL version: 2.1.3
% 20.03/3.17 % (904145)Termination reason: Instruction limit
% 20.03/3.17 % (904145)Termination phase: Saturation
% 20.03/3.17 % (904145)Time elapsed: 0.149 s
% 20.03/3.17 % (904145)Peak memory usage: 12 MB
% 20.03/3.17 % (904145)Instructions burned: 379 (million)
% 20.03/3.17 % (904099)Instruction limit reached!
% 20.03/3.17 % (904099)------------------------------
% 20.03/3.17 % (904099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.03/3.17 % (904099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.03/3.17 % (904099)CaDiCaL version: 2.1.3
% 20.03/3.17 % (904099)Termination reason: Instruction limit
% 20.03/3.17 % (904099)Termination phase: Saturation
% 20.03/3.17 % (904099)Time elapsed: 0.880 s
% 20.03/3.17 % (904099)Peak memory usage: 22 MB
% 20.03/3.17 % (904099)Instructions burned: 2188 (million)
% 20.88/3.39 % (904143)Instruction limit reached!
% 20.88/3.39 % (904143)------------------------------
% 20.88/3.39 % (904143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.88/3.39 % (904143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.88/3.39 % (904143)CaDiCaL version: 2.1.3
% 20.88/3.39 % (904143)Termination reason: Instruction limit
% 20.88/3.39 % (904143)Termination phase: Saturation
% 20.88/3.39 % (904143)Time elapsed: 0.224 s
% 20.88/3.39 % (904143)Peak memory usage: 12 MB
% 20.88/3.39 % (904143)Instructions burned: 569 (million)
% 20.88/3.39 % (904153)Instruction limit reached!
% 20.88/3.39 % (904153)------------------------------
% 20.88/3.39 % (904153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.88/3.39 % (904153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.88/3.39 % (904153)CaDiCaL version: 2.1.3
% 20.88/3.39 % (904153)Termination reason: Instruction limit
% 20.88/3.39 % (904153)Termination phase: Function definition elimination
% 20.88/3.39 % (904153)Time elapsed: 0.015 s
% 20.88/3.39 % (904153)Peak memory usage: 10 MB
% 20.88/3.39 % (904153)Instructions burned: 72 (million)
% 20.88/3.39 % (904155)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3623252478:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2972 on theBenchmark for (2972ds/302Mi)
% 20.88/3.39 % (904156)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=2476724394:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2972 on theBenchmark for (2972ds/4980Mi)
% 20.88/3.39 % (904157)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 20.88/3.39 % (904157)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 20.88/3.39 % (904157)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2552445467:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2972 on theBenchmark for (2972ds/100Mi)
% 20.88/3.39 % (904158)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2415931776:i=76:piset=equals:rtra=on:ntd=on_2972 on theBenchmark for (2972ds/76Mi)
% 20.88/3.39 % (904158)Instruction limit reached!
% 20.88/3.39 % (904158)------------------------------
% 20.88/3.39 % (904158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.88/3.39 % (904158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.88/3.39 % (904158)CaDiCaL version: 2.1.3
% 20.88/3.39 % (904158)Termination reason: Instruction limit
% 20.88/3.39 % (904158)Termination phase: Function definition elimination
% 20.88/3.39 % (904158)Time elapsed: 0.017 s
% 20.88/3.39 % (904158)Peak memory usage: 11 MB
% 20.88/3.39 % (904158)Instructions burned: 81 (million)
% 20.88/3.39 % (904156)Refutation not found, incomplete strategy
% 20.88/3.39 % (904156)------------------------------
% 20.88/3.39 % (904156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.88/3.39 % (904156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.88/3.39 % (904156)CaDiCaL version: 2.1.3
% 20.88/3.39 % (904156)Termination reason: Refutation not found, incomplete strategy
% 20.88/3.39 % (904156)Time elapsed: 0.026 s
% 20.88/3.39 % (904156)Peak memory usage: 13 MB
% 20.88/3.39 % (904156)Instructions burned: 51 (million)
% 20.88/3.39 % (904156)------------------------------
% 20.88/3.39 % (904156)------------------------------
% 20.88/3.39 % (904163)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=1943106127:i=289:rtra=on_2972 on theBenchmark for (2972ds/289Mi)
% 20.88/3.39 % (904157)Instruction limit reached!
% 20.88/3.39 % (904157)------------------------------
% 20.88/3.39 % (904157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.88/3.39 % (904157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.88/3.39 % (904157)CaDiCaL version: 2.1.3
% 20.88/3.39 % (904157)Termination reason: Instruction limit
% 20.88/3.39 % (904157)Termination phase: Twee Goal Transformation
% 20.88/3.39 % (904157)Time elapsed: 0.040 s
% 20.88/3.39 % (904157)Peak memory usage: 11 MB
% 20.88/3.39 % (904157)Instructions burned: 102 (million)
% 20.88/3.39 % (904146)Instruction limit reached!
% 20.88/3.39 % (904146)------------------------------
% 22.54/3.62 % (904146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.54/3.62 % (904146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.54/3.62 % (904146)CaDiCaL version: 2.1.3
% 22.54/3.62 % (904146)Termination reason: Instruction limit
% 22.54/3.62 % (904146)Termination phase: Saturation
% 22.54/3.62 % (904146)Time elapsed: 0.209 s
% 22.54/3.62 % (904146)Peak memory usage: 12 MB
% 22.54/3.62 % (904146)Instructions burned: 429 (million)
% 22.54/3.62 % (904164)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=985748903:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2972 on theBenchmark for (2972ds/493Mi)
% 22.54/3.62 % (904168)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 22.54/3.62 % (904167)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1208479030:cond=on:i=34:hud=10:nm=10:rtra=on_2971 on theBenchmark for (2971ds/34Mi)
% 22.54/3.62 % (904168)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=3155293004:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2971 on theBenchmark for (2971ds/372Mi)
% 22.54/3.62 % (904167)Instruction limit reached!
% 22.54/3.62 % (904167)------------------------------
% 22.54/3.62 % (904167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.54/3.62 % (904167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.54/3.62 % (904167)CaDiCaL version: 2.1.3
% 22.54/3.62 % (904167)Termination reason: Instruction limit
% 22.54/3.62 % (904167)Termination phase: Property scanning
% 22.54/3.62 % (904167)Time elapsed: 0.015 s
% 22.54/3.62 % (904167)Peak memory usage: 11 MB
% 22.54/3.62 % (904167)Instructions burned: 35 (million)
% 22.54/3.62 % (904163)Instruction limit reached!
% 22.54/3.62 % (904163)------------------------------
% 22.54/3.62 % (904163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.54/3.62 % (904163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.54/3.62 % (904163)CaDiCaL version: 2.1.3
% 22.54/3.62 % (904163)Termination reason: Instruction limit
% 22.54/3.62 % (904163)Termination phase: Property scanning
% 22.54/3.62 % (904163)Time elapsed: 0.059 s
% 22.54/3.62 % (904163)Peak memory usage: 11 MB
% 22.54/3.62 % (904163)Instructions burned: 293 (million)
% 22.54/3.62 % (904171)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=3523019509:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2971 on theBenchmark for (2971ds/670Mi)
% 22.54/3.62 % (904172)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4125127863:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2971 on theBenchmark for (2971ds/647Mi)
% 22.54/3.62 % (904155)Instruction limit reached!
% 22.54/3.62 % (904155)------------------------------
% 22.54/3.62 % (904155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.54/3.62 % (904155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.54/3.62 % (904155)CaDiCaL version: 2.1.3
% 22.54/3.62 % (904155)Termination reason: Instruction limit
% 22.54/3.62 % (904155)Termination phase: Saturation
% 22.54/3.62 % (904155)Time elapsed: 0.116 s
% 22.54/3.62 % (904155)Peak memory usage: 12 MB
% 22.54/3.62 % (904155)Instructions burned: 304 (million)
% 22.54/3.62 % (904151)Instruction limit reached!
% 22.54/3.62 % (904151)------------------------------
% 22.54/3.62 % (904151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.54/3.62 % (904151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.54/3.62 % (904151)CaDiCaL version: 2.1.3
% 22.54/3.62 % (904151)Termination reason: Instruction limit
% 22.54/3.62 % (904151)Termination phase: Saturation
% 22.54/3.62 % (904151)Time elapsed: 0.176 s
% 22.54/3.62 % (904151)Peak memory usage: 12 MB
% 22.54/3.62 % (904151)Instructions burned: 447 (million)
% 22.54/3.62 % (904175)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=1914982153:i=857:add=off:kws=frequency:rtra=on:ntd=on_2971 on theBenchmark for (2971ds/857Mi)
% 22.54/3.62 % (904176)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=3439685324:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2971 on theBenchmark for (2971ds/693Mi)
% 23.25/3.81 % (904168)Instruction limit reached!
% 23.25/3.81 % (904168)------------------------------
% 23.25/3.81 % (904168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.25/3.81 % (904168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/3.81 % (904168)CaDiCaL version: 2.1.3
% 23.25/3.81 % (904168)Termination reason: Instruction limit
% 23.25/3.81 % (904168)Termination phase: Saturation
% 23.25/3.81 % (904168)Time elapsed: 0.145 s
% 23.25/3.81 % (904168)Peak memory usage: 12 MB
% 23.25/3.81 % (904168)Instructions burned: 374 (million)
% 23.25/3.81 % (904179)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=3889379736:i=285:hud=10:bd=all:rtra=on:ss=axioms_2970 on theBenchmark for (2970ds/285Mi)
% 23.25/3.81 % (904164)Instruction limit reached!
% 23.25/3.81 % (904164)------------------------------
% 23.25/3.81 % (904164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.25/3.81 % (904164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/3.81 % (904164)CaDiCaL version: 2.1.3
% 23.25/3.81 % (904164)Termination reason: Instruction limit
% 23.25/3.81 % (904164)Termination phase: Saturation
% 23.25/3.81 % (904164)Time elapsed: 0.193 s
% 23.25/3.81 % (904164)Peak memory usage: 12 MB
% 23.25/3.81 % (904164)Instructions burned: 493 (million)
% 23.25/3.81 % (904172)Instruction limit reached!
% 23.25/3.81 % (904172)------------------------------
% 23.25/3.81 % (904172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.25/3.81 % (904172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/3.81 % (904172)CaDiCaL version: 2.1.3
% 23.25/3.81 % (904172)Termination reason: Instruction limit
% 23.25/3.81 % (904172)Termination phase: Saturation
% 23.25/3.81 % (904172)Time elapsed: 0.139 s
% 23.25/3.81 % (904172)Peak memory usage: 14 MB
% 23.25/3.81 % (904172)Instructions burned: 651 (million)
% 23.25/3.81 % (904182)dis+10_1_si=on:random_seed=2319817783:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2969 on theBenchmark for (2969ds/407Mi)
% 23.25/3.81 % (904181)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 23.25/3.81 % (904181)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=3137541132:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2969 on theBenchmark for (2969ds/52Mi)
% 23.25/3.81 % (904181)Instruction limit reached!
% 23.25/3.81 % (904181)------------------------------
% 23.25/3.81 % (904181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.25/3.81 % (904181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/3.81 % (904181)CaDiCaL version: 2.1.3
% 23.25/3.81 % (904181)Termination reason: Instruction limit
% 23.25/3.81 % (904181)Termination phase: Function definition elimination
% 23.25/3.81 % (904181)Time elapsed: 0.023 s
% 23.25/3.81 % (904181)Peak memory usage: 11 MB
% 23.25/3.81 % (904181)Instructions burned: 54 (million)
% 23.25/3.81 % (904185)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3832935168:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2969 on theBenchmark for (2969ds/2240Mi)
% 23.25/3.81 % (904182)Instruction limit reached!
% 23.25/3.81 % (904182)------------------------------
% 23.25/3.81 % (904182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.25/3.81 % (904182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/3.81 % (904182)CaDiCaL version: 2.1.3
% 23.25/3.81 % (904182)Termination reason: Instruction limit
% 23.25/3.81 % (904182)Termination phase: Saturation
% 23.25/3.81 % (904182)Time elapsed: 0.083 s
% 23.25/3.81 % (904182)Peak memory usage: 12 MB
% 23.25/3.81 % (904182)Instructions burned: 408 (million)
% 23.25/3.81 % (904187)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=1713581969:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2968 on theBenchmark for (2968ds/336Mi)
% 23.25/3.81 % (904179)Instruction limit reached!
% 23.25/3.81 % (904179)------------------------------
% 23.25/3.81 % (904179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.25/3.81 % (904179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/3.81 % (904179)CaDiCaL version: 2.1.3
% 23.83/4.03 % (904179)Termination reason: Instruction limit
% 23.83/4.03 % (904179)Termination phase: Saturation
% 23.83/4.03 % (904179)Time elapsed: 0.121 s
% 23.83/4.03 % (904179)Peak memory usage: 15 MB
% 23.83/4.03 % (904179)Instructions burned: 286 (million)
% 23.83/4.03 % (904189)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=803199447:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2968 on theBenchmark for (2968ds/1142Mi)
% 23.83/4.03 % (904171)Instruction limit reached!
% 23.83/4.03 % (904171)------------------------------
% 23.83/4.03 % (904171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/4.03 % (904171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/4.03 % (904171)CaDiCaL version: 2.1.3
% 23.83/4.03 % (904171)Termination reason: Instruction limit
% 23.83/4.03 % (904171)Termination phase: Saturation
% 23.83/4.03 % (904171)Time elapsed: 0.291 s
% 23.83/4.03 % (904171)Peak memory usage: 13 MB
% 23.83/4.03 % (904171)Instructions burned: 670 (million)
% 23.83/4.03 % (904191)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=1745562888:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2968 on theBenchmark for (2968ds/376Mi)
% 23.83/4.03 % (904187)Instruction limit reached!
% 23.83/4.03 % (904187)------------------------------
% 23.83/4.03 % (904187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/4.03 % (904187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/4.03 % (904187)CaDiCaL version: 2.1.3
% 23.83/4.03 % (904187)Termination reason: Instruction limit
% 23.83/4.03 % (904187)Termination phase: Saturation
% 23.83/4.03 % (904187)Time elapsed: 0.066 s
% 23.83/4.03 % (904187)Peak memory usage: 12 MB
% 23.83/4.03 % (904187)Instructions burned: 341 (million)
% 23.83/4.03 % (904193)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=2364002424:i=766:bd=all:rtra=on_2968 on theBenchmark for (2968ds/766Mi)
% 23.83/4.03 % (904176)Instruction limit reached!
% 23.83/4.03 % (904176)------------------------------
% 23.83/4.03 % (904176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/4.03 % (904176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/4.03 % (904176)CaDiCaL version: 2.1.3
% 23.83/4.03 % (904176)Termination reason: Instruction limit
% 23.83/4.03 % (904176)Termination phase: Saturation
% 23.83/4.03 % (904176)Time elapsed: 0.300 s
% 23.83/4.03 % (904176)Peak memory usage: 13 MB
% 23.83/4.03 % (904176)Instructions burned: 693 (million)
% 23.83/4.03 % (904175)Refutation not found, incomplete strategy
% 23.83/4.03 % (904175)------------------------------
% 23.83/4.03 % (904175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/4.03 % (904175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/4.03 % (904175)CaDiCaL version: 2.1.3
% 23.83/4.03 % (904175)Termination reason: Refutation not found, incomplete strategy
% 23.83/4.03 % (904175)Time elapsed: 0.314 s
% 23.83/4.03 % (904175)Peak memory usage: 19 MB
% 23.83/4.03 % (904175)Instructions burned: 758 (million)
% 23.83/4.03 % (904175)------------------------------
% 23.83/4.03 % (904175)------------------------------
% 23.83/4.03 % (904195)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 23.83/4.03 % (904195)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=991022242:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2967 on theBenchmark for (2967ds/959Mi)
% 23.83/4.03 % (904196)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=2035026731:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2967 on theBenchmark for (2967ds/6359Mi)
% 23.83/4.03 % (904191)Instruction limit reached!
% 23.83/4.03 % (904191)------------------------------
% 23.83/4.03 % (904191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/4.03 % (904191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/4.03 % (904191)CaDiCaL version: 2.1.3
% 23.83/4.03 % (904191)Termination reason: Instruction limit
% 23.83/4.03 % (904191)Termination phase: Saturation
% 23.83/4.03 % (904191)Time elapsed: 0.150 s
% 23.83/4.03 % (904191)Peak memory usage: 12 MB
% 23.83/4.03 % (904191)Instructions burned: 378 (million)
% 23.83/4.03 % (904199)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=731172913:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2966 on theBenchmark for (2966ds/35Mi)
% 26.61/4.10 % (904193)Instruction limit reached!
% 26.61/4.10 % (904193)------------------------------
% 26.61/4.10 % (904193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.61/4.10 % (904193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.61/4.10 % (904193)CaDiCaL version: 2.1.3
% 26.61/4.10 % (904193)Termination reason: Instruction limit
% 26.61/4.10 % (904193)Termination phase: Saturation
% 26.61/4.10 % (904193)Time elapsed: 0.163 s
% 26.61/4.10 % (904193)Peak memory usage: 13 MB
% 26.61/4.10 % (904193)Instructions burned: 771 (million)
% 26.61/4.10 % (904199)Instruction limit reached!
% 26.61/4.10 % (904199)------------------------------
% 26.61/4.10 % (904199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.61/4.10 % (904199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.61/4.10 % (904199)CaDiCaL version: 2.1.3
% 26.61/4.10 % (904199)Termination reason: Instruction limit
% 26.61/4.10 % (904199)Termination phase: Preprocessing 2
% 26.61/4.10 % (904199)Time elapsed: 0.016 s
% 26.61/4.10 % (904199)Peak memory usage: 11 MB
% 26.61/4.10 % (904199)Instructions burned: 37 (million)
% 26.61/4.10 % (904201)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=1766351156:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2966 on theBenchmark for (2966ds/53Mi)
% 26.61/4.10 % (904201)Instruction limit reached!
% 26.61/4.10 % (904201)------------------------------
% 26.61/4.10 % (904201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.61/4.10 % (904201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.61/4.10 % (904201)CaDiCaL version: 2.1.3
% 26.61/4.10 % (904201)Termination reason: Instruction limit
% 26.61/4.10 % (904201)Termination phase: Function definition elimination
% 26.61/4.10 % (904201)Time elapsed: 0.012 s
% 26.61/4.10 % (904201)Peak memory usage: 10 MB
% 26.61/4.10 % (904201)Instructions burned: 57 (million)
% 26.61/4.10 % (904202)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=1156944512:s2a=on:i=876:s2at=6:nm=2:rtra=on_2966 on theBenchmark for (2966ds/876Mi)
% 26.61/4.10 % (904204)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=572286487:i=57:ep=R:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/57Mi)
% 26.61/4.10 % (904204)Instruction limit reached!
% 26.61/4.10 % (904204)------------------------------
% 26.61/4.10 % (904204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.61/4.10 % (904204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.61/4.10 % (904204)CaDiCaL version: 2.1.3
% 26.61/4.10 % (904204)Termination reason: Instruction limit
% 26.61/4.10 % (904204)Termination phase: Function definition elimination
% 26.61/4.10 % (904204)Time elapsed: 0.013 s
% 26.61/4.10 % (904204)Peak memory usage: 10 MB
% 26.61/4.10 % (904204)Instructions burned: 59 (million)
% 26.61/4.10 % (904207)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 26.61/4.10 % (904207)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=303844161:i=306:bd=all:rtra=on_2965 on theBenchmark for (2965ds/306Mi)
% 26.61/4.11 % (904207)Instruction limit reached!
% 26.61/4.11 % (904207)------------------------------
% 26.61/4.11 % (904207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.61/4.11 % (904207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.61/4.11 % (904207)CaDiCaL version: 2.1.3
% 26.61/4.11 % (904207)Termination reason: Instruction limit
% 26.61/4.11 % (904207)Termination phase: Property scanning
% 26.61/4.11 % (904207)Time elapsed: 0.061 s
% 26.61/4.11 % (904207)Peak memory usage: 11 MB
% 26.61/4.11 % (904207)Instructions burned: 310 (million)
% 26.61/4.11 % (904209)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=237482066:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2965 on theBenchmark for (2965ds/262Mi)
% 26.61/4.11 % (904209)Instruction limit reached!
% 26.61/4.11 % (904209)------------------------------
% 26.61/4.11 % (904209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.61/4.11 % (904209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.61/4.11 % (904209)CaDiCaL version: 2.1.3
% 27.27/4.30 % (904209)Termination reason: Instruction limit
% 27.27/4.30 % (904209)Termination phase: Saturation
% 27.27/4.30 % (904209)Time elapsed: 0.054 s
% 27.27/4.30 % (904209)Peak memory usage: 12 MB
% 27.27/4.30 % (904209)Instructions burned: 263 (million)
% 27.27/4.30 % (904211)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 27.27/4.30 % (904211)ott+1002_16_sil=128000:si=on:random_seed=1344743945:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2964 on theBenchmark for (2964ds/409Mi)
% 27.27/4.30 % (904195)Instruction limit reached!
% 27.27/4.30 % (904195)------------------------------
% 27.27/4.30 % (904195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.27/4.30 % (904195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.27/4.30 % (904195)CaDiCaL version: 2.1.3
% 27.27/4.30 % (904195)Termination reason: Instruction limit
% 27.27/4.30 % (904195)Termination phase: Saturation
% 27.27/4.30 % (904195)Time elapsed: 0.384 s
% 27.27/4.30 % (904195)Peak memory usage: 13 MB
% 27.27/4.30 % (904195)Instructions burned: 961 (million)
% 27.27/4.30 % (904213)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=1770309067:s2a=on:i=381:rtra=on_2963 on theBenchmark for (2963ds/381Mi)
% 27.27/4.30 % (904211)Instruction limit reached!
% 27.27/4.30 % (904211)------------------------------
% 27.27/4.30 % (904211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.27/4.30 % (904211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.27/4.30 % (904211)CaDiCaL version: 2.1.3
% 27.27/4.30 % (904211)Termination reason: Instruction limit
% 27.27/4.30 % (904211)Termination phase: Saturation
% 27.27/4.30 % (904211)Time elapsed: 0.085 s
% 27.27/4.30 % (904211)Peak memory usage: 13 MB
% 27.27/4.30 % (904211)Instructions burned: 412 (million)
% 27.27/4.30 % (904185)Refutation not found, incomplete strategy
% 27.27/4.30 % (904185)------------------------------
% 27.27/4.30 % (904185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.27/4.30 % (904185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.27/4.30 % (904185)CaDiCaL version: 2.1.3
% 27.27/4.30 % (904185)Termination reason: Refutation not found, incomplete strategy
% 27.27/4.30 % (904185)Time elapsed: 0.574 s
% 27.27/4.30 % (904185)Peak memory usage: 30 MB
% 27.27/4.30 % (904185)Instructions burned: 1362 (million)
% 27.27/4.30 % (904185)------------------------------
% 27.27/4.30 % (904185)------------------------------
% 27.27/4.30 % (904215)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4280625009:cond=on:i=324:rtra=on:ntd=on_2963 on theBenchmark for (2963ds/324Mi)
% 27.27/4.30 % (904216)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=2066827157:i=240:kws=inv_precedence:rtra=on_2963 on theBenchmark for (2963ds/240Mi)
% 27.27/4.30 % (904215)Instruction limit reached!
% 27.27/4.30 % (904215)------------------------------
% 27.27/4.30 % (904215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.27/4.30 % (904215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.27/4.30 % (904215)CaDiCaL version: 2.1.3
% 27.27/4.30 % (904215)Termination reason: Instruction limit
% 27.27/4.30 % (904215)Termination phase: Saturation
% 27.27/4.30 % (904215)Time elapsed: 0.071 s
% 27.27/4.30 % (904215)Peak memory usage: 12 MB
% 27.27/4.30 % (904215)Instructions burned: 329 (million)
% 27.27/4.30 % (904219)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 27.27/4.30 % (904219)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=606033844:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2962 on theBenchmark for (2962ds/124Mi)
% 27.27/4.30 % (904202)Instruction limit reached!
% 27.27/4.30 % (904202)------------------------------
% 27.27/4.30 % (904202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.27/4.30 % (904202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.27/4.30 % (904202)CaDiCaL version: 2.1.3
% 27.27/4.30 % (904202)Termination reason: Instruction limit
% 27.27/4.30 % (904202)Termination phase: Saturation
% 27.27/4.30 % (904202)Time elapsed: 0.353 s
% 27.27/4.30 % (904202)Peak memory usage: 14 MB
% 27.27/4.30 % (904202)Instructions burned: 876 (million)
% 27.27/4.30 % (904219)Instruction limit reached!
% 27.27/4.30 % (904219)------------------------------
% 27.27/4.30 % (904219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.27/4.30 % (904219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.59 % (904219)CaDiCaL version: 2.1.3
% 28.96/4.59 % (904219)Termination reason: Instruction limit
% 28.96/4.59 % (904219)Termination phase: Property scanning
% 28.96/4.59 % (904219)Time elapsed: 0.027 s
% 28.96/4.59 % (904219)Peak memory usage: 11 MB
% 28.96/4.59 % (904219)Instructions burned: 129 (million)
% 28.96/4.59 % (904221)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=3391159553:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2962 on theBenchmark for (2962ds/223Mi)
% 28.96/4.59 % (904216)Instruction limit reached!
% 28.96/4.59 % (904216)------------------------------
% 28.96/4.59 % (904216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.59 % (904216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.59 % (904216)CaDiCaL version: 2.1.3
% 28.96/4.59 % (904216)Termination reason: Instruction limit
% 28.96/4.59 % (904216)Termination phase: Saturation
% 28.96/4.59 % (904216)Time elapsed: 0.102 s
% 28.96/4.59 % (904216)Peak memory usage: 14 MB
% 28.96/4.59 % (904216)Instructions burned: 241 (million)
% 28.96/4.59 % (904213)Instruction limit reached!
% 28.96/4.59 % (904213)------------------------------
% 28.96/4.59 % (904213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.59 % (904213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.59 % (904213)CaDiCaL version: 2.1.3
% 28.96/4.59 % (904213)Termination reason: Instruction limit
% 28.96/4.59 % (904213)Termination phase: Saturation
% 28.96/4.59 % (904213)Time elapsed: 0.150 s
% 28.96/4.59 % (904213)Peak memory usage: 12 MB
% 28.96/4.59 % (904213)Instructions burned: 381 (million)
% 28.96/4.59 % (904222)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=914619600:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2962 on theBenchmark for (2962ds/282Mi)
% 28.96/4.59 % (904224)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=2467033206:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2962 on theBenchmark for (2962ds/464Mi)
% 28.96/4.59 % (904189)Instruction limit reached!
% 28.96/4.59 % (904189)------------------------------
% 28.96/4.59 % (904189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.59 % (904189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.59 % (904189)CaDiCaL version: 2.1.3
% 28.96/4.59 % (904189)Termination reason: Instruction limit
% 28.96/4.59 % (904189)Termination phase: Saturation
% 28.96/4.59 % (904189)Time elapsed: 0.649 s
% 28.96/4.59 % (904189)Peak memory usage: 21 MB
% 28.96/4.59 % (904189)Instructions burned: 1143 (million)
% 28.96/4.59 % (904225)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=605246256:i=88:s2at=3:nm=2:rtra=on:rawr=on_2962 on theBenchmark for (2962ds/88Mi)
% 28.96/4.59 % (904228)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=4108706401:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2962 on theBenchmark for (2962ds/280Mi)
% 28.96/4.59 % (904221)Instruction limit reached!
% 28.96/4.59 % (904221)------------------------------
% 28.96/4.59 % (904221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.59 % (904221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.59 % (904221)CaDiCaL version: 2.1.3
% 28.96/4.59 % (904221)Termination reason: Instruction limit
% 28.96/4.59 % (904221)Termination phase: Property scanning
% 28.96/4.59 % (904221)Time elapsed: 0.046 s
% 28.96/4.59 % (904221)Peak memory usage: 11 MB
% 28.96/4.59 % (904221)Instructions burned: 226 (million)
% 28.96/4.59 % (904231)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 28.96/4.59 % (904231)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2035007413:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2961 on theBenchmark for (2961ds/4386Mi)
% 28.96/4.59 % (904225)Instruction limit reached!
% 28.96/4.59 % (904225)------------------------------
% 28.96/4.59 % (904225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.59 % (904225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.59 % (904225)CaDiCaL version: 2.1.3
% 28.96/4.59 % (904225)Termination reason: Instruction limit
% 28.96/4.59 % (904225)Termination phase: Function definition elimination
% 30.76/5.00 % (904225)Time elapsed: 0.036 s
% 30.76/5.00 % (904225)Peak memory usage: 11 MB
% 30.76/5.00 % (904225)Instructions burned: 89 (million)
% 30.76/5.00 % (904233)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 30.76/5.00 % (904233)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 30.76/5.00 % (904233)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=2467738248:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2961 on theBenchmark for (2961ds/483Mi)
% 30.76/5.00 % (904228)Instruction limit reached!
% 30.76/5.00 % (904228)------------------------------
% 30.76/5.00 % (904228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.76/5.00 % (904228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.76/5.00 % (904228)CaDiCaL version: 2.1.3
% 30.76/5.00 % (904228)Termination reason: Instruction limit
% 30.76/5.00 % (904228)Termination phase: Property scanning
% 30.76/5.00 % (904228)Time elapsed: 0.109 s
% 30.76/5.00 % (904228)Peak memory usage: 11 MB
% 30.76/5.00 % (904228)Instructions burned: 282 (million)
% 30.76/5.00 % (904235)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2600945874:i=73:rtra=on_2960 on theBenchmark for (2960ds/73Mi)
% 30.76/5.00 % (904235)Instruction limit reached!
% 30.76/5.00 % (904235)------------------------------
% 30.76/5.00 % (904235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.76/5.00 % (904235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.76/5.00 % (904235)CaDiCaL version: 2.1.3
% 30.76/5.00 % (904235)Termination reason: Instruction limit
% 30.76/5.00 % (904235)Termination phase: Function definition elimination
% 30.76/5.00 % (904235)Time elapsed: 0.031 s
% 30.76/5.00 % (904235)Peak memory usage: 11 MB
% 30.76/5.00 % (904235)Instructions burned: 75 (million)
% 30.76/5.00 % (904222)Instruction limit reached!
% 30.76/5.00 % (904222)------------------------------
% 30.76/5.00 % (904222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.76/5.00 % (904222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.76/5.00 % (904222)CaDiCaL version: 2.1.3
% 30.76/5.00 % (904222)Termination reason: Instruction limit
% 30.76/5.00 % (904222)Termination phase: Saturation
% 30.76/5.00 % (904222)Time elapsed: 0.191 s
% 30.76/5.00 % (904222)Peak memory usage: 15 MB
% 30.76/5.00 % (904222)Instructions burned: 282 (million)
% 30.76/5.00 % (904237)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2535446401:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2960 on theBenchmark for (2960ds/176Mi)
% 30.76/5.00 % (904238)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 30.76/5.00 % (904224)Instruction limit reached!
% 30.76/5.00 % (904224)------------------------------
% 30.76/5.00 % (904224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.76/5.00 % (904224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.76/5.00 % (904224)CaDiCaL version: 2.1.3
% 30.76/5.00 % (904224)Termination reason: Instruction limit
% 30.76/5.00 % (904224)Termination phase: Saturation
% 30.76/5.00 % (904224)Time elapsed: 0.206 s
% 30.76/5.00 % (904224)Peak memory usage: 14 MB
% 30.76/5.00 % (904224)Instructions burned: 465 (million)
% 30.76/5.00 % (904238)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3600672212:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2960 on theBenchmark for (2960ds/39Mi)
% 30.76/5.00 % (904238)Instruction limit reached!
% 30.76/5.00 % (904238)------------------------------
% 30.76/5.00 % (904238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.76/5.00 % (904238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.76/5.00 % (904238)CaDiCaL version: 2.1.3
% 30.76/5.00 % (904238)Termination reason: Instruction limit
% 30.76/5.00 % (904238)Termination phase: Property scanning
% 30.76/5.00 % (904238)Time elapsed: 0.017 s
% 30.76/5.00 % (904238)Peak memory usage: 11 MB
% 30.76/5.00 % (904238)Instructions burned: 41 (million)
% 30.76/5.00 % (904241)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2627617587:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2960 on theBenchmark for (2960ds/708Mi)
% 30.76/5.00 % (904243)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 34.37/5.17 % (904243)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=268178894:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2959 on theBenchmark for (2959ds/252Mi)
% 34.37/5.17 % (904237)Instruction limit reached!
% 34.37/5.17 % (904237)------------------------------
% 34.37/5.17 % (904237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.37/5.17 % (904237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.37/5.17 % (904237)CaDiCaL version: 2.1.3
% 34.37/5.17 % (904237)Termination reason: Instruction limit
% 34.37/5.17 % (904237)Termination phase: Property scanning
% 34.37/5.17 % (904237)Time elapsed: 0.074 s
% 34.37/5.17 % (904237)Peak memory usage: 11 MB
% 34.37/5.17 % (904237)Instructions burned: 177 (million)
% 34.37/5.17 % (904245)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=202460609:i=823:fsr=off:rtra=on_2959 on theBenchmark for (2959ds/823Mi)
% 34.37/5.17 % (904233)Instruction limit reached!
% 34.37/5.17 % (904233)------------------------------
% 34.37/5.17 % (904233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.37/5.17 % (904233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.37/5.17 % (904233)CaDiCaL version: 2.1.3
% 34.37/5.17 % (904233)Termination reason: Instruction limit
% 34.37/5.17 % (904233)Termination phase: Saturation
% 34.37/5.17 % (904233)Time elapsed: 0.261 s
% 34.37/5.17 % (904233)Peak memory usage: 17 MB
% 34.37/5.17 % (904233)Instructions burned: 483 (million)
% 34.37/5.17 % (904247)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 34.37/5.17 % (904247)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=3308401104:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2958 on theBenchmark for (2958ds/16202Mi)
% 34.37/5.17 % (904243)Instruction limit reached!
% 34.37/5.17 % (904243)------------------------------
% 34.37/5.17 % (904243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.37/5.17 % (904243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.37/5.17 % (904243)CaDiCaL version: 2.1.3
% 34.37/5.17 % (904243)Termination reason: Instruction limit
% 34.37/5.17 % (904243)Termination phase: Property scanning
% 34.37/5.17 % (904243)Time elapsed: 0.153 s
% 34.37/5.17 % (904243)Peak memory usage: 11 MB
% 34.37/5.17 % (904243)Instructions burned: 252 (million)
% 34.37/5.17 % (904249)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=2887504187:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2958 on theBenchmark for (2958ds/300Mi)
% 34.37/5.17 % (904241)Instruction limit reached!
% 34.37/5.17 % (904241)------------------------------
% 34.37/5.17 % (904241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.37/5.17 % (904241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.37/5.17 % (904241)CaDiCaL version: 2.1.3
% 34.37/5.17 % (904241)Termination reason: Instruction limit
% 34.37/5.17 % (904241)Termination phase: Saturation
% 34.37/5.17 % (904241)Time elapsed: 0.278 s
% 34.37/5.17 % (904241)Peak memory usage: 13 MB
% 34.37/5.17 % (904241)Instructions burned: 710 (million)
% 34.37/5.17 % (904251)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 34.37/5.17 % (904251)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 34.37/5.17 % (904251)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=144133609:i=177:add=on:bd=preordered:rtra=on:rawr=on_2957 on theBenchmark for (2957ds/177Mi)
% 34.37/5.17 % (904249)Instruction limit reached!
% 34.37/5.17 % (904249)------------------------------
% 34.37/5.17 % (904249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.37/5.17 % (904249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.37/5.17 % (904249)CaDiCaL version: 2.1.3
% 34.37/5.17 % (904249)Termination reason: Instruction limit
% 34.37/5.17 % (904249)Termination phase: Property scanning
% 34.37/5.17 % (904249)Time elapsed: 0.117 s
% 34.37/5.17 % (904249)Peak memory usage: 11 MB
% 37.00/5.65 % (904249)Instructions burned: 301 (million)
% 37.00/5.65 % (904253)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=672220038:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2956 on theBenchmark for (2956ds/715Mi)
% 37.00/5.65 % (904251)Instruction limit reached!
% 37.00/5.65 % (904251)------------------------------
% 37.00/5.65 % (904251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.00/5.65 % (904251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.00/5.65 % (904251)CaDiCaL version: 2.1.3
% 37.00/5.65 % (904251)Termination reason: Instruction limit
% 37.00/5.65 % (904251)Termination phase: Property scanning
% 37.00/5.65 % (904251)Time elapsed: 0.070 s
% 37.00/5.65 % (904251)Peak memory usage: 11 MB
% 37.00/5.65 % (904251)Instructions burned: 178 (million)
% 37.00/5.65 % (904255)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 37.00/5.65 % (904255)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 37.00/5.65 % (904255)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=1868527133:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2956 on theBenchmark for (2956ds/230Mi)
% 37.00/5.65 % (904245)Instruction limit reached!
% 37.00/5.65 % (904245)------------------------------
% 37.00/5.65 % (904245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.00/5.65 % (904245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.00/5.65 % (904245)CaDiCaL version: 2.1.3
% 37.00/5.65 % (904245)Termination reason: Instruction limit
% 37.00/5.65 % (904245)Termination phase: Saturation
% 37.00/5.65 % (904245)Time elapsed: 0.332 s
% 37.00/5.65 % (904245)Peak memory usage: 13 MB
% 37.00/5.65 % (904245)Instructions burned: 824 (million)
% 37.00/5.65 % (904257)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=2930021860:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2955 on theBenchmark for (2955ds/606Mi)
% 37.00/5.65 % (904255)Instruction limit reached!
% 37.00/5.65 % (904255)------------------------------
% 37.00/5.65 % (904255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.00/5.65 % (904255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.00/5.65 % (904255)CaDiCaL version: 2.1.3
% 37.00/5.65 % (904255)Termination reason: Instruction limit
% 37.00/5.65 % (904255)Termination phase: Property scanning
% 37.00/5.65 % (904255)Time elapsed: 0.089 s
% 37.00/5.65 % (904255)Peak memory usage: 11 MB
% 37.00/5.65 % (904255)Instructions burned: 232 (million)
% 37.00/5.65 % (904259)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 37.00/5.65 % (904259)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=1356789218:lrd=on:i=841:nm=0:rtra=on_2955 on theBenchmark for (2955ds/841Mi)
% 37.00/5.65 % (904257)Instruction limit reached!
% 37.00/5.65 % (904257)------------------------------
% 37.00/5.65 % (904257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.00/5.65 % (904257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.00/5.65 % (904257)CaDiCaL version: 2.1.3
% 37.00/5.65 % (904257)Termination reason: Instruction limit
% 37.00/5.65 % (904257)Termination phase: Saturation
% 37.00/5.65 % (904257)Time elapsed: 0.241 s
% 37.00/5.65 % (904257)Peak memory usage: 13 MB
% 37.00/5.65 % (904257)Instructions burned: 607 (million)
% 37.00/5.65 % (904261)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=507257772:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2953 on theBenchmark for (2953ds/445Mi)
% 37.00/5.65 % (904253)Instruction limit reached!
% 37.00/5.65 % (904253)------------------------------
% 37.00/5.65 % (904253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.00/5.65 % (904253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.00/5.65 % (904253)CaDiCaL version: 2.1.3
% 37.00/5.65 % (904253)Termination reason: Instruction limit
% 37.00/5.65 % (904253)Termination phase: Saturation
% 37.00/5.65 % (904253)Time elapsed: 0.368 s
% 37.00/5.65 % (904253)Peak memory usage: 15 MB
% 37.00/5.65 % (904253)Instructions burned: 715 (million)
% 37.00/5.65 % (904263)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=2522740581:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2952 on theBenchmark for (2952ds/71Mi)
% 38.11/5.99 % (904263)Instruction limit reached!
% 38.11/5.99 % (904263)------------------------------
% 38.11/5.99 % (904263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.11/5.99 % (904263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.11/5.99 % (904263)CaDiCaL version: 2.1.3
% 38.11/5.99 % (904263)Termination reason: Instruction limit
% 38.11/5.99 % (904263)Termination phase: Function definition elimination
% 38.11/5.99 % (904263)Time elapsed: 0.055 s
% 38.11/5.99 % (904263)Peak memory usage: 11 MB
% 38.11/5.99 % (904263)Instructions burned: 72 (million)
% 38.11/5.99 % (904265)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 38.11/5.99 % (904265)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 38.11/5.99 % (904265)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1991713120:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2952 on theBenchmark for (2952ds/100Mi)
% 38.11/5.99 % (904231)Instruction limit reached!
% 38.11/5.99 % (904231)------------------------------
% 38.11/5.99 % (904231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.11/5.99 % (904231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.11/5.99 % (904231)CaDiCaL version: 2.1.3
% 38.11/5.99 % (904231)Termination reason: Instruction limit
% 38.11/5.99 % (904231)Termination phase: Saturation
% 38.11/5.99 % (904231)Time elapsed: 0.989 s
% 38.11/5.99 % (904231)Peak memory usage: 43 MB
% 38.11/5.99 % (904231)Instructions burned: 4387 (million)
% 38.11/5.99 % (904267)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 38.11/5.99 % (904267)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=3436605050:i=1352:add=on:aac=none:rtra=on_2951 on theBenchmark for (2951ds/1352Mi)
% 38.11/5.99 % (904259)Instruction limit reached!
% 38.11/5.99 % (904259)------------------------------
% 38.11/5.99 % (904259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.11/5.99 % (904259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.11/5.99 % (904259)CaDiCaL version: 2.1.3
% 38.11/5.99 % (904259)Termination reason: Instruction limit
% 38.11/5.99 % (904259)Termination phase: Saturation
% 38.11/5.99 % (904259)Time elapsed: 0.331 s
% 38.11/5.99 % (904259)Peak memory usage: 13 MB
% 38.11/5.99 % (904259)Instructions burned: 841 (million)
% 38.11/5.99 % (904265)Instruction limit reached!
% 38.11/5.99 % (904265)------------------------------
% 38.11/5.99 % (904265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.11/5.99 % (904265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.11/5.99 % (904265)CaDiCaL version: 2.1.3
% 38.11/5.99 % (904265)Termination reason: Instruction limit
% 38.11/5.99 % (904265)Termination phase: Twee Goal Transformation
% 38.11/5.99 % (904265)Time elapsed: 0.040 s
% 38.11/5.99 % (904265)Peak memory usage: 11 MB
% 38.11/5.99 % (904265)Instructions burned: 100 (million)
% 38.11/5.99 % (904269)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=2629269678:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2951 on theBenchmark for (2951ds/646Mi)
% 38.11/5.99 % (904270)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=2269210322:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2951 on theBenchmark for (2951ds/1924Mi)
% 38.11/5.99 % (904261)Instruction limit reached!
% 38.11/5.99 % (904261)------------------------------
% 38.11/5.99 % (904261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.11/5.99 % (904261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.11/5.99 % (904261)CaDiCaL version: 2.1.3
% 38.11/5.99 % (904261)Termination reason: Instruction limit
% 38.11/5.99 % (904261)Termination phase: Saturation
% 38.11/5.99 % (904261)Time elapsed: 0.174 s
% 38.11/5.99 % (904261)Peak memory usage: 12 MB
% 38.11/5.99 % (904261)Instructions burned: 445 (million)
% 38.11/5.99 % (904273)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1794594022:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2951 on theBenchmark for (2951ds/984Mi)
% 40.79/6.05 % (904269)Instruction limit reached!
% 40.79/6.05 % (904269)------------------------------
% 40.79/6.05 % (904269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904269)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904269)Termination reason: Instruction limit
% 40.79/6.05 % (904269)Termination phase: Saturation
% 40.79/6.05 % (904269)Time elapsed: 0.256 s
% 40.79/6.05 % (904269)Peak memory usage: 13 MB
% 40.79/6.05 % (904269)Instructions burned: 646 (million)
% 40.79/6.05 % (904267)Instruction limit reached!
% 40.79/6.05 % (904267)------------------------------
% 40.79/6.05 % (904267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904267)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904267)Termination reason: Instruction limit
% 40.79/6.05 % (904267)Termination phase: Saturation
% 40.79/6.05 % (904267)Time elapsed: 0.300 s
% 40.79/6.05 % (904267)Peak memory usage: 27 MB
% 40.79/6.05 % (904267)Instructions burned: 1358 (million)
% 40.79/6.05 % (904275)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=938594897:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2948 on theBenchmark for (2948ds/592Mi)
% 40.79/6.05 % (904276)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=3471234997:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2948 on theBenchmark for (2948ds/872Mi)
% 40.79/6.05 % (904273)Instruction limit reached!
% 40.79/6.05 % (904273)------------------------------
% 40.79/6.05 % (904273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904273)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904273)Termination reason: Instruction limit
% 40.79/6.05 % (904273)Termination phase: Saturation
% 40.79/6.05 % (904273)Time elapsed: 0.391 s
% 40.79/6.05 % (904273)Peak memory usage: 13 MB
% 40.79/6.05 % (904273)Instructions burned: 985 (million)
% 40.79/6.05 % (904279)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 40.79/6.05 % (904279)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1711308379:i=999:add=on:rtra=on_2947 on theBenchmark for (2947ds/999Mi)
% 40.79/6.05 % (904276)Instruction limit reached!
% 40.79/6.05 % (904276)------------------------------
% 40.79/6.05 % (904276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904276)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904276)Termination reason: Instruction limit
% 40.79/6.05 % (904276)Termination phase: Saturation
% 40.79/6.05 % (904276)Time elapsed: 0.182 s
% 40.79/6.05 % (904276)Peak memory usage: 13 MB
% 40.79/6.05 % (904276)Instructions burned: 873 (million)
% 40.79/6.05 % (904281)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 40.79/6.05 % (904281)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=355448713:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2946 on theBenchmark for (2946ds/244Mi)
% 40.79/6.05 % (904045)Instruction limit reached!
% 40.79/6.05 % (904045)------------------------------
% 40.79/6.05 % (904045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904045)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904045)Termination reason: Instruction limit
% 40.79/6.05 % (904045)Termination phase: Saturation
% 40.79/6.05 % (904045)Time elapsed: 4.372 s
% 40.79/6.05 % (904045)Peak memory usage: 30 MB
% 40.79/6.05 % (904045)Instructions burned: 9842 (million)
% 40.79/6.05 % (904281)Instruction limit reached!
% 40.79/6.05 % (904281)------------------------------
% 40.79/6.05 % (904281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904281)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904281)Termination reason: Instruction limit
% 40.79/6.05 % (904281)Termination phase: Property scanning
% 40.79/6.05 % (904281)Time elapsed: 0.049 s
% 40.79/6.05 % (904281)Peak memory usage: 10 MB
% 40.79/6.05 % (904281)Instructions burned: 245 (million)
% 40.79/6.05 % (904284)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1881109007:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2946 on theBenchmark for (2946ds/7795Mi)
% 40.79/6.05 % (904283)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=2060172687:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2946 on theBenchmark for (2946ds/113Mi)
% 40.79/6.05 % (904275)Instruction limit reached!
% 40.79/6.05 % (904275)------------------------------
% 40.79/6.05 % (904275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904275)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904275)Termination reason: Instruction limit
% 40.79/6.05 % (904275)Termination phase: Saturation
% 40.79/6.05 % (904275)Time elapsed: 0.292 s
% 40.79/6.05 % (904275)Peak memory usage: 15 MB
% 40.79/6.05 % (904275)Instructions burned: 592 (million)
% 40.79/6.05 % (904283)Instruction limit reached!
% 40.79/6.05 % (904283)------------------------------
% 40.79/6.05 % (904283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904283)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904283)Termination reason: Instruction limit
% 40.79/6.05 % (904283)Termination phase: Property scanning
% 40.79/6.05 % (904283)Time elapsed: 0.046 s
% 40.79/6.05 % (904283)Peak memory usage: 11 MB
% 40.79/6.05 % (904283)Instructions burned: 116 (million)
% 40.79/6.05 % (904287)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=326223544:st=2:i=5026:sd=1:rtra=on:ss=axioms_2945 on theBenchmark for (2945ds/5026Mi)
% 40.79/6.05 % (904288)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 40.79/6.05 % (904288)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=1708564896:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2945 on theBenchmark for (2945ds/763Mi)
% 40.79/6.05 % (904270)Instruction limit reached!
% 40.79/6.05 % (904270)------------------------------
% 40.79/6.05 % (904270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904270)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904270)Termination reason: Instruction limit
% 40.79/6.05 % (904270)Termination phase: Saturation
% 40.79/6.05 % (904270)Time elapsed: 0.796 s
% 40.79/6.05 % (904270)Peak memory usage: 13 MB
% 40.79/6.05 % (904270)Instructions burned: 1926 (million)
% 40.79/6.05 % (904288) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-903875-904288"...
% 40.79/6.05 % (904291)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4106857476:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2943 on theBenchmark for (2943ds/1144Mi)
% 40.79/6.05 % (904196)Instruction limit reached!
% 40.79/6.05 % (904196)------------------------------
% 40.79/6.05 % (904196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904196)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904196)Termination reason: Instruction limit
% 40.79/6.05 % (904196)Termination phase: Saturation
% 40.79/6.05 % (904196)Time elapsed: 2.462 s
% 40.79/6.05 % (904196)Peak memory usage: 13 MB
% 40.79/6.05 % (904196)Instructions burned: 6361 (million)
% 40.79/6.05 % (904279)Instruction limit reached!
% 40.79/6.05 % (904279)------------------------------
% 40.79/6.05 % (904279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904279)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904279)Termination reason: Instruction limit
% 40.79/6.05 % (904279)Termination phase: Saturation
% 40.79/6.05 % (904279)Time elapsed: 0.395 s
% 40.79/6.05 % (904279)Peak memory usage: 13 MB
% 40.79/6.05 % (904279)Instructions burned: 1000 (million)
% 40.79/6.05 % (904293)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 40.79/6.05 % (904293)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=1472377076:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2942 on theBenchmark for (2942ds/52Mi)
% 40.79/6.05 % (904294)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=1730552669:i=1724:fsr=off:rtra=on:fe=abstraction_2942 on theBenchmark for (2942ds/1724Mi)
% 40.79/6.05 % (904293)Instruction limit reached!
% 40.79/6.05 % (904293)------------------------------
% 40.79/6.05 % (904293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.05 % (904293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.05 % (904293)CaDiCaL version: 2.1.3
% 40.79/6.05 % (904293)Termination reason: Instruction limit
% 40.79/6.05 % (904293)Termination phase: Function definition elimination
% 40.79/6.05 % (904293)Time elapsed: 0.022 s
% 40.79/6.05 % (904293)Peak memory usage: 11 MB
% 40.79/6.05 % (904293)Instructions burned: 53 (million)
% 40.79/6.05 % (904297)dis-1004_128_to=kbo:sil=128000:tgt=full:si=on:fdtod=off:sp=const_frequency:spb=goal:uwa=off:slsqc=3:slsq=on:random_seed=2466971969:i=439:add=on:slsql=off:rtra=on:ntd=on_2942 on theBenchmark for (2942ds/439Mi)
% 40.79/6.05 % (904288)...printing done.
% 40.79/6.05 % (904288)Refutation found. Thanks to Tanya!
% 40.79/6.05 % SZS status Theorem for theBenchmark
% 40.79/6.05 % SZS output start Proof for theBenchmark
% See solution above
% 40.79/6.06 % (904288)------------------------------
% 40.79/6.06 % (904288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.79/6.06 % (904288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.79/6.06 % (904288)CaDiCaL version: 2.1.3
% 40.79/6.06 % (904288)Termination reason: Refutation
% 40.79/6.06 % (904288)Time elapsed: 0.319 s
% 40.79/6.06 % (904288)Peak memory usage: 18 MB
% 40.79/6.06 % (904288)Instructions burned: 731 (million)
% 40.79/6.06 % (903875)Success in time 5.786 s
% 40.79/6.06 % Vampire exiting
%------------------------------------------------------------------------------