%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV526^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:41:27 AM UTC 2026
% Result : Theorem 48.64s 8.23s
% Output : Refutation 48.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 164 ( 47 unt; 0 typ; 8 def)
% Number of atoms : 8765 ( 366 equ; 0 cnn)
% Maximal formula atoms : 133 ( 53 avg)
% Number of connectives : 44834 ( 131 ~; 302 |; 0 &;42411 @)
% ( 8 <=>; 886 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12196 (12196 >; 0 *; 0 +; 0 <<)
% Number of symbols : 141 ( 136 usr; 17 con; 0-14 aty)
% (1089 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 9387 (9102 ^; 283 !; 2 ?;9387 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
c_Eps_i: ( $i > $o ) > $i ).
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_133,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
sK3: ( ( ( $i > $i ) > $i ) > $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_136,type,
sK4: ( ( ( $i > $i ) > $i ) > $i > $o ) > $i > $i ).
thf(func_def_137,type,
sK5: ( ( ( ( ( $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_138,type,
sK6: ( ( $i > $i ) > ( $i > $i ) > $o ) > ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i ).
thf(func_def_139,type,
sK7: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i ).
thf(func_def_140,type,
sK8: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i ).
thf(func_def_141,type,
sK9: ( ( ( $i > $i ) > $i ) > $i > $o ) > ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $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 > $i ) > $i ) > $i > $o ) > ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i ).
thf(func_def_143,type,
sK11: ( ( ( ( ( $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 > ( $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 ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $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 > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( ( ( ( ( $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 > $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 > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( ( ( ( ( $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 > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( ( ( ( ( $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 > $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 > $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 > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_153,type,
sK21: ( ( ( ( ( $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 > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_155,type,
sK23: ( ( ( ( ( $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(f768,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f351,f526,f550,f609,f652,f702,f732,f741,f762]) ).
thf(f762,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f761]) ).
thf(f761,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f760]) ).
thf(f760,plain,
( ( $true = $false )
| ~ spl0_7 ),
inference(duplicate_literal_removal,[status(thm)],[f759]) ).
thf(f759,plain,
( ( $true = $false )
| ( $true = $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f747]) ).
thf(f747,plain,
( ( $false
= ( ^ [Y0: ( $i > $i ) > $i,Y1: $i] : $true
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i] : $true
@ ^ [Y1: $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 ) ) )
| ~ spl0_7 ),
inference(primitive_instantiation,[status(thm)],[f578]) ).
thf(f578,plain,
( ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( X4
@ ^ [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 ) ) )
| ( ( X4
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty )
= $false ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f577]) ).
thf(f577,definition,
( spl0_7
<=> ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( X4
@ ^ [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 ) ) )
| ( ( X4
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f741,plain,
( spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f739,f607,f577]) ).
thf(f607,definition,
( spl0_10
<=> ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( X4
@ ^ [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 ) ) )
| ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f739,plain,
( ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( X4
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty )
= $false )
| ( $false
= ( X4
@ ^ [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 ) ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f737]) ).
thf(f737,plain,
( ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( ( X4
@ ^ [Y0: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y0: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) )
| ( $false
= ( X4
@ ^ [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 ) ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f736]) ).
thf(f736,plain,
( ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( X4
@ ^ [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
= ( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK9 @ X4
@ ^ [Y0: $i,Y1: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y0: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y0: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f735]) ).
thf(f735,plain,
( ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( X4
@ ^ [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 ) ) )
| ( ( ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) )
@ ( sK9 @ X4 ) )
= $false ) )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f608]) ).
thf(f608,plain,
( ! [X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( $false
= ( X4
@ ^ [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 ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f607]) ).
thf(f732,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[status(thm)],[f731]) ).
thf(f731,plain,
( $false
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f730]) ).
thf(f730,plain,
( ( $true = $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f729]) ).
thf(f729,plain,
( ( $false
= ( ^ [Y0: $i] : $true
@ sK26 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f728]) ).
thf(f728,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f727]) ).
thf(f727,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true )
@ sK25 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f726]) ).
thf(f726,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f725]) ).
thf(f725,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : $true ) )
@ sK24 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f651]) ).
thf(f651,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : $true ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f649]) ).
thf(f649,definition,
( spl0_12
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f702,plain,
( spl0_12
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f699,f646,f649]) ).
thf(f646,definition,
( spl0_11
<=> ! [X3: ( ( ( ( $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_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f699,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : $true ) ) ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f698]) ).
thf(f698,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> $true ) ) ) )
= $false )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f697]) ).
thf(f697,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ $false ) ) ) )
= $false )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f696]) ).
thf(f696,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ $false ) ) ) )
= $false )
| ( $true = $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f689]) ).
thf(f689,plain,
( ( $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
@ ( sK19
@ ^ [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
@ ( sK18
@ ^ [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
@ ( sK20
@ ^ [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
@ ( sK19
@ ^ [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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ ( ^ [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 > $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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false )
| ~ spl0_11 ),
inference(primitive_instantiation,[status(thm)],[f675]) ).
thf(f675,plain,
( ! [X3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( ( X3
@ ^ [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 @ ( sK19 @ X3 ) )
@ ( c_Repl @ ( sK18 @ X3 ) @ 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
@ ( sK20 @ X3
@ ^ [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 @ ( sK19 @ X3 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f673]) ).
thf(f673,plain,
( ! [X3: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( ( ( X3
@ ^ [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 @ ( sK19 @ X3 ) )
@ ( c_Repl @ ( sK18 @ X3 ) @ 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
@ ( sK20 @ X3
@ ^ [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 @ ( sK19 @ X3 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ ( sK17 @ X3 )
@ ( 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 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f672]) ).
thf(f672,plain,
( ! [X3: ( ( ( ( $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_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false )
| ( ( ^ [Y0: ( $i > $i ) > $i] :
( ( X3
@ ^ [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 @ ( sK19 @ X3 ) )
@ ( c_Repl @ ( sK18 @ X3 ) @ 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
@ ( Y0
@ ^ [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 @ ( sK19 @ X3 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ ( sK17 @ X3 )
@ ( 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 ) ) ) )
@ ( sK20 @ X3 ) )
= $false ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f671]) ).
thf(f671,plain,
( ! [X3: ( ( ( ( $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 )
@ ^ [Y0: ( $i > $i ) > $i] :
( ( X3
@ ^ [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 @ ( sK19 @ X3 ) )
@ ( c_Repl @ ( sK18 @ X3 ) @ 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
@ ( Y0
@ ^ [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 @ ( sK19 @ X3 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( c_In @ ( sK17 @ X3 )
@ ( 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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f670]) ).
thf(f670,plain,
( ! [X3: ( ( ( ( $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_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y1: ( $i > $i ) > $i] :
( ( X3
@ ^ [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 @ ( sK18 @ X3 ) @ 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
@ ( Y1
@ ^ [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 @ ( sK17 @ X3 )
@ ( 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 ) ) ) ) )
@ ( sK19 @ X3 ) ) ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f663]) ).
thf(f663,plain,
( ! [X3: ( ( ( ( $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 > $i ) > $i )
@ ^ [Y1: ( $i > $i ) > $i] :
( ( X3
@ ^ [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 @ ( sK18 @ X3 ) @ 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
@ ( Y1
@ ^ [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 @ ( sK17 @ X3 )
@ ( 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 @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f662]) ).
thf(f662,plain,
( ! [X3: ( ( ( ( $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
@ ^ [Y1: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y2: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y2
@ ^ [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 @ ( sK17 @ X3 )
@ ( 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 ) ) ) ) ) )
@ ( sK18 @ X3 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f661]) ).
thf(f661,plain,
( ! [X3: ( ( ( ( $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 > $i ) > $i )
@ ^ [Y2: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y2
@ ^ [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 @ ( sK17 @ X3 )
@ ( 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 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f660]) ).
thf(f660,plain,
( ! [X3: ( ( ( ( $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
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) ) ) ) ) ) )
@ ( sK17 @ X3 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f647]) ).
thf(f647,plain,
( ! [X3: ( ( ( ( $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] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f646]) ).
thf(f652,plain,
( spl0_11
| spl0_12
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f634,f604,f649,f646]) ).
thf(f604,definition,
( spl0_9
<=> ! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X3: ( ( ( ( $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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f634,plain,
( ! [X3: ( ( ( ( $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_Inj1 @ Y1 ) @ Y2 )
=> ~ ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : $true ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) )
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f633]) ).
thf(f633,plain,
( ! [X3: ( ( ( ( $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] : $true ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 )
=> $false ) ) ) ) )
= $false ) )
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f632]) ).
thf(f632,plain,
( ! [X3: ( ( ( ( $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] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> $true ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 )
=> $false ) ) ) ) )
= $false ) )
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f631]) ).
thf(f631,plain,
( ! [X3: ( ( ( ( $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 @ Y2 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( $false
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 )
=> $false ) ) ) ) )
= $false ) )
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f630]) ).
thf(f630,plain,
( ! [X3: ( ( ( ( $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_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 )
=> $false ) ) ) ) )
= $false )
| ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 @ Y2 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( $false
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
= $false ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f628]) ).
thf(f628,plain,
( ! [X3: ( ( ( ( $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,Y1: $i,Y2: $i > $i,Y3: $i] : $false
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( sK13 @ X3
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK12 @ X3
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false )
@ c_Inj1 ) )
@ c_Empty
@ ^ [Y0: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK12 @ X3
@ ^ [Y1: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i > $i,Y4: $i] : $false )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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 )
=> ( ^ [Y3: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i > $i,Y6: $i] : $false
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 @ Y2 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
=> ( ( ^ [Y3: ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i,Y4: $i,Y5: $i > $i,Y6: $i] : $false
@ ^ [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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) )
| ~ spl0_9 ),
inference(primitive_instantiation,[status(thm)],[f619]) ).
thf(f619,plain,
( ! [X3: ( ( ( ( $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] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $true
= ( X1
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( sK13 @ X3 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK12 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y0: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK12 @ X3 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f616]) ).
thf(f616,plain,
( ! [X3: ( ( ( ( $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] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( ( X1
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( sK13 @ X3 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK12 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y0: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK12 @ X3 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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_binunion
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y0: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y0
@ ^ [Y1: $i] : ( sK11 @ X3 @ X1 )
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X3 @ X1 ) @ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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_Inj1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f615]) ).
thf(f615,plain,
( ! [X3: ( ( ( ( $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] :
( ( $false
= ( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
=> ( ( X1
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl @ ( sK13 @ X3 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK12 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y0: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK12 @ X3 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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_binunion
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i,Y2: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y0: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y0
@ ^ [Y1: $i] : ( sK11 @ X3 @ X1 )
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ ( sK14 @ X3 @ X1 ) @ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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_Inj1 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f614]) ).
thf(f614,plain,
( ! [X3: ( ( ( ( $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] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $false
= ( ^ [Y0: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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 @ ( sK13 @ X3 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK12 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK12 @ X3 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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_binunion
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y1
@ ^ [Y2: $i] : ( sK11 @ X3 @ X1 )
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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_Inj1 ) ) ) ) )
@ ( sK14 @ X3 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
( ! [X3: ( ( ( ( $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] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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 @ ( sK13 @ X3 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK12 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y1: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK12 @ X3 @ X1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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_binunion
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i,Y3: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ^ [Y1: ( $i > $i ) > $i > $i] :
( c_binunion
@ ( c_Repl
@ ( c_Inj1
@ ( Y1
@ ^ [Y2: $i] : ( sK11 @ X3 @ X1 )
@ ( 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 @ ( sK13 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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_Inj1 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f612]) ).
thf(f612,plain,
( ! [X3: ( ( ( ( $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_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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 @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK12 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK12 @ X3 @ X1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 @ Y0 @ 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 @ Y1 @ 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 ) ) ) ) ) )
@ ( sK13 @ X3 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f611]) ).
thf(f611,plain,
( ! [X3: ( ( ( ( $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] :
( ( c_In
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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 @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK12 @ X3 @ X1 ) @ c_Inj1 ) )
@ c_Empty
@ ^ [Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK12 @ X3 @ X1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y0 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 @ Y0 @ 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 @ Y1 @ 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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f610]) ).
thf(f610,plain,
( ! [X3: ( ( ( ( $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_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $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 @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 ) ) ) ) ) ) )
@ ( sK12 @ X3 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f605]) ).
thf(f605,plain,
( ! [X3: ( ( ( ( $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 @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f604]) ).
thf(f609,plain,
( spl0_9
| spl0_10
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f601,f346,f607,f604]) ).
thf(f346,definition,
( spl0_1
<=> ! [X4: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X3: ( ( ( ( $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] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f601,plain,
( ! [X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $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 @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f599]) ).
thf(f599,plain,
( ! [X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( ( X3
@ ^ [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
@ ( sK10 @ 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
@ ( sK10 @ 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 )
=> ( X4
@ ^ [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 > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f598]) ).
thf(f598,plain,
( ! [X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $false
= ( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_Repl
@ ( sK10 @ 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 ) )
=> ( ( X3
@ ^ [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
@ ( sK10 @ 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
@ ( sK10 @ 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 )
=> ( X4
@ ^ [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 ) ) ) ) )
| ( ( !! @ $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 @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f597]) ).
thf(f597,plain,
( ! [X3: ( ( ( ( $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,X4: ( ( $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 @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) ) ) )
@ ( sK10 @ X3 @ X4 ) ) )
| ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f592]) ).
thf(f592,plain,
( ! [X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( ( ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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 @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y1 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( sK11 @ X3 @ X1 ) @ 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] : ( sK11 @ X3 @ X1 )
@ ( 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 ) )
@ 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 @ Y2 @ 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 )
| ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f591]) ).
thf(f591,plain,
( ! [X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( ^ [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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) ) ) ) ) ) ) )
@ ( sK11 @ X3 @ X1 ) )
= $false )
| ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) > $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f347]) ).
thf(f347,plain,
( ! [X3: ( ( ( ( $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,X4: ( ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f346]) ).
thf(f550,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f549]) ).
thf(f549,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f548]) ).
thf(f548,plain,
( ( $true = $false )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f547]) ).
thf(f547,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f539,f433]) ).
thf(f433,plain,
( ! [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( $true
= ( X0
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f432]) ).
thf(f432,definition,
( spl0_3
<=> ! [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( $true
= ( X0
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f539,plain,
( ! [X3: ( $i > $i ) > ( $i > $i ) > $o] :
( $true
= ( ~ ( X3
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f533]) ).
thf(f533,plain,
( ! [X3: ( $i > $i ) > ( $i > $i ) > $o] :
( ( ^ [Y0: $i > $i,Y1: $i > $i] :
~ ( X3 @ Y0 @ Y1 )
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty )
= $true )
| ~ spl0_3 ),
inference(primitive_instantiation,[status(thm)],[f433]) ).
thf(f526,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f523,f349,f432]) ).
thf(f349,definition,
( spl0_2
<=> ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : 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 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f523,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f521]) ).
thf(f521,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $true = $false )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f425,f441]) ).
thf(f441,plain,
( ! [X0: $i,X1: $i] :
( ( c_In @ X1 @ X0 )
= $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f316,f428]) ).
thf(f428,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f379,f379]) ).
thf(f379,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 )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f378]) ).
thf(f378,plain,
( ! [X1: $i] :
( ( ^ [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 )
= ( ^ [Y0: $i] : Y0
@ X1 ) )
| ~ spl0_2 ),
inference(argument_congruence,[status(thm)],[f375]) ).
thf(f375,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 ) ) ) ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f374]) ).
thf(f374,plain,
( ( ( ( ^ [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 ) ) ) )
= ( ^ [Y0: $i] : Y0 ) )
= $true )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f366]) ).
thf(f366,plain,
( ( $false
= ( ( ^ [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 ) ) ) )
!= ( ^ [Y0: $i] : Y0 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f365]) ).
thf(f365,plain,
( ( $true = $false )
| ( $false
= ( ( ^ [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 ) ) ) )
!= ( ^ [Y0: $i] : Y0 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f364]) ).
thf(f364,plain,
( ( $false
= ( ( ^ [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 ) ) ) )
!= ( ^ [Y0: $i] : Y0 ) ) )
| ( ( ~ $true ) = $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f363]) ).
thf(f363,plain,
( ( $false
= ( ( ^ [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 ) ) ) )
!= ( ^ [Y0: $i] : Y0 ) ) )
| ( ( ( ^ [Y0: $i] : c_Empty )
!= ( ^ [Y0: $i] : c_Empty ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f359]) ).
thf(f359,plain,
( ( ( ^ [Y0: $i > $i,Y1: $i > $i] : ( Y1 != Y0 )
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty )
= $true )
| ( ( ^ [Y0: $i > $i,Y1: $i > $i] : ( Y1 != Y0 )
@ ^ [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 )
| ~ spl0_2 ),
inference(primitive_instantiation,[status(thm)],[f356]) ).
thf(f356,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $false
= ( 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 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f355]) ).
thf(f355,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $false
= ( ( c_In @ ( sK7 @ X2 )
@ ( sK6 @ X2
@ ^ [Y0: ( $i > $i ) > $i,Y1: $i,Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( sK7 @ 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 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f354]) ).
thf(f354,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ( $false
= ( ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK6 @ 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 ) ) ) ) )
@ ( sK7 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f353]) ).
thf(f353,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ Y0
@ ( sK6 @ 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 ) ) ) ) ) ) )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f352]) ).
thf(f352,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( $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 ) ) ) ) ) )
@ ( sK6 @ X2 ) ) )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f350]) ).
thf(f350,plain,
( ! [X2: ( $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
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f349]) ).
thf(f316,plain,
! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f315]) ).
thf(f315,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f314]) ).
thf(f314,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ),
inference(not_proxy_clausification,[status(thm)],[f313]) ).
thf(f313,plain,
( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(boolean_simplification,[status(thm)],[f310]) ).
thf(f310,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
=> $false )
= $true ),
inference(backward_demodulation,[status(thm)],[f305,f308]) ).
thf(f308,plain,
( ( !! @ $o
@ ^ [Y0: $o] : Y0 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f307]) ).
thf(f307,plain,
( ( ( !! @ ( ( ( ( ( ( $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 ) > $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 > $o )
@ ^ [Y3: ( ( $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 )
=> ( Y2
@ ^ [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 ) @ Y6 )
=> ( ( Y2
@ ^ [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 @ Y6
@ ^ [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 @ Y6
@ ^ [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] : Y6
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y4 @ 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 @ Y6
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ 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 @ Y4 @ 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 @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y2
@ ^ [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 @ Y6 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ 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] : Y4
@ ( 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 ) )
@ 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 @ Y7 @ 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 ) )
=> ( ( Y2
@ ^ [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 )
=> ( Y3
@ ^ [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 ) )
=> ( ( Y3
@ ^ [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 ) ) )
=> ( Y3
@ ^ [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 @ Y6 @ ( 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 @ Y4 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [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 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y7: ( $i > $i ) > $i] :
( ( Y2
@ ^ [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
@ ( Y7
@ ^ [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 @ Y4
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y4: $o] : Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f306]) ).
thf(f306,plain,
( ( ~ ( ( !! @ ( ( ( ( ( ( $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 ) > $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 > $o )
@ ^ [Y3: ( ( $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 )
=> ( Y2
@ ^ [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 ) @ Y6 )
=> ( ( Y2
@ ^ [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 @ Y6
@ ^ [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 @ Y6
@ ^ [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] : Y6
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y4 @ 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 @ Y6
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ 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 @ Y4 @ 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 @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y2
@ ^ [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 @ Y6 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ 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] : Y4
@ ( 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 ) )
@ 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 @ Y7 @ 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 ) )
=> ( ( Y2
@ ^ [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 )
=> ( Y3
@ ^ [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 ) )
=> ( ( Y3
@ ^ [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 ) ) )
=> ( Y3
@ ^ [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 @ Y6 @ ( 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 @ Y4 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [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 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y7: ( $i > $i ) > $i] :
( ( Y2
@ ^ [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
@ ( Y7
@ ^ [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 @ Y4
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y4: $o] : Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f301]) ).
thf(f301,plain,
( ( ~ ( ^ [Y0: $o] :
( Y0
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ ( !! @ ( ( ( ( ( ( $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 ) > $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 > $o )
@ ^ [Y3: ( ( $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 )
=> ( Y2
@ ^ [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 ) @ Y6 )
=> ( ( Y2
@ ^ [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 ) ) )
@ Y6
@ ( ^ [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 ) ) )
@ 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 ) ) )
@ ( ^ [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] : Y6
@ ( 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 ) )
@ Y4 )
@ 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 ) ) )
@ Y6
@ Y5 )
@ Y6 )
@ ( ^ [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
@ Y4 )
@ ( ^ [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 ) ) )
@ Y6
@ Y5 )
@ 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 ) ) )
@ Y5
@ c_Empty ) )
@ c_Empty )
=> ( Y2
@ ^ [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 )
@ Y6 )
@ Y4 ) )
@ ^ [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] : Y4
@ ( ^ [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 ) ) )
@ Y6 )
@ 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 ) )
@ Y7 )
@ ( ^ [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 ) ) )
=> ( ( Y2
@ ^ [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 )
=> ( Y3
@ ^ [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 ) ) ) ) )
=> ( ( Y3
@ ^ [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 ) ) ) ) )
=> ( Y3
@ ^ [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 @ Y6
@ ( ^ [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 ) )
@ Y4 )
@ ^ [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 )
=> ( Y2
@ ^ [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 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y7: ( $i > $i ) > $i] :
( ( Y2
@ ^ [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 ) ) )
@ ( Y7
@ ^ [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 @ 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_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 ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y4: $o] : Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f294,f299,f298,f298,f298,f298,f298,f298,f290,f290,f298,f298,f298,f298,f290,f298,f298,f290,f298,f298,f298,f290,f298,f290,f298,f298,f298,f298,f298,f290,f290,f298,f290,f298,f298,f298,f298,f298,f298,f298,f298,f298,f290,f290,f290,f298,f298,f290,f298,f290,f298,f290,f290,f298,f298,f298,f290,f298,f298,f298,f298,f298,f298,f298,f298,f290,f298,f298,f298,f298,f298,f290,f298,f298,f298,f290,f290,f290,f298,f298,f290,f290,f298,f298,f298,f290,f298,f290,f298,f298,f290,f298,f290,f298,f290,f290,f298,f290,f298,f298,f298,f298,f298,f298,f298,f290,f298,f290,f289]) ).
thf(f289,plain,
( c_False
= ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
thf(f158,plain,
( c_False
= ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ),
inference(fool_elimination,[status(thm)],[f157]) ).
thf(f157,plain,
( c_False
= ( ! [X0: $o] : X0 ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( c_False
= ( ! [X0: $o] : X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax11) ).
thf(f290,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
thf(f125,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f70]) ).
thf(f70,axiom,
( ( ^ [X0: $i] :
( c_Repl @ X0
@ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) )
= c_Inj0 ),
file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax70) ).
thf(f298,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,[status(thm)],[f297,f290]) ).
thf(f297,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,[status(thm)],[f179]) ).
thf(f179,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,[status(thm)],[f178]) ).
thf(f178,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,[status(thm)],[f73]) ).
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/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax73) ).
thf(f299,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f291,f289]) ).
thf(f291,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
thf(f155,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(fool_elimination,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ^ [X0: $o] :
( X0
=> c_False ) )
= c_not ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( ( ^ [X0: $o] :
( X0
=> c_False ) )
= c_not ),
file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax13) ).
thf(f294,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 ) > $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 > $o )
@ ^ [Y3: ( ( $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 )
=> ( Y2
@ ^ [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 ) @ Y6 )
=> ( ( Y2
@ ^ [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 @ Y6 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ Y6 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ Y5 ) ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y6
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ Y4 ) @ c_Empty ) )
@ ^ [Y7: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ Y6 @ Y5 ) @ Y6 ) @ ( 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 @ Y4 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ Y6 @ Y5 )
@ c_Empty
@ ^ [Y8: $i] : ( c_Inj0 @ ( c_setsum @ Y5 @ c_Empty ) )
@ c_Empty )
=> ( Y2
@ ^ [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 ) @ Y6 ) @ Y4 ) )
@ ^ [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] : Y4
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ Y6 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ Y7 ) @ ( 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 ) ) )
=> ( ( Y2
@ ^ [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 )
=> ( Y3
@ ^ [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 ) ) ) ) )
=> ( ( Y3
@ ^ [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 ) ) ) ) )
=> ( Y3
@ ^ [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 @ Y6 @ ( c_Inj0 @ c_Empty ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ Y5 )
@ ( c_Inj0 @ Y4 )
@ ^ [Y7: $i] : ( c_setsum @ c_Empty @ Y7 )
@ c_Empty )
=> ( Y2
@ ^ [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 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y7: ( $i > $i ) > $i] :
( ( Y2
@ ^ [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
@ ( Y7
@ ^ [Y8: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ Y6 ) ) ) )
=> ( c_In @ Y4 @ ( 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,[status(thm)],[f278]) ).
thf(f278,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 ) > $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 > $o )
@ ^ [Y3: ( ( $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 )
=> ( Y2
@ ^ [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 ) @ Y6 )
=> ( ( Y2
@ ^ [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 @ Y6 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ Y6 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ Y5 ) ) )
@ c_Empty )
=> ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : Y6
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ Y4 ) @ c_Empty ) )
@ ^ [Y7: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ Y6 @ Y5 ) @ Y6 ) @ ( 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 @ Y4 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( Y0
@ ^ [Y8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ Y6 @ Y5 )
@ c_Empty
@ ^ [Y8: $i] : ( c_Inj0 @ ( c_setsum @ Y5 @ c_Empty ) )
@ c_Empty )
=> ( Y2
@ ^ [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 ) @ Y6 ) @ Y4 ) )
@ ^ [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] : Y4
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ Y6 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ Y7 ) @ ( 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 ) ) )
=> ( ( Y2
@ ^ [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 )
=> ( Y3
@ ^ [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 ) ) ) ) )
=> ( ( Y3
@ ^ [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 ) ) ) ) )
=> ( Y3
@ ^ [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 @ Y6 @ ( c_Inj0 @ c_Empty ) )
=> ( ( Y0
@ ^ [Y7: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ Y5 )
@ ( c_Inj0 @ Y4 )
@ ^ [Y7: $i] : ( c_setsum @ c_Empty @ Y7 )
@ c_Empty )
=> ( Y2
@ ^ [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 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y7: ( $i > $i ) > $i] :
( ( Y2
@ ^ [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
@ ( Y7
@ ^ [Y8: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ Y6 ) ) ) )
=> ( c_In @ Y4 @ ( 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,[status(thm)],[f277]) ).
thf(f277,plain,
~ ( c_not
@ ! [X0: ( ( $i > $i ) > $i ) > $i > $o,X1: ( ( ( ( $i > $i > $i ) > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > ( ( ( $i > $i ) > $i > $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] :
( ! [X4: $i,X6: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i] :
( ( c_In @ X4
@ ( X6
@ ^ [X8: ( $i > $i ) > $i,X9: $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ X4 @ ( 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 ) ) ) ) ) )
=> ( ! [X14: $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 ) ) ) @ X14 )
=> ( ( X2
@ ^ [X17: $i] : c_Empty
@ ^ [X18: $i] : c_Empty )
=> ( X1
@ ^ [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] : X14
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) ) )
=> ( ! [X26: $i,X27: $i,X29: $i] :
( ( c_In @ ( c_Inj1 @ X27 ) @ X26 )
=> ( ( X1
@ ^ [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 @ X26 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
@ ^ [X35: ( $i > $i ) > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ ( c_setsum @ X26 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ X27 ) ) )
@ c_Empty )
=> ( X3
@ ^ [X36: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : X26
@ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ X29 ) @ c_Empty ) )
@ ^ [X37: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ X26 @ X27 ) @ X26 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ c_Empty ) ) )
=> ( ! [X38: $i,X39: $i,X40: $i,X41: $i] :
( ( c_In @ ( c_setsum @ c_Empty @ X41 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ( X3
@ ^ [X42: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ X39 @ X40 )
@ c_Empty
@ ^ [X43: $i] : ( c_Inj0 @ ( c_setsum @ X40 @ c_Empty ) )
@ c_Empty )
=> ( X1
@ ^ [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 ) @ X39 ) @ X41 ) )
@ ^ [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] : X41
@ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ X39 )
@ c_Empty
@ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) @ X38 ) @ ( 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 ) ) )
=> ( ( X1
@ ^ [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 )
=> ( X0
@ ^ [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 ) ) ) )
=> ( ! [X73: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X74: $i > $i,X75: ( $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
@ ( X73
@ ^ [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 ) ) ) ) )
=> ( ( X0
@ ^ [X78: $i > $i] : ( X74 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X75
@ ^ [X79: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
=> ( X0
@ ^ [X80: $i > $i] :
( c_Inj1
@ ( c_setsum @ ( X80 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X75
@ ^ [X81: $i] : c_Empty ) ) ) )
@ c_Empty ) ) )
=> ( ! [X82: $i,X83: $i,X84: $i] :
( ( c_In @ X82 @ ( c_Inj0 @ c_Empty ) )
=> ( ( X3
@ ^ [X86: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ X83 )
@ ( c_Inj0 @ X84 )
@ ^ [X87: $i] : ( c_setsum @ c_Empty @ X87 )
@ c_Empty )
=> ( X1
@ ^ [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 )
@ X84 ) ) )
=> ( ! [X94: ( $i > $i ) > $i,X95: $i,X96: $i,X97: $i] :
( ( X1
@ ^ [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
@ ( X94
@ ^ [X110: $i] : c_Empty )
@ c_Empty )
@ ( c_setsum @ c_Empty @ X95 ) ) ) )
=> ( c_In @ X97 @ ( 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,[status(thm)],[f110]) ).
thf(f110,negated_conjecture,
~ ( c_not
@ ! [X1: ( ( $i > $i ) > $i ) > $i > $o,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,X3: ( $i > $i ) > ( $i > $i ) > $o,X2: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ! [X7: $i,X5: $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 ) ) ) ) ) )
=> ( ! [X6: $i,X5: $i,X7: $i,X4: $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 ) ) ) )
=> ( ! [X7: $i,X6: $i,X5: $i,X4: $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 ) ) )
=> ( ! [X4: $i,X7: $i,X5: $i,X6: $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 ) ) ) ) ) ) )
=> ( ! [X4: $i,X7: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i,X6: $i,X5: $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 ) ) ) )
=> ( ! [X5: $i,X4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X6: $i > $i,X7: ( $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
@ ( 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 ) ) )
=> ( ! [X4: $i,X5: $i,X7: $i,X6: $i > $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 ) ) )
=> ( ! [X6: ( $i > $i ) > $i,X5: $i,X7: $i,X4: $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(f109,conjecture,
( c_not
@ ! [X1: ( ( $i > $i ) > $i ) > $i > $o,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,X3: ( $i > $i ) > ( $i > $i ) > $o,X2: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ! [X7: $i,X5: $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 ) ) ) ) ) )
=> ( ! [X6: $i,X5: $i,X7: $i,X4: $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 ) ) ) )
=> ( ! [X7: $i,X6: $i,X5: $i,X4: $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 ) ) )
=> ( ! [X4: $i,X7: $i,X5: $i,X6: $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 ) ) ) ) ) ) )
=> ( ! [X4: $i,X7: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i,X6: $i,X5: $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 ) ) ) )
=> ( ! [X5: $i,X4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X6: $i > $i,X7: ( $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
@ ( 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 ) ) )
=> ( ! [X4: $i,X5: $i,X7: $i,X6: $i > $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 ) ) )
=> ( ! [X6: ( $i > $i ) > $i,X5: $i,X7: $i,X4: $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/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',conj) ).
thf(f305,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f302]) ).
thf(f302,plain,
( ( ^ [Y0: $o] :
( Y0
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f296,f299]) ).
thf(f296,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
thf(f214,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(fool_elimination,[status(thm)],[f213]) ).
thf(f213,plain,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax5) ).
thf(f425,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( ( c_In @ ( sK7 @ X2 )
@ ( 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 ) ) ) )
= $true )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f357,f379]) ).
thf(f357,plain,
( ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ( ( c_In @ ( sK7 @ X2 )
@ ( sK6 @ X2
@ ^ [Y0: ( $i > $i ) > $i,Y1: $i,Y2: $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( sK7 @ 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 ) ) ) ) )
= $true )
| ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f355]) ).
thf(f351,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f344,f349,f346]) ).
thf(f344,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $true
= ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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(binary_proxy_clausification,[status(thm)],[f341]) ).
thf(f341,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( ( ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty )
=> ( X3
@ ^ [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] : ( sK5 @ X3 @ X2 )
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
= $false )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) > $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) ),
inference(binary_proxy_clausification,[status(thm)],[f340]) ).
thf(f340,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( $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 ) ) ) ) ) ) ) )
| ( ( ( 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 ) )
@ ( sK5 @ X3 @ X2 ) )
=> ( ( X2
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i] : c_Empty )
=> ( X3
@ ^ [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] : ( sK5 @ X3 @ X2 )
@ c_Empty
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ ( ( ( ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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(beta_eta_normalization,[status(thm)],[f339]) ).
thf(f339,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $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
= ( ^ [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 )
=> ( X3
@ ^ [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 ) ) ) )
@ ( sK5 @ X3 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ ( ( ( ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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_clausification,[status(thm)],[f338]) ).
thf(f338,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ $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 )
=> ( X3
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 > $i )
@ ^ [Y0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i,Y2: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y1: $i > $i] :
( sK4 @ X4
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y1: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y1: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
= $false )
| ( $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 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f337]) ).
thf(f337,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( ( ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y1: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ^ [Y2: $i,Y3: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y2: $i > $i] :
( Y0
@ ( 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_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y3: $i] : c_Empty )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) ) ) )
@ ( sK4 @ X4 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $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 ) ) ) ) ) ) ) )
| ( ( !! @ $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 )
=> ( X3
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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_clausification,[status(thm)],[f336]) ).
thf(f336,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i )
@ ^ [Y1: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i] :
( ( c_In
@ ( c_Inj1
@ ( c_binunion
@ ( 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 ) )
@ ^ [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 ) ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ^ [Y2: $i,Y3: $i > $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
=> ( ( X4
@ ^ [Y2: $i > $i] :
( Y0
@ ( 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_binunion
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y2: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i > $i] :
( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ( 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_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK3 @ X4
@ ^ [Y3: $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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
@ ^ [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 )
=> ( X3
@ ^ [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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $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 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f335]) ).
thf(f335,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( ( ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 ) ) ) ) )
@ ( sK3 @ X4 ) )
= $false )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
=> ( X3
@ ^ [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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $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 ) ) ) ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f334]) ).
thf(f334,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 > $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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
@ ^ [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 )
=> ( X3
@ ^ [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 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( $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 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f333]) ).
thf(f333,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 > $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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) ) )
| ( ( !! @ ( ( ( ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
=> ( X3
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) ),
inference(binary_proxy_clausification,[status(thm)],[f332]) ).
thf(f332,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
=> ( X3
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 > $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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 > $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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(binary_proxy_clausification,[status(thm)],[f331]) ).
thf(f331,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( ( !! @ ( ( ( ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 )
=> ( X3
@ ^ [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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f330]) ).
thf(f330,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( $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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) ) ) ) ) ) ) )
| ( ( !! @ $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 )
=> ( X3
@ ^ [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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 )
| ( $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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(binary_proxy_clausification,[status(thm)],[f329]) ).
thf(f329,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $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 ) ) ) ) ) ) ) )
| ( ( ( !! @ $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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 )
| ( ( !! @ $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 )
=> ( X3
@ ^ [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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 ) ),
inference(binary_proxy_clausification,[status(thm)],[f328]) ).
thf(f328,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ Y1 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 > $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 )
=> ( X3
@ ^ [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 ) ),
inference(binary_proxy_clausification,[status(thm)],[f327]) ).
thf(f327,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $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 ) ) ) ) ) ) ) )
| ( ( ( !! @ $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 )
=> ( X3
@ ^ [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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) ),
inference(binary_proxy_clausification,[status(thm)],[f326]) ).
thf(f326,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( ( ( $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 )
=> ( X3
@ ^ [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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ),
inference(boolean_simplification,[status(thm)],[f325]) ).
thf(f325,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( ( ( $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 )
=> ( X3
@ ^ [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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f324,f308]) ).
thf(f324,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $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 )
=> ( X3
@ ^ [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 ) @ Y2 )
=> ( ( X3
@ ^ [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 @ Y2
@ ^ [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 @ Y2
@ ^ [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] : Y2
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y0 @ 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 @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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 @ Y0 @ 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 @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y2 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y0 @ 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] : Y0
@ ( 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 ) )
@ 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 @ Y3 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( X4
@ ^ [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 ) )
=> ( ( X4
@ ^ [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 ) ) )
=> ( X4
@ ^ [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 @ Y2 @ ( 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 @ Y0 @ c_Inj1 )
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y0 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y3: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y3
@ ^ [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 @ Y0
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f323]) ).
thf(f323,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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,X4: ( ( $i > $i ) > $i ) > $i > $o] :
( $true
= ( ^ [Y0: ( ( $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 )
=> ( X3
@ ^ [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 ) @ Y3 )
=> ( ( X3
@ ^ [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 @ Y3
@ ^ [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 @ Y3
@ ^ [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] : Y3
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ 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 @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ 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 @ Y1 @ 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 @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y3 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ 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] : Y1
@ ( 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 ) )
@ 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 @ Y4 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( Y0
@ ^ [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 ) )
=> ( ( Y0
@ ^ [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 ) ) )
=> ( Y0
@ ^ [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 @ Y3 @ ( 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 @ Y1 @ c_Inj1 )
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y4
@ ^ [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 @ Y1
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f322]) ).
thf(f322,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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 > $i ) > $i ) > $i > $o )
@ ^ [Y0: ( ( $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 )
=> ( X3
@ ^ [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 ) @ Y3 )
=> ( ( X3
@ ^ [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 @ Y3
@ ^ [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 @ Y3
@ ^ [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] : Y3
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y1 @ 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 @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ 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 @ Y1 @ 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 @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( X3
@ ^ [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 @ Y3 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ 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] : Y1
@ ( 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 ) )
@ 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 @ Y4 @ 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 ) )
=> ( ( X3
@ ^ [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 )
=> ( Y0
@ ^ [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 ) )
=> ( ( Y0
@ ^ [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 ) ) )
=> ( Y0
@ ^ [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 @ Y3 @ ( 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 @ Y1 @ c_Inj1 )
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty )
=> ( X3
@ ^ [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 )
@ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y4: ( $i > $i ) > $i] :
( ( X3
@ ^ [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
@ ( Y4
@ ^ [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 @ Y1
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f321]) ).
thf(f321,plain,
! [X2: ( $i > $i ) > ( $i > $i ) > $o,X3: ( ( ( ( $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] :
( $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 > $o )
@ ^ [Y1: ( ( $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 )
=> ( Y0
@ ^ [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 ) @ Y4 )
=> ( ( Y0
@ ^ [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 @ Y4
@ ^ [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 @ Y4
@ ^ [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] : Y4
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ 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 @ Y4
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ 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 @ Y2 @ 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 @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y0
@ ^ [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 @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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] : Y2
@ ( 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 ) )
@ 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 @ Y5 @ 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 ) )
=> ( ( Y0
@ ^ [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 )
=> ( Y1
@ ^ [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 ) )
=> ( ( Y1
@ ^ [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 ) ) )
=> ( Y1
@ ^ [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 @ Y4 @ ( 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 @ Y2 @ c_Inj1 )
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [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 )
@ Y2 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y5: ( $i > $i ) > $i] :
( ( Y0
@ ^ [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
@ ( Y5
@ ^ [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 @ Y2
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y2: $o] : Y2 ) ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f320]) ).
thf(f320,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 ) > $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 > $o )
@ ^ [Y1: ( ( $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 )
=> ( Y0
@ ^ [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 ) @ Y4 )
=> ( ( Y0
@ ^ [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 @ Y4
@ ^ [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 @ Y4
@ ^ [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] : Y4
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y2 @ 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 @ Y4
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ 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 @ Y2 @ 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 @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y0
@ ^ [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 @ Y4 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ 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] : Y2
@ ( 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 ) )
@ 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 @ Y5 @ 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 ) )
=> ( ( Y0
@ ^ [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 )
=> ( Y1
@ ^ [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 ) )
=> ( ( Y1
@ ^ [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 ) ) )
=> ( Y1
@ ^ [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 @ Y4 @ ( 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 @ Y2 @ c_Inj1 )
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty )
=> ( Y0
@ ^ [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 )
@ Y2 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y5: ( $i > $i ) > $i] :
( ( Y0
@ ^ [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
@ ( Y5
@ ^ [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 @ Y2
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y2: $o] : Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f319]) ).
thf(f319,plain,
! [X2: ( $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 > $o )
@ ^ [Y2: ( ( $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 )
=> ( Y1
@ ^ [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 ) @ Y5 )
=> ( ( Y1
@ ^ [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 @ Y5
@ ^ [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 @ Y5
@ ^ [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] : Y5
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y3 @ 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 @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ 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 @ Y3 @ 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 @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y1
@ ^ [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 @ Y5 @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ 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] : Y3
@ ( 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 ) )
@ 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 @ Y6 @ 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 ) )
=> ( ( Y1
@ ^ [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 )
=> ( Y2
@ ^ [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 ) )
=> ( ( Y2
@ ^ [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 ) ) )
=> ( Y2
@ ^ [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 @ Y5 @ ( 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 @ Y3 @ c_Inj1 )
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty )
=> ( Y1
@ ^ [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 )
@ Y3 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y6: ( $i > $i ) > $i] :
( ( Y1
@ ^ [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
@ ( Y6
@ ^ [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 @ Y3
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] : Y3 ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f318]) ).
thf(f318,plain,
! [X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o] :
( ( !! @ ( ( $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 > $o )
@ ^ [Y2: ( ( $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 )
=> ( Y1
@ ^ [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 ) @ Y5 )
=> ( ( Y1
@ ^ [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 @ Y5
@ ^ [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 @ Y5
@ ^ [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] : Y5
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y3 @ 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 @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ 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 @ Y3 @ 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 @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y1
@ ^ [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 @ Y5 @ c_Inj1 ) )
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ 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] : Y3
@ ( 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 ) )
@ 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 @ Y6 @ 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 ) )
=> ( ( Y1
@ ^ [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 )
=> ( Y2
@ ^ [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 ) )
=> ( ( Y2
@ ^ [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 ) ) )
=> ( Y2
@ ^ [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 @ Y5 @ ( 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 @ Y3 @ c_Inj1 )
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ c_Inj1 ) )
@ c_Empty )
=> ( Y1
@ ^ [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 )
@ Y3 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y6: ( $i > $i ) > $i] :
( ( Y1
@ ^ [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
@ ( Y6
@ ^ [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 @ Y3
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] : Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f317]) ).
thf(f317,plain,
! [X1: ( ( ( ( ( $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 ) > $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 > $o )
@ ^ [Y3: ( ( $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 )
=> ( Y2
@ ^ [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 ) @ Y6 )
=> ( ( Y2
@ ^ [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 @ Y6
@ ^ [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 @ Y6
@ ^ [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] : Y6
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y4 @ 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 @ Y6
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ 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 @ Y4 @ 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 @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y2
@ ^ [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 @ Y6 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ 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] : Y4
@ ( 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 ) )
@ 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 @ Y7 @ 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 ) )
=> ( ( Y2
@ ^ [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 )
=> ( Y3
@ ^ [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 ) )
=> ( ( Y3
@ ^ [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 ) ) )
=> ( Y3
@ ^ [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 @ Y6 @ ( 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 @ Y4 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [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 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y7: ( $i > $i ) > $i] :
( ( Y2
@ ^ [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
@ ( Y7
@ ^ [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 @ Y4
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y4: $o] : Y4 ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f309]) ).
thf(f309,plain,
( ( !! @ ( ( ( ( ( ( $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 ) > $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 > $o )
@ ^ [Y3: ( ( $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 )
=> ( Y2
@ ^ [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 ) @ Y6 )
=> ( ( Y2
@ ^ [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 @ Y6
@ ^ [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 @ Y6
@ ^ [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] : Y6
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ Y4 @ 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 @ Y6
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y6 @ 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 @ Y4 @ 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 @ Y6
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ c_Empty
@ ^ [Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Empty )
=> ( Y2
@ ^ [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 @ Y6 @ c_Inj1 ) )
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ 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] : Y4
@ ( 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 ) )
@ 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 @ Y7 @ 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 ) )
=> ( ( Y2
@ ^ [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 )
=> ( Y3
@ ^ [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 ) )
=> ( ( Y3
@ ^ [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 ) ) )
=> ( Y3
@ ^ [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 @ Y6 @ ( 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 @ Y4 @ c_Inj1 )
@ ^ [Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ Y7 @ c_Inj1 ) )
@ c_Empty )
=> ( Y2
@ ^ [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 )
@ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ ( ( $i > $i ) > $i )
@ ^ [Y7: ( $i > $i ) > $i] :
( ( Y2
@ ^ [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
@ ( Y7
@ ^ [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 @ Y4
@ ( 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 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y4: $o] : Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV526^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n023.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:49:34 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.38 ---- Original DTF file ---
% 0.19/0.38 thf(spec,logic,$$dhol).
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 % File : SEV526^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.38 % Domain : Set Theory
% 0.19/0.38 % Problem : ProofGold problem HOSetConstr_84_neg_th0
% 0.19/0.38 % Version : Especial.
% 0.19/0.38 % English :
% 0.19/0.38
% 0.19/0.38 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.19/0.38 % Source : [Urb20]
% 0.19/0.38 % Names : HOSetConstr_84_neg_th0.p [Urb20]
% 0.19/0.38
% 0.19/0.38 % Status : Theorem
% 0.19/0.38 % Rating : 0.89 v9.1.0, 0.88 v9.0.0, 1.00 v7.5.0
% 0.19/0.38 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.19/0.38 % Number of atoms : 489 ( 135 equ; 0 cnn)
% 0.19/0.38 % Maximal formula atoms : 10 ( 4 avg)
% 0.19/0.38 % Number of connectives : 1464 ( 0 ~; 0 |; 0 &;1353 @)
% 0.19/0.38 % ( 0 <=>; 111 =>; 0 <=; 0 <~>)
% 0.19/0.38 % Maximal formula depth : 34 ( 2 avg)
% 0.19/0.38 % Number of types : 2 ( 0 usr)
% 0.19/0.38 % Number of type conns : 758 ( 758 >; 0 *; 0 +; 0 <<)
% 0.19/0.38 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.19/0.38 % Number of variables : 516 ( 350 ^; 129 !; 37 ?; 516 :)
% 0.19/0.38 % SPC : TH0_THM_EQU_NAR
% 0.19/0.38
% 0.19/0.38 % Comments : See https://proofgold.org
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 thf(c_Eps_i_tp,type,
% 0.19/0.38 c_Eps_i: ( $i > $o ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_False_tp,type,
% 0.19/0.38 c_False: $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_True_tp,type,
% 0.19/0.38 c_True: $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_not_tp,type,
% 0.19/0.38 c_not: $o > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_and_tp,type,
% 0.19/0.38 c_and: $o > $o > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_or_tp,type,
% 0.19/0.38 c_or: $o > $o > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_iff_tp,type,
% 0.19/0.38 c_iff: $o > $o > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_In_tp,type,
% 0.19/0.38 c_In: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_Subq_tp,type,
% 0.19/0.38 c_Subq: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_Empty_tp,type,
% 0.19/0.38 c_Empty: $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Union_tp,type,
% 0.19/0.38 c_Union: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Power_tp,type,
% 0.19/0.38 c_Power: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Repl_tp,type,
% 0.19/0.38 c_Repl: $i > ( $i > $i ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_TransSet_tp,type,
% 0.19/0.38 c_TransSet: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_atleast2_tp,type,
% 0.19/0.38 c_atleast2: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_atleast3_tp,type,
% 0.19/0.38 c_atleast3: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_atleast4_tp,type,
% 0.19/0.38 c_atleast4: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_atleast5_tp,type,
% 0.19/0.38 c_atleast5: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_atleast6_tp,type,
% 0.19/0.38 c_atleast6: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_exactly2_tp,type,
% 0.19/0.38 c_exactly2: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_exactly3_tp,type,
% 0.19/0.38 c_exactly3: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_exactly4_tp,type,
% 0.19/0.38 c_exactly4: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_exactly5_tp,type,
% 0.19/0.38 c_exactly5: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_exu_i_tp,type,
% 0.19/0.38 c_exu_i: ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_reflexive_i_tp,type,
% 0.19/0.38 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_irreflexive_i_tp,type,
% 0.19/0.38 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_symmetric_i_tp,type,
% 0.19/0.38 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_antisymmetric_i_tp,type,
% 0.19/0.38 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_transitive_i_tp,type,
% 0.19/0.38 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_eqreln_i_tp,type,
% 0.19/0.38 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_per_i_tp,type,
% 0.19/0.38 c_per_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_linear_i_tp,type,
% 0.19/0.38 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_trichotomous_or_i_tp,type,
% 0.19/0.38 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_partialorder_i_tp,type,
% 0.19/0.38 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_totalorder_i_tp,type,
% 0.19/0.38 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_strictpartialorder_i_tp,type,
% 0.19/0.38 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_stricttotalorder_i_tp,type,
% 0.19/0.38 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_If_i_tp,type,
% 0.19/0.38 c_If_i: $o > $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_exactly1of2_tp,type,
% 0.19/0.38 c_exactly1of2: $o > $o > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_exactly1of3_tp,type,
% 0.19/0.38 c_exactly1of3: $o > $o > $o > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_nIn_tp,type,
% 0.19/0.38 c_nIn: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_nSubq_tp,type,
% 0.19/0.38 c_nSubq: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_UPair_tp,type,
% 0.19/0.38 c_UPair: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Sing_tp,type,
% 0.19/0.38 c_Sing: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_binunion_tp,type,
% 0.19/0.38 c_binunion: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_SetAdjoin_tp,type,
% 0.19/0.38 c_SetAdjoin: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_famunion_tp,type,
% 0.19/0.38 c_famunion: $i > ( $i > $i ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Sep_tp,type,
% 0.19/0.38 c_Sep: $i > ( $i > $o ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_ReplSep_tp,type,
% 0.19/0.38 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_binintersect_tp,type,
% 0.19/0.38 c_binintersect: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_setminus_tp,type,
% 0.19/0.38 c_setminus: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_inj_tp,type,
% 0.19/0.38 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_bij_tp,type,
% 0.19/0.38 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_atleastp_tp,type,
% 0.19/0.38 c_atleastp: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_equip_tp,type,
% 0.19/0.38 c_equip: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_In_rec_poly_G_i_tp,type,
% 0.19/0.38 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_In_rec_poly_i_tp,type,
% 0.19/0.38 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_ordsucc_tp,type,
% 0.19/0.38 c_ordsucc: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_nat_p_tp,type,
% 0.19/0.38 c_nat_p: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_nat_primrec_tp,type,
% 0.19/0.38 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_add_nat_tp,type,
% 0.19/0.38 c_add_nat: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_mul_nat_tp,type,
% 0.19/0.38 c_mul_nat: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_ordinal_tp,type,
% 0.19/0.38 c_ordinal: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_V__tp,type,
% 0.19/0.38 c_V_: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Inj1_tp,type,
% 0.19/0.38 c_Inj1: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Inj0_tp,type,
% 0.19/0.38 c_Inj0: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Unj_tp,type,
% 0.19/0.38 c_Unj: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_combine_funcs_tp,type,
% 0.19/0.38 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_setsum_tp,type,
% 0.19/0.38 c_setsum: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_proj0_tp,type,
% 0.19/0.38 c_proj0: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_proj1_tp,type,
% 0.19/0.38 c_proj1: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_binrep_tp,type,
% 0.19/0.38 c_binrep: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_lam_tp,type,
% 0.19/0.38 c_lam: $i > ( $i > $i ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_setprod_tp,type,
% 0.19/0.38 c_setprod: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_ap_tp,type,
% 0.19/0.38 c_ap: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_setsum_p_tp,type,
% 0.19/0.38 c_setsum_p: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_tuple_p_tp,type,
% 0.19/0.38 c_tuple_p: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_Pi_tp,type,
% 0.19/0.38 c_Pi: $i > ( $i > $i ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_setexp_tp,type,
% 0.19/0.38 c_setexp: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_Sep2_tp,type,
% 0.19/0.38 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_set_of_pairs_tp,type,
% 0.19/0.38 c_set_of_pairs: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_lam2_tp,type,
% 0.19/0.38 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_PNoEq__tp,type,
% 0.19/0.38 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_PNoLt__tp,type,
% 0.19/0.38 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_PNoLt_tp,type,
% 0.19/0.38 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_PNoLe_tp,type,
% 0.19/0.38 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_PNo_downc_tp,type,
% 0.19/0.38 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_PNo_upc_tp,type,
% 0.19/0.38 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_SNoElts__tp,type,
% 0.19/0.38 c_SNoElts_: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_SNo__tp,type,
% 0.19/0.38 c_SNo_: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_PSNo_tp,type,
% 0.19/0.38 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_SNo_tp,type,
% 0.19/0.38 c_SNo: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_SNoLev_tp,type,
% 0.19/0.38 c_SNoLev: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(c_SNoEq__tp,type,
% 0.19/0.38 c_SNoEq_: $i > $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_SNoLt_tp,type,
% 0.19/0.38 c_SNoLt: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_SNoLe_tp,type,
% 0.19/0.38 c_SNoLe: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_binop_on_tp,type,
% 0.19/0.38 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_Loop_tp,type,
% 0.19/0.38 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_Loop_with_defs_tp,type,
% 0.19/0.38 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 ).
% 0.19/0.38
% 0.19/0.38 thf(c_Loop_with_defs_cex1_tp,type,
% 0.19/0.38 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 ).
% 0.19/0.38
% 0.19/0.38 thf(c_Loop_with_defs_cex2_tp,type,
% 0.19/0.38 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 ).
% 0.19/0.38
% 0.19/0.38 thf(c_combinator_tp,type,
% 0.19/0.38 c_combinator: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_combinator_equiv_tp,type,
% 0.19/0.38 c_combinator_equiv: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(c_equip_mod_tp,type,
% 0.19/0.38 c_equip_mod: $i > $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(ax1,axiom,
% 0.19/0.38 ! [X0: $i > $o,X1: $i] :
% 0.19/0.38 ( ( X0 @ X1 )
% 0.19/0.38 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax2,axiom,
% 0.19/0.38 ! [X0: $o] :
% 0.19/0.38 ( ( c_not @ ( c_not @ X0 ) )
% 0.19/0.38 => X0 ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax3,axiom,
% 0.19/0.38 ! [X0: $o,X1: $o] :
% 0.19/0.38 ( ( c_iff @ X0 @ X1 )
% 0.19/0.38 => ( X0 = X1 ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax4,axiom,
% 0.19/0.38 ! [X0: $i,X1: $i] :
% 0.19/0.38 ( ( c_Subq @ X0 @ X1 )
% 0.19/0.38 => ( ( c_Subq @ X1 @ X0 )
% 0.19/0.38 => ( X0 = X1 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax5,axiom,
% 0.19/0.38 ( c_not
% 0.19/0.38 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax6,axiom,
% 0.19/0.38 ! [X0: $i,X1: $i] :
% 0.19/0.38 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.19/0.38 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax7,axiom,
% 0.19/0.38 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax8,axiom,
% 0.19/0.38 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.19/0.38 ( c_iff
% 0.19/0.38 @ ( c_In @ X2
% 0.19/0.38 @ ( c_Repl @ X0
% 0.19/0.38 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.19/0.38 @ ? [X3: $i] :
% 0.19/0.38 ( c_and @ ( c_In @ X3 @ X0 )
% 0.19/0.38 @ ( X2
% 0.19/0.38 = ( X1 @ X3 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax9,axiom,
% 0.19/0.38 ! [X0: $i > $o] :
% 0.19/0.38 ( ! [X1: $i] :
% 0.19/0.38 ( ( X0 @ X1 )
% 0.19/0.38 => ! [X2: $i] :
% 0.19/0.38 ( ( c_In @ X2 @ X1 )
% 0.19/0.38 => ( X0 @ X2 ) ) )
% 0.19/0.38 => ( ( X0 @ c_Empty )
% 0.19/0.38 => ( ! [X1: $i] :
% 0.19/0.38 ( ( X0 @ X1 )
% 0.19/0.38 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.19/0.38 => ( ! [X1: $i] :
% 0.19/0.38 ( ( X0 @ X1 )
% 0.19/0.38 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.19/0.38 => ( ! [X1: $i] :
% 0.19/0.38 ( ( X0 @ X1 )
% 0.19/0.38 => ! [X2: $i > $i] :
% 0.19/0.38 ( ! [X3: $i] :
% 0.19/0.38 ( ( c_In @ X3 @ X1 )
% 0.19/0.38 => ( X0 @ ( X2 @ X3 ) ) )
% 0.19/0.38 => ( X0
% 0.19/0.38 @ ( c_Repl @ X1
% 0.19/0.38 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.19/0.38 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax10,axiom,
% 0.19/0.38 ! [X0: $i > $o] :
% 0.19/0.38 ( ! [X1: $i] :
% 0.19/0.38 ( ! [X2: $i] :
% 0.19/0.38 ( ( c_In @ X2 @ X1 )
% 0.19/0.38 => ( X0 @ X2 ) )
% 0.19/0.38 => ( X0 @ X1 ) )
% 0.19/0.38 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax11,axiom,
% 0.19/0.38 ( c_False
% 0.19/0.38 = ( ! [X0: $o] : X0 ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax12,axiom,
% 0.19/0.38 ( c_True
% 0.19/0.38 = ( ! [X0: $o] :
% 0.19/0.38 ( X0
% 0.19/0.38 => X0 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax13,axiom,
% 0.19/0.38 ( c_not
% 0.19/0.38 = ( ^ [X0: $o] :
% 0.19/0.38 ( X0
% 0.19/0.38 => c_False ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax14,axiom,
% 0.19/0.38 ( c_and
% 0.19/0.38 = ( ^ [X0: $o,X1: $o] :
% 0.19/0.38 ! [X2: $o] :
% 0.19/0.38 ( ( X0
% 0.19/0.38 => ( X1
% 0.19/0.38 => X2 ) )
% 0.19/0.38 => X2 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax15,axiom,
% 0.19/0.38 ( c_or
% 0.19/0.38 = ( ^ [X0: $o,X1: $o] :
% 0.19/0.38 ! [X2: $o] :
% 0.19/0.38 ( ( X0
% 0.19/0.38 => X2 )
% 0.19/0.38 => ( ( X1
% 0.19/0.38 => X2 )
% 0.19/0.38 => X2 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax16,axiom,
% 0.19/0.38 ( c_iff
% 0.19/0.38 = ( ^ [X0: $o,X1: $o] :
% 0.19/0.38 ( c_and
% 0.19/0.38 @ ( X0
% 0.19/0.38 => X1 )
% 0.19/0.38 @ ( X1
% 0.19/0.38 => X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax17,axiom,
% 0.19/0.38 ( c_Subq
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ! [X2: $i] :
% 0.19/0.38 ( ( c_In @ X2 @ X0 )
% 0.19/0.38 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax18,axiom,
% 0.19/0.38 ( c_TransSet
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ! [X1: $i] :
% 0.19/0.38 ( ( c_In @ X1 @ X0 )
% 0.19/0.38 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax19,axiom,
% 0.19/0.38 ( c_atleast2
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax20,axiom,
% 0.19/0.38 ( c_atleast3
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax21,axiom,
% 0.19/0.38 ( c_atleast4
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax22,axiom,
% 0.19/0.38 ( c_atleast5
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax23,axiom,
% 0.19/0.38 ( c_atleast6
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax24,axiom,
% 0.19/0.38 ( c_exactly2
% 0.19/0.38 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax25,axiom,
% 0.19/0.38 ( c_exactly3
% 0.19/0.38 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax26,axiom,
% 0.19/0.38 ( c_exactly4
% 0.19/0.38 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax27,axiom,
% 0.19/0.38 ( c_exactly5
% 0.19/0.38 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax28,axiom,
% 0.19/0.38 ( c_exu_i
% 0.19/0.38 = ( ^ [X0: $i > $o] :
% 0.19/0.38 ( c_and
% 0.19/0.38 @ ? [X1: $i] : ( X0 @ X1 )
% 0.19/0.38 @ ! [X1: $i,X2: $i] :
% 0.19/0.38 ( ( X0 @ X1 )
% 0.19/0.38 => ( ( X0 @ X2 )
% 0.19/0.38 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax29,axiom,
% 0.19/0.38 ( c_reflexive_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] :
% 0.19/0.38 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax30,axiom,
% 0.19/0.38 ( c_irreflexive_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] :
% 0.19/0.38 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax31,axiom,
% 0.19/0.38 ( c_symmetric_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] :
% 0.19/0.38 ! [X1: $i,X2: $i] :
% 0.19/0.38 ( ( X0 @ X1 @ X2 )
% 0.19/0.38 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax32,axiom,
% 0.19/0.38 ( c_antisymmetric_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] :
% 0.19/0.38 ! [X1: $i,X2: $i] :
% 0.19/0.38 ( ( X0 @ X1 @ X2 )
% 0.19/0.38 => ( ( X0 @ X2 @ X1 )
% 0.19/0.38 => ( X1 = X2 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax33,axiom,
% 0.19/0.38 ( c_transitive_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] :
% 0.19/0.38 ! [X1: $i,X2: $i,X3: $i] :
% 0.19/0.38 ( ( X0 @ X1 @ X2 )
% 0.19/0.38 => ( ( X0 @ X2 @ X3 )
% 0.19/0.38 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax34,axiom,
% 0.19/0.38 ( c_eqreln_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax35,axiom,
% 0.19/0.38 ( c_per_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax36,axiom,
% 0.19/0.38 ( c_linear_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] :
% 0.19/0.38 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax37,axiom,
% 0.19/0.38 ( c_trichotomous_or_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] :
% 0.19/0.38 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax38,axiom,
% 0.19/0.38 ( c_partialorder_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax39,axiom,
% 0.19/0.38 ( c_totalorder_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax40,axiom,
% 0.19/0.38 ( c_strictpartialorder_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax41,axiom,
% 0.19/0.38 ( c_stricttotalorder_i
% 0.19/0.38 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax42,axiom,
% 0.19/0.38 ( c_If_i
% 0.19/0.38 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.19/0.38 ( c_Eps_i
% 0.19/0.38 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax43,axiom,
% 0.19/0.38 ( c_exactly1of2
% 0.19/0.38 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax44,axiom,
% 0.19/0.38 ( c_exactly1of3
% 0.19/0.38 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax45,axiom,
% 0.19/0.38 ( c_nIn
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax46,axiom,
% 0.19/0.38 ( c_nSubq
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax47,axiom,
% 0.19/0.38 ( c_UPair
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.19/0.38 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax48,axiom,
% 0.19/0.38 ( c_Sing
% 0.19/0.38 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax49,axiom,
% 0.19/0.38 ( c_binunion
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax50,axiom,
% 0.19/0.38 ( c_SetAdjoin
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax51,axiom,
% 0.19/0.38 ( c_famunion
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i] :
% 0.19/0.38 ( c_Union
% 0.19/0.38 @ ( c_Repl @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax52,axiom,
% 0.19/0.38 ( c_Sep
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $o] :
% 0.19/0.38 ( c_If_i
% 0.19/0.38 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.19/0.38 @ ( c_Repl @ X0
% 0.19/0.38 @ ^ [X2: $i] :
% 0.19/0.38 ( ^ [X3: $i] :
% 0.19/0.38 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.19/0.38 @ ( c_Eps_i
% 0.19/0.38 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.19/0.38 @ X2 ) )
% 0.19/0.38 @ c_Empty ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax53,axiom,
% 0.19/0.38 ( c_ReplSep
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.19/0.38 ( c_Repl
% 0.19/0.38 @ ( c_Sep @ X0
% 0.19/0.38 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.19/0.38 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax54,axiom,
% 0.19/0.38 ( c_binintersect
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_Sep @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax55,axiom,
% 0.19/0.38 ( c_setminus
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_Sep @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax56,axiom,
% 0.19/0.38 ( c_inj
% 0.19/0.38 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.19/0.38 ( c_and
% 0.19/0.38 @ ! [X3: $i] :
% 0.19/0.38 ( ( c_In @ X3 @ X0 )
% 0.19/0.38 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.19/0.38 @ ! [X3: $i] :
% 0.19/0.38 ( ( c_In @ X3 @ X0 )
% 0.19/0.38 => ! [X4: $i] :
% 0.19/0.38 ( ( c_In @ X4 @ X0 )
% 0.19/0.38 => ( ( ( X2 @ X3 )
% 0.19/0.38 = ( X2 @ X4 ) )
% 0.19/0.38 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax57,axiom,
% 0.19/0.38 ( c_bij
% 0.19/0.38 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.19/0.38 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.19/0.38 @ ! [X3: $i] :
% 0.19/0.38 ( ( c_In @ X3 @ X1 )
% 0.19/0.38 => ? [X4: $i] :
% 0.19/0.38 ( c_and @ ( c_In @ X4 @ X0 )
% 0.19/0.38 @ ( ( X2 @ X4 )
% 0.19/0.38 = X3 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax58,axiom,
% 0.19/0.38 ( c_atleastp
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax59,axiom,
% 0.19/0.38 ( c_equip
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax60,axiom,
% 0.19/0.38 ( c_In_rec_poly_G_i
% 0.19/0.38 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.19/0.38 ! [X3: $i > $i > $o] :
% 0.19/0.38 ( ! [X4: $i,X5: $i > $i] :
% 0.19/0.38 ( ! [X6: $i] :
% 0.19/0.38 ( ( c_In @ X6 @ X4 )
% 0.19/0.38 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.19/0.38 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.19/0.38 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax61,axiom,
% 0.19/0.38 ( c_In_rec_poly_i
% 0.19/0.38 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.19/0.38 ( c_Eps_i
% 0.19/0.38 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax62,axiom,
% 0.19/0.38 ( c_ordsucc
% 0.19/0.38 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax63,axiom,
% 0.19/0.38 ( c_nat_p
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ! [X1: $i > $o] :
% 0.19/0.38 ( ( X1 @ c_Empty )
% 0.19/0.38 => ( ! [X2: $i] :
% 0.19/0.38 ( ( X1 @ X2 )
% 0.19/0.38 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.19/0.38 => ( X1 @ X0 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax64,axiom,
% 0.19/0.38 ( c_nat_primrec
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.19/0.38 ( c_In_rec_poly_i
% 0.19/0.38 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax65,axiom,
% 0.19/0.38 ( c_add_nat
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_nat_primrec @ X0
% 0.19/0.38 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.19/0.38 @ X1 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax66,axiom,
% 0.19/0.38 ( c_mul_nat
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_nat_primrec @ c_Empty
% 0.19/0.38 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.19/0.38 @ X1 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax67,axiom,
% 0.19/0.38 ( c_ordinal
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ( c_and @ ( c_TransSet @ X0 )
% 0.19/0.38 @ ! [X1: $i] :
% 0.19/0.38 ( ( c_In @ X1 @ X0 )
% 0.19/0.38 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax68,axiom,
% 0.19/0.38 ( c_V_
% 0.19/0.38 = ( c_In_rec_poly_i
% 0.19/0.38 @ ^ [X0: $i,X1: $i > $i] :
% 0.19/0.38 ( c_famunion @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax69,axiom,
% 0.19/0.38 ( c_Inj1
% 0.19/0.38 = ( c_In_rec_poly_i
% 0.19/0.38 @ ^ [X0: $i,X1: $i > $i] :
% 0.19/0.38 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.19/0.38 @ ( c_Repl @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax70,axiom,
% 0.19/0.38 ( c_Inj0
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ( c_Repl @ X0
% 0.19/0.38 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax71,axiom,
% 0.19/0.38 ( c_Unj
% 0.19/0.38 = ( c_In_rec_poly_i
% 0.19/0.38 @ ^ [X0: $i,X1: $i > $i] :
% 0.19/0.38 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.19/0.38 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax72,axiom,
% 0.19/0.38 ( c_combine_funcs
% 0.19/0.38 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.19/0.38 ( c_If_i
% 0.19/0.38 @ ( X4
% 0.19/0.38 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.19/0.38 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.19/0.38 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax73,axiom,
% 0.19/0.38 ( c_setsum
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_binunion
% 0.19/0.38 @ ( c_Repl @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.19/0.38 @ ( c_Repl @ X1
% 0.19/0.38 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax74,axiom,
% 0.19/0.38 ( c_proj0
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ( c_ReplSep @ X0
% 0.19/0.38 @ ^ [X1: $i] :
% 0.19/0.38 ? [X2: $i] :
% 0.19/0.38 ( ( c_Inj0 @ X2 )
% 0.19/0.38 = X1 )
% 0.19/0.38 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax75,axiom,
% 0.19/0.38 ( c_proj1
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ( c_ReplSep @ X0
% 0.19/0.38 @ ^ [X1: $i] :
% 0.19/0.38 ? [X2: $i] :
% 0.19/0.38 ( ( c_Inj1 @ X2 )
% 0.19/0.38 = X1 )
% 0.19/0.38 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax76,axiom,
% 0.19/0.38 ( c_binrep
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax77,axiom,
% 0.19/0.38 ( c_lam
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i] :
% 0.19/0.38 ( c_famunion @ X0
% 0.19/0.38 @ ^ [X2: $i] :
% 0.19/0.38 ( c_Repl @ ( X1 @ X2 )
% 0.19/0.38 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax78,axiom,
% 0.19/0.38 ( c_setprod
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_lam @ X0
% 0.19/0.38 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax79,axiom,
% 0.19/0.38 ( c_ap
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_ReplSep @ X0
% 0.19/0.38 @ ^ [X2: $i] :
% 0.19/0.38 ? [X3: $i] :
% 0.19/0.38 ( X2
% 0.19/0.38 = ( c_setsum @ X1 @ X3 ) )
% 0.19/0.38 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax80,axiom,
% 0.19/0.38 ( c_setsum_p
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.19/0.38 = X0 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax81,axiom,
% 0.19/0.38 ( c_tuple_p
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ! [X2: $i] :
% 0.19/0.38 ( ( c_In @ X2 @ X1 )
% 0.19/0.38 => ? [X3: $i] :
% 0.19/0.38 ( c_and @ ( c_In @ X3 @ X0 )
% 0.19/0.38 @ ? [X4: $i] :
% 0.19/0.38 ( X2
% 0.19/0.38 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax82,axiom,
% 0.19/0.38 ( c_Pi
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i] :
% 0.19/0.38 ( c_Sep
% 0.19/0.38 @ ( c_Power
% 0.19/0.38 @ ( c_lam @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.19/0.38 @ ^ [X2: $i] :
% 0.19/0.38 ! [X3: $i] :
% 0.19/0.38 ( ( c_In @ X3 @ X0 )
% 0.19/0.38 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax83,axiom,
% 0.19/0.38 ( c_setexp
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_Pi @ X1
% 0.19/0.38 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax84,axiom,
% 0.19/0.38 ( c_Sep2
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.19/0.38 ( c_Sep
% 0.19/0.38 @ ( c_lam @ X0
% 0.19/0.38 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.19/0.38 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax85,axiom,
% 0.19/0.38 ( c_set_of_pairs
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ! [X1: $i] :
% 0.19/0.38 ( ( c_In @ X1 @ X0 )
% 0.19/0.38 => ? [X2: $i,X3: $i] :
% 0.19/0.38 ( X1
% 0.19/0.38 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.19/0.38 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax86,axiom,
% 0.19/0.38 ( c_lam2
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.19/0.38 ( c_lam @ X0
% 0.19/0.38 @ ^ [X3: $i] :
% 0.19/0.38 ( c_lam @ ( X1 @ X3 )
% 0.19/0.38 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax87,axiom,
% 0.19/0.38 ( c_PNoEq_
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.19/0.38 ! [X3: $i] :
% 0.19/0.38 ( ( c_In @ X3 @ X0 )
% 0.19/0.38 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax88,axiom,
% 0.19/0.38 ( c_PNoLt_
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.19/0.38 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax89,axiom,
% 0.19/0.38 ( c_PNoLt
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax90,axiom,
% 0.19/0.38 ( c_PNoLe
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax91,axiom,
% 0.19/0.38 ( c_PNo_downc
% 0.19/0.38 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.19/0.38 ? [X3: $i] :
% 0.19/0.38 ( c_and @ ( c_ordinal @ X3 )
% 0.19/0.38 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax92,axiom,
% 0.19/0.38 ( c_PNo_upc
% 0.19/0.38 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.19/0.38 ? [X3: $i] :
% 0.19/0.38 ( c_and @ ( c_ordinal @ X3 )
% 0.19/0.38 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax93,axiom,
% 0.19/0.38 ( c_SNoElts_
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ( c_binunion @ X0
% 0.19/0.38 @ ( c_Repl @ X0
% 0.19/0.38 @ ^ [X1: $i] :
% 0.19/0.38 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.19/0.38 @ X1 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax94,axiom,
% 0.19/0.38 ( c_SNo_
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.19/0.38 @ ! [X2: $i] :
% 0.19/0.38 ( ( c_In @ X2 @ X0 )
% 0.19/0.38 => ( c_exactly1of2
% 0.19/0.38 @ ( c_In
% 0.19/0.38 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.19/0.38 @ X2 )
% 0.19/0.38 @ X1 )
% 0.19/0.38 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax95,axiom,
% 0.19/0.38 ( c_PSNo
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $o] :
% 0.19/0.38 ( c_binunion
% 0.19/0.38 @ ( c_Sep @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.19/0.38 @ ( c_ReplSep @ X0
% 0.19/0.38 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.19/0.38 @ ^ [X2: $i] :
% 0.19/0.38 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.19/0.38 @ X2 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax96,axiom,
% 0.19/0.38 ( c_SNo
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax97,axiom,
% 0.19/0.38 ( c_SNoLev
% 0.19/0.38 = ( ^ [X0: $i] :
% 0.19/0.38 ( c_Eps_i
% 0.19/0.38 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax98,axiom,
% 0.19/0.38 ( c_SNoEq_
% 0.19/0.38 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.19/0.38 ( c_PNoEq_ @ X0
% 0.19/0.38 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.19/0.38 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax99,axiom,
% 0.19/0.38 ( c_SNoLt
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.19/0.38 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.19/0.38 @ ( c_SNoLev @ X1 )
% 0.19/0.38 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax100,axiom,
% 0.19/0.38 ( c_SNoLe
% 0.19/0.38 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.38 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.19/0.38 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.19/0.38 @ ( c_SNoLev @ X1 )
% 0.19/0.38 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax101,axiom,
% 0.19/0.38 ( c_binop_on
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.19/0.38 ! [X2: $i] :
% 0.19/0.38 ( ( c_In @ X2 @ X0 )
% 0.19/0.38 => ! [X3: $i] :
% 0.19/0.38 ( ( c_In @ X3 @ X0 )
% 0.19/0.38 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax102,axiom,
% 0.19/0.38 ( c_Loop
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.19/0.38 ( c_and
% 0.19/0.38 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.19/0.38 @ ! [X5: $i] :
% 0.19/0.38 ( ( c_In @ X5 @ X0 )
% 0.19/0.38 => ( c_and
% 0.19/0.38 @ ( ( X1 @ X4 @ X5 )
% 0.19/0.38 = X5 )
% 0.19/0.38 @ ( ( X1 @ X5 @ X4 )
% 0.19/0.38 = X5 ) ) ) )
% 0.19/0.38 @ ! [X5: $i] :
% 0.19/0.38 ( ( c_In @ X5 @ X0 )
% 0.19/0.38 => ! [X6: $i] :
% 0.19/0.38 ( ( c_In @ X6 @ X0 )
% 0.19/0.38 => ( c_and
% 0.19/0.38 @ ( c_and
% 0.19/0.38 @ ( c_and
% 0.19/0.38 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.19/0.38 = X6 )
% 0.19/0.38 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.19/0.38 = X6 ) )
% 0.19/0.38 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.19/0.38 = X5 ) )
% 0.19/0.38 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.19/0.38 = X5 ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax103,axiom,
% 0.19/0.38 ( c_Loop_with_defs
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.19/0.38 ( c_and
% 0.19/0.38 @ ( c_and
% 0.19/0.38 @ ( c_and
% 0.19/0.38 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.19/0.38 @ ! [X14: $i] :
% 0.19/0.38 ( ( c_In @ X14 @ X0 )
% 0.19/0.38 => ! [X15: $i] :
% 0.19/0.38 ( ( c_In @ X15 @ X0 )
% 0.19/0.38 => ( ( X5 @ X14 @ X15 )
% 0.19/0.38 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.19/0.38 @ ! [X14: $i] :
% 0.19/0.38 ( ( c_In @ X14 @ X0 )
% 0.19/0.38 => ! [X15: $i] :
% 0.19/0.38 ( ( c_In @ X15 @ X0 )
% 0.19/0.38 => ! [X16: $i] :
% 0.19/0.38 ( ( c_In @ X16 @ X0 )
% 0.19/0.38 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.19/0.38 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.19/0.38 @ ! [X14: $i] :
% 0.19/0.38 ( ( c_In @ X14 @ X0 )
% 0.19/0.38 => ! [X15: $i] :
% 0.19/0.38 ( ( c_In @ X15 @ X0 )
% 0.19/0.38 => ( c_and
% 0.19/0.38 @ ( c_and
% 0.19/0.38 @ ( c_and
% 0.19/0.38 @ ( c_and
% 0.19/0.38 @ ( ( X7 @ X14 @ X15 )
% 0.19/0.38 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.19/0.38 @ ( ( X10 @ X14 @ X15 )
% 0.19/0.38 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.19/0.38 @ ( ( X11 @ X14 @ X15 )
% 0.19/0.38 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.19/0.38 @ ( ( X12 @ X14 @ X15 )
% 0.19/0.38 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.19/0.38 @ ( ( X13 @ X14 @ X15 )
% 0.19/0.38 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.19/0.38 @ ! [X14: $i] :
% 0.19/0.38 ( ( c_In @ X14 @ X0 )
% 0.19/0.38 => ! [X15: $i] :
% 0.19/0.38 ( ( c_In @ X15 @ X0 )
% 0.19/0.38 => ! [X16: $i] :
% 0.19/0.38 ( ( c_In @ X16 @ X0 )
% 0.19/0.38 => ( c_and
% 0.19/0.38 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.19/0.38 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.19/0.38 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.19/0.38 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax104,axiom,
% 0.19/0.38 ( c_Loop_with_defs_cex1
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.19/0.38 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.19/0.38 @ ? [X14: $i] :
% 0.19/0.38 ( c_and @ ( c_In @ X14 @ X0 )
% 0.19/0.38 @ ? [X15: $i] :
% 0.19/0.38 ( c_and @ ( c_In @ X15 @ X0 )
% 0.19/0.38 @ ? [X16: $i] :
% 0.19/0.38 ( c_and @ ( c_In @ X16 @ X0 )
% 0.19/0.38 @ ? [X17: $i] :
% 0.19/0.38 ( c_and @ ( c_In @ X17 @ X0 )
% 0.19/0.38 @ ( c_not
% 0.19/0.38 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.19/0.38 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(ax105,axiom,
% 0.19/0.38 ( c_Loop_with_defs_cex2
% 0.19/0.38 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.19/0.39 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.19/0.39 @ ? [X14: $i] :
% 0.19/0.39 ( c_and @ ( c_In @ X14 @ X0 )
% 0.19/0.39 @ ? [X15: $i] :
% 0.19/0.39 ( c_and @ ( c_In @ X15 @ X0 )
% 0.19/0.39 @ ? [X16: $i] :
% 0.19/0.39 ( c_and @ ( c_In @ X16 @ X0 )
% 0.19/0.39 @ ? [X17: $i] :
% 0.19/0.39 ( c_and @ ( c_In @ X17 @ X0 )
% 0.19/0.39 @ ? [X18: $i] :
% 0.19/0.39 ( c_and @ ( c_In @ X18 @ X0 )
% 0.19/0.39 @ ( c_not
% 0.19/0.39 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.19/0.39 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(ax106,axiom,
% 0.19/0.39 ( c_combinator
% 0.19/0.39 = ( ^ [X0: $i] :
% 0.19/0.39 ! [X1: $i > $o] :
% 0.19/0.39 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.19/0.39 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.19/0.39 => ( ! [X2: $i,X3: $i] :
% 0.19/0.39 ( ( X1 @ X2 )
% 0.19/0.39 => ( ( X1 @ X3 )
% 0.19/0.39 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.19/0.39 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(ax107,axiom,
% 0.19/0.39 ( c_combinator_equiv
% 0.19/0.39 = ( ^ [X0: $i,X1: $i] :
% 0.19/0.39 ! [X2: $i > $i > $o] :
% 0.19/0.39 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.19/0.39 ( ( c_per_i @ X2 )
% 0.19/0.39 => ( ! [X6: $i] :
% 0.19/0.39 ( ( c_combinator @ X6 )
% 0.19/0.39 => ( X2 @ X6 @ X6 ) )
% 0.19/0.39 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.19/0.39 ( ( c_combinator @ X6 )
% 0.19/0.39 => ( ( c_combinator @ X7 )
% 0.19/0.39 => ( ( c_combinator @ X8 )
% 0.19/0.39 => ( ( c_combinator @ X9 )
% 0.19/0.39 => ( ( X2 @ X6 @ X8 )
% 0.19/0.39 => ( ( X2 @ X7 @ X9 )
% 0.19/0.39 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.19/0.39 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.19/0.39 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.19/0.39 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.19/0.39 @ ( c_Inj0 @ c_Empty )
% 0.19/0.39 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.19/0.39 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(ax108,axiom,
% 0.19/0.39 ( c_equip_mod
% 0.19/0.39 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.19/0.39 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(conj,conjecture,
% 0.19/0.39 ( c_not
% 0.19/0.39 @ ! [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 ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X3: ( $i > $i ) > ( $i > $i ) > $o] :
% 0.19/0.39 ( ! [X4: ( ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i,X7: $i] :
% 0.19/0.39 ( ( c_In @ X7
% 0.19/0.39 @ ( X6
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i,X9: $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ X7 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 0.19/0.39 => ( X3
% 0.19/0.39 @ ^ [X8: $i] : X8
% 0.19/0.39 @ ^ [X8: $i] : ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
% 0.19/0.39 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 0.19/0.39 ( ( 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 )
% 0.19/0.39 => ( ( X3
% 0.19/0.39 @ ^ [X8: $i] : c_Empty
% 0.19/0.39 @ ^ [X8: $i] : c_Empty )
% 0.19/0.39 => ( X0
% 0.19/0.39 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ c_Empty )
% 0.19/0.39 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] :
% 0.19/0.39 ( X9
% 0.19/0.39 @ ^ [X11: $i] : c_Empty )
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i] : X5
% 0.19/0.39 @ c_Empty
% 0.19/0.39 @ ( c_Inj0 @ c_Empty ) ) ) )
% 0.19/0.39 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 0.19/0.39 ( ( c_In @ ( c_Inj1 @ X6 ) @ X7 )
% 0.19/0.39 => ( ( X0
% 0.19/0.39 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
% 0.19/0.39 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ X7 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i] : c_Empty
% 0.19/0.39 @ ( c_setsum @ c_Empty @ ( c_setsum @ X7 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ X6 ) ) )
% 0.19/0.39 @ c_Empty )
% 0.19/0.39 => ( X2
% 0.19/0.39 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : X7
% 0.19/0.39 @ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ X4 ) @ c_Empty ) )
% 0.19/0.39 @ ^ [X8: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ X7 @ X6 ) @ X7 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
% 0.19/0.39 @ c_Empty ) ) )
% 0.19/0.39 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 0.19/0.39 ( ( c_In @ ( c_setsum @ c_Empty @ X6 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
% 0.19/0.39 => ( ( X2
% 0.19/0.39 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ X7 @ X5 )
% 0.19/0.39 @ c_Empty
% 0.19/0.39 @ ^ [X8: $i] : ( c_Inj0 @ ( c_setsum @ X5 @ c_Empty ) )
% 0.19/0.39 @ c_Empty )
% 0.19/0.39 => ( X0
% 0.19/0.39 @ ^ [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 ) )
% 0.19/0.39 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i] :
% 0.19/0.39 ( c_setsum
% 0.19/0.39 @ ( c_Inj1
% 0.19/0.39 @ ( X8
% 0.19/0.39 @ ^ [X9: $i] : X6
% 0.19/0.39 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
% 0.19/0.39 @ X7 )
% 0.19/0.39 @ c_Empty
% 0.19/0.39 @ ( 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 ) ) ) ) ) ) )
% 0.19/0.39 => ( ! [X4: $i,X5: $i,X6: $i,X7: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
% 0.19/0.39 ( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
% 0.19/0.39 @ ( c_Inj0
% 0.19/0.39 @ ( c_setsum
% 0.19/0.39 @ ( c_Inj0
% 0.19/0.39 @ ( X7
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
% 0.19/0.39 @ c_Empty
% 0.19/0.39 @ ^ [X8: $i] : c_Empty
% 0.19/0.39 @ c_Empty ) )
% 0.19/0.39 @ c_Empty ) ) )
% 0.19/0.39 => ( ( X0
% 0.19/0.39 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
% 0.19/0.39 @ ^ [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 ) ) ) )
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i] :
% 0.19/0.39 ( X8
% 0.19/0.39 @ ^ [X9: $i] :
% 0.19/0.39 ( c_setsum
% 0.19/0.39 @ ( X7
% 0.19/0.39 @ ^ [X10: ( $i > $i ) > $i > $i,X11: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
% 0.19/0.39 @ c_Empty
% 0.19/0.39 @ ^ [X10: $i] : ( c_Inj0 @ c_Empty )
% 0.19/0.39 @ X9 )
% 0.19/0.39 @ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
% 0.19/0.39 @ c_Empty )
% 0.19/0.39 @ ( c_setsum @ c_Empty
% 0.19/0.39 @ ( c_Inj1
% 0.19/0.39 @ ( c_setsum
% 0.19/0.39 @ ( X7
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
% 0.19/0.39 @ c_Empty
% 0.19/0.39 @ ^ [X8: $i] : c_Empty
% 0.19/0.39 @ c_Empty )
% 0.19/0.39 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 0.19/0.39 @ c_Empty )
% 0.19/0.39 => ( X1
% 0.19/0.39 @ ^ [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 ) )
% 0.19/0.39 @ ( c_Inj1 @ c_Empty ) ) ) )
% 0.19/0.39 => ( ! [X4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X5: $i,X6: $i > $i,X7: ( $i > $i ) > $i] :
% 0.19/0.39 ( ( 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 ) ) ) )
% 0.19/0.39 @ ( c_Inj0
% 0.19/0.39 @ ( c_setsum @ c_Empty
% 0.19/0.39 @ ( X4
% 0.19/0.39 @ ^ [X8: $i,X9: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
% 0.19/0.39 @ ( c_setsum @ c_Empty @ c_Empty )
% 0.19/0.39 @ ( c_Inj0 @ c_Empty )
% 0.19/0.39 @ ( c_Inj0 @ c_Empty ) ) ) ) )
% 0.19/0.39 => ( ( X1
% 0.19/0.39 @ ^ [X8: $i > $i] : ( X6 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 0.19/0.39 @ ( c_setsum
% 0.19/0.39 @ ( X7
% 0.19/0.39 @ ^ [X8: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
% 0.19/0.39 @ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
% 0.19/0.39 => ( X1
% 0.19/0.39 @ ^ [X8: $i > $i] :
% 0.19/0.39 ( c_Inj1
% 0.19/0.39 @ ( c_setsum @ ( X8 @ ( c_setsum @ c_Empty @ c_Empty ) )
% 0.19/0.39 @ ( c_setsum @ ( c_Inj1 @ c_Empty )
% 0.19/0.39 @ ( X7
% 0.19/0.39 @ ^ [X9: $i] : c_Empty ) ) ) )
% 0.19/0.39 @ c_Empty ) ) )
% 0.19/0.39 => ( ! [X4: $i,X5: $i,X6: $i > $i,X7: $i] :
% 0.19/0.39 ( ( c_In @ X4 @ ( c_Inj0 @ c_Empty ) )
% 0.19/0.39 => ( ( X2
% 0.19/0.39 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ X5 )
% 0.19/0.39 @ ( c_Inj0 @ X7 )
% 0.19/0.39 @ ^ [X8: $i] : ( c_setsum @ c_Empty @ X8 )
% 0.19/0.39 @ c_Empty )
% 0.19/0.39 => ( X0
% 0.19/0.39 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
% 0.19/0.39 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : c_Empty
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i] : ( c_setsum @ ( c_Inj1 @ c_Empty ) @ X5 )
% 0.19/0.39 @ ( c_Inj0 @ c_Empty )
% 0.19/0.39 @ X7 ) ) )
% 0.19/0.39 => ( ! [X4: $i,X5: $i,X6: ( $i > $i ) > $i,X7: $i] :
% 0.19/0.39 ( ( X0
% 0.19/0.39 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] :
% 0.19/0.39 ( X9
% 0.19/0.39 @ ( c_setsum
% 0.19/0.39 @ ( X8
% 0.19/0.39 @ ^ [X10: $i > $i > $i] : ( c_Inj0 @ c_Empty ) )
% 0.19/0.39 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
% 0.19/0.39 @ ^ [X10: $i] :
% 0.19/0.39 ( X9
% 0.19/0.39 @ ( X8
% 0.19/0.39 @ ^ [X11: $i > $i > $i] : c_Empty )
% 0.19/0.39 @ ^ [X11: $i] :
% 0.19/0.39 ( X9
% 0.19/0.39 @ ( X9 @ c_Empty
% 0.19/0.39 @ ^ [X12: $i] : c_Empty )
% 0.19/0.39 @ ^ [X12: $i] : c_Empty ) ) )
% 0.19/0.39 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ X10 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
% 0.19/0.39 @ ^ [X8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ X5 )
% 0.19/0.39 @ ( c_Inj0 @ X7 )
% 0.19/0.39 @ ( c_setsum @ c_Empty
% 0.19/0.39 @ ( c_setsum
% 0.19/0.39 @ ( c_setsum
% 0.19/0.39 @ ( X6
% 0.19/0.39 @ ^ [X8: $i] : c_Empty )
% 0.19/0.39 @ c_Empty )
% 0.19/0.39 @ ( c_setsum @ c_Empty @ X5 ) ) ) )
% 0.19/0.39 => ( 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 ) ) ) ) )
% 0.19/0.39 => c_False ) ) ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 2.47/1.53 ---- Embedded in THF ---
% 2.47/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.47/1.53 %%% Generated on Tue Feb 24 12:49:35 EST 2026
% 2.47/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.47/1.53 %%% Logic specification used:
% 2.47/1.53 %%% thf(spec, logic, $$dhol).
% 2.47/1.53
% 2.47/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2DTF32257.p
% See solution above
% 2.47/1.53 ------------------------
% 2.47/1.56 ---- Cleaned THF ---
% 2.47/1.56 thf(c_Eps_i_tp,type,
% 2.47/1.56 c_Eps_i: ( $i > $o ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_False_tp,type,
% 2.47/1.56 c_False: $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_True_tp,type,
% 2.47/1.56 c_True: $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_not_tp,type,
% 2.47/1.56 c_not: $o > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_and_tp,type,
% 2.47/1.56 c_and: $o > $o > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_or_tp,type,
% 2.47/1.56 c_or: $o > $o > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_iff_tp,type,
% 2.47/1.56 c_iff: $o > $o > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_In_tp,type,
% 2.47/1.56 c_In: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_Subq_tp,type,
% 2.47/1.56 c_Subq: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_Empty_tp,type,
% 2.47/1.56 c_Empty: $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Union_tp,type,
% 2.47/1.56 c_Union: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Power_tp,type,
% 2.47/1.56 c_Power: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Repl_tp,type,
% 2.47/1.56 c_Repl: $i > ( $i > $i ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_TransSet_tp,type,
% 2.47/1.56 c_TransSet: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_atleast2_tp,type,
% 2.47/1.56 c_atleast2: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_atleast3_tp,type,
% 2.47/1.56 c_atleast3: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_atleast4_tp,type,
% 2.47/1.56 c_atleast4: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_atleast5_tp,type,
% 2.47/1.56 c_atleast5: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_atleast6_tp,type,
% 2.47/1.56 c_atleast6: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_exactly2_tp,type,
% 2.47/1.56 c_exactly2: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_exactly3_tp,type,
% 2.47/1.56 c_exactly3: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_exactly4_tp,type,
% 2.47/1.56 c_exactly4: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_exactly5_tp,type,
% 2.47/1.56 c_exactly5: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_exu_i_tp,type,
% 2.47/1.56 c_exu_i: ( $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_reflexive_i_tp,type,
% 2.47/1.56 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_irreflexive_i_tp,type,
% 2.47/1.56 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_symmetric_i_tp,type,
% 2.47/1.56 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_antisymmetric_i_tp,type,
% 2.47/1.56 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_transitive_i_tp,type,
% 2.47/1.56 c_transitive_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_eqreln_i_tp,type,
% 2.47/1.56 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_per_i_tp,type,
% 2.47/1.56 c_per_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_linear_i_tp,type,
% 2.47/1.56 c_linear_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_trichotomous_or_i_tp,type,
% 2.47/1.56 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_partialorder_i_tp,type,
% 2.47/1.56 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_totalorder_i_tp,type,
% 2.47/1.56 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_strictpartialorder_i_tp,type,
% 2.47/1.56 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_stricttotalorder_i_tp,type,
% 2.47/1.56 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_If_i_tp,type,
% 2.47/1.56 c_If_i: $o > $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_exactly1of2_tp,type,
% 2.47/1.56 c_exactly1of2: $o > $o > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_exactly1of3_tp,type,
% 2.47/1.56 c_exactly1of3: $o > $o > $o > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_nIn_tp,type,
% 2.47/1.56 c_nIn: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_nSubq_tp,type,
% 2.47/1.56 c_nSubq: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_UPair_tp,type,
% 2.47/1.56 c_UPair: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Sing_tp,type,
% 2.47/1.56 c_Sing: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_binunion_tp,type,
% 2.47/1.56 c_binunion: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_SetAdjoin_tp,type,
% 2.47/1.56 c_SetAdjoin: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_famunion_tp,type,
% 2.47/1.56 c_famunion: $i > ( $i > $i ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Sep_tp,type,
% 2.47/1.56 c_Sep: $i > ( $i > $o ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_ReplSep_tp,type,
% 2.47/1.56 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_binintersect_tp,type,
% 2.47/1.56 c_binintersect: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_setminus_tp,type,
% 2.47/1.56 c_setminus: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_inj_tp,type,
% 2.47/1.56 c_inj: $i > $i > ( $i > $i ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_bij_tp,type,
% 2.47/1.56 c_bij: $i > $i > ( $i > $i ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_atleastp_tp,type,
% 2.47/1.56 c_atleastp: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_equip_tp,type,
% 2.47/1.56 c_equip: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_In_rec_poly_G_i_tp,type,
% 2.47/1.56 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_In_rec_poly_i_tp,type,
% 2.47/1.56 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_ordsucc_tp,type,
% 2.47/1.56 c_ordsucc: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_nat_p_tp,type,
% 2.47/1.56 c_nat_p: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_nat_primrec_tp,type,
% 2.47/1.56 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_add_nat_tp,type,
% 2.47/1.56 c_add_nat: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_mul_nat_tp,type,
% 2.47/1.56 c_mul_nat: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_ordinal_tp,type,
% 2.47/1.56 c_ordinal: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_V__tp,type,
% 2.47/1.56 c_V_: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Inj1_tp,type,
% 2.47/1.56 c_Inj1: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Inj0_tp,type,
% 2.47/1.56 c_Inj0: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Unj_tp,type,
% 2.47/1.56 c_Unj: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_combine_funcs_tp,type,
% 2.47/1.56 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_setsum_tp,type,
% 2.47/1.56 c_setsum: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_proj0_tp,type,
% 2.47/1.56 c_proj0: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_proj1_tp,type,
% 2.47/1.56 c_proj1: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_binrep_tp,type,
% 2.47/1.56 c_binrep: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_lam_tp,type,
% 2.47/1.56 c_lam: $i > ( $i > $i ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_setprod_tp,type,
% 2.47/1.56 c_setprod: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_ap_tp,type,
% 2.47/1.56 c_ap: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_setsum_p_tp,type,
% 2.47/1.56 c_setsum_p: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_tuple_p_tp,type,
% 2.47/1.56 c_tuple_p: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_Pi_tp,type,
% 2.47/1.56 c_Pi: $i > ( $i > $i ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_setexp_tp,type,
% 2.47/1.56 c_setexp: $i > $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_Sep2_tp,type,
% 2.47/1.56 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_set_of_pairs_tp,type,
% 2.47/1.56 c_set_of_pairs: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_lam2_tp,type,
% 2.47/1.56 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_PNoEq__tp,type,
% 2.47/1.56 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_PNoLt__tp,type,
% 2.47/1.56 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_PNoLt_tp,type,
% 2.47/1.56 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_PNoLe_tp,type,
% 2.47/1.56 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_PNo_downc_tp,type,
% 2.47/1.56 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_PNo_upc_tp,type,
% 2.47/1.56 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_SNoElts__tp,type,
% 2.47/1.56 c_SNoElts_: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_SNo__tp,type,
% 2.47/1.56 c_SNo_: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_PSNo_tp,type,
% 2.47/1.56 c_PSNo: $i > ( $i > $o ) > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_SNo_tp,type,
% 2.47/1.56 c_SNo: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_SNoLev_tp,type,
% 2.47/1.56 c_SNoLev: $i > $i ).
% 2.47/1.56
% 2.47/1.56 thf(c_SNoEq__tp,type,
% 2.47/1.56 c_SNoEq_: $i > $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_SNoLt_tp,type,
% 2.47/1.56 c_SNoLt: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_SNoLe_tp,type,
% 2.47/1.56 c_SNoLe: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_binop_on_tp,type,
% 2.47/1.56 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_Loop_tp,type,
% 2.47/1.56 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_Loop_with_defs_tp,type,
% 2.47/1.56 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 ).
% 2.47/1.56
% 2.47/1.56 thf(c_Loop_with_defs_cex1_tp,type,
% 2.47/1.56 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 ).
% 2.47/1.56
% 2.47/1.56 thf(c_Loop_with_defs_cex2_tp,type,
% 2.47/1.56 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 ).
% 2.47/1.56
% 2.47/1.56 thf(c_combinator_tp,type,
% 2.47/1.56 c_combinator: $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_combinator_equiv_tp,type,
% 2.47/1.56 c_combinator_equiv: $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(c_equip_mod_tp,type,
% 2.47/1.56 c_equip_mod: $i > $i > $i > $o ).
% 2.47/1.56
% 2.47/1.56 thf(ax1,axiom,
% 2.47/1.56 ! [X0: $i > $o,X1: $i] :
% 2.47/1.56 ( ( X0 @ X1 )
% 2.47/1.56 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax2,axiom,
% 2.47/1.56 ! [X0: $o] :
% 2.47/1.56 ( ( c_not @ ( c_not @ X0 ) )
% 2.47/1.56 => X0 ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax3,axiom,
% 2.47/1.56 ! [X0: $o,X1: $o] :
% 2.47/1.56 ( ( c_iff @ X0 @ X1 )
% 2.47/1.56 => ( X0 = X1 ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax4,axiom,
% 2.47/1.56 ! [X0: $i,X1: $i] :
% 2.47/1.56 ( ( c_Subq @ X0 @ X1 )
% 2.47/1.56 => ( ( c_Subq @ X1 @ X0 )
% 2.47/1.56 => ( X0 = X1 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax5,axiom,
% 2.47/1.56 ( c_not
% 2.47/1.56 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax6,axiom,
% 2.47/1.56 ! [X0: $i,X1: $i] :
% 2.47/1.56 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 2.47/1.56 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax7,axiom,
% 2.47/1.56 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax8,axiom,
% 2.47/1.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 2.47/1.56 ( c_iff
% 2.47/1.56 @ ( c_In @ X2
% 2.47/1.56 @ ( c_Repl @ X0
% 2.47/1.56 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 2.47/1.56 @ ? [X3: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X3 @ X0 )
% 2.47/1.56 @ ( X2
% 2.47/1.56 = ( X1 @ X3 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax9,axiom,
% 2.47/1.56 ! [X0: $i > $o] :
% 2.47/1.56 ( ! [X1: $i] :
% 2.47/1.56 ( ( X0 @ X1 )
% 2.47/1.56 => ! [X2: $i] :
% 2.47/1.56 ( ( c_In @ X2 @ X1 )
% 2.47/1.56 => ( X0 @ X2 ) ) )
% 2.47/1.56 => ( ( X0 @ c_Empty )
% 2.47/1.56 => ( ! [X1: $i] :
% 2.47/1.56 ( ( X0 @ X1 )
% 2.47/1.56 => ( X0 @ ( c_Union @ X1 ) ) )
% 2.47/1.56 => ( ! [X1: $i] :
% 2.47/1.56 ( ( X0 @ X1 )
% 2.47/1.56 => ( X0 @ ( c_Power @ X1 ) ) )
% 2.47/1.56 => ( ! [X1: $i] :
% 2.47/1.56 ( ( X0 @ X1 )
% 2.47/1.56 => ! [X2: $i > $i] :
% 2.47/1.56 ( ! [X3: $i] :
% 2.47/1.56 ( ( c_In @ X3 @ X1 )
% 2.47/1.56 => ( X0 @ ( X2 @ X3 ) ) )
% 2.47/1.56 => ( X0
% 2.47/1.56 @ ( c_Repl @ X1
% 2.47/1.56 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 2.47/1.56 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax10,axiom,
% 2.47/1.56 ! [X0: $i > $o] :
% 2.47/1.56 ( ! [X1: $i] :
% 2.47/1.56 ( ! [X2: $i] :
% 2.47/1.56 ( ( c_In @ X2 @ X1 )
% 2.47/1.56 => ( X0 @ X2 ) )
% 2.47/1.56 => ( X0 @ X1 ) )
% 2.47/1.56 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax11,axiom,
% 2.47/1.56 ( c_False
% 2.47/1.56 = ( ! [X0: $o] : X0 ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax12,axiom,
% 2.47/1.56 ( c_True
% 2.47/1.56 = ( ! [X0: $o] :
% 2.47/1.56 ( X0
% 2.47/1.56 => X0 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax13,axiom,
% 2.47/1.56 ( c_not
% 2.47/1.56 = ( ^ [X0: $o] :
% 2.47/1.56 ( X0
% 2.47/1.56 => c_False ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax14,axiom,
% 2.47/1.56 ( c_and
% 2.47/1.56 = ( ^ [X0: $o,X1: $o] :
% 2.47/1.56 ! [X2: $o] :
% 2.47/1.56 ( ( X0
% 2.47/1.56 => ( X1
% 2.47/1.56 => X2 ) )
% 2.47/1.56 => X2 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax15,axiom,
% 2.47/1.56 ( c_or
% 2.47/1.56 = ( ^ [X0: $o,X1: $o] :
% 2.47/1.56 ! [X2: $o] :
% 2.47/1.56 ( ( X0
% 2.47/1.56 => X2 )
% 2.47/1.56 => ( ( X1
% 2.47/1.56 => X2 )
% 2.47/1.56 => X2 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax16,axiom,
% 2.47/1.56 ( c_iff
% 2.47/1.56 = ( ^ [X0: $o,X1: $o] :
% 2.47/1.56 ( c_and
% 2.47/1.56 @ ( X0
% 2.47/1.56 => X1 )
% 2.47/1.56 @ ( X1
% 2.47/1.56 => X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax17,axiom,
% 2.47/1.56 ( c_Subq
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ! [X2: $i] :
% 2.47/1.56 ( ( c_In @ X2 @ X0 )
% 2.47/1.56 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax18,axiom,
% 2.47/1.56 ( c_TransSet
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ! [X1: $i] :
% 2.47/1.56 ( ( c_In @ X1 @ X0 )
% 2.47/1.56 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax19,axiom,
% 2.47/1.56 ( c_atleast2
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax20,axiom,
% 2.47/1.56 ( c_atleast3
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax21,axiom,
% 2.47/1.56 ( c_atleast4
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax22,axiom,
% 2.47/1.56 ( c_atleast5
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax23,axiom,
% 2.47/1.56 ( c_atleast6
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax24,axiom,
% 2.47/1.56 ( c_exactly2
% 2.47/1.56 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax25,axiom,
% 2.47/1.56 ( c_exactly3
% 2.47/1.56 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax26,axiom,
% 2.47/1.56 ( c_exactly4
% 2.47/1.56 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax27,axiom,
% 2.47/1.56 ( c_exactly5
% 2.47/1.56 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax28,axiom,
% 2.47/1.56 ( c_exu_i
% 2.47/1.56 = ( ^ [X0: $i > $o] :
% 2.47/1.56 ( c_and
% 2.47/1.56 @ ? [X1: $i] : ( X0 @ X1 )
% 2.47/1.56 @ ! [X1: $i,X2: $i] :
% 2.47/1.56 ( ( X0 @ X1 )
% 2.47/1.56 => ( ( X0 @ X2 )
% 2.47/1.56 => ( X1 = X2 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax29,axiom,
% 2.47/1.56 ( c_reflexive_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] :
% 2.47/1.56 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax30,axiom,
% 2.47/1.56 ( c_irreflexive_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] :
% 2.47/1.56 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax31,axiom,
% 2.47/1.56 ( c_symmetric_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] :
% 2.47/1.56 ! [X1: $i,X2: $i] :
% 2.47/1.56 ( ( X0 @ X1 @ X2 )
% 2.47/1.56 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax32,axiom,
% 2.47/1.56 ( c_antisymmetric_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] :
% 2.47/1.56 ! [X1: $i,X2: $i] :
% 2.47/1.56 ( ( X0 @ X1 @ X2 )
% 2.47/1.56 => ( ( X0 @ X2 @ X1 )
% 2.47/1.56 => ( X1 = X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax33,axiom,
% 2.47/1.56 ( c_transitive_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] :
% 2.47/1.56 ! [X1: $i,X2: $i,X3: $i] :
% 2.47/1.56 ( ( X0 @ X1 @ X2 )
% 2.47/1.56 => ( ( X0 @ X2 @ X3 )
% 2.47/1.56 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax34,axiom,
% 2.47/1.56 ( c_eqreln_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax35,axiom,
% 2.47/1.56 ( c_per_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax36,axiom,
% 2.47/1.56 ( c_linear_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] :
% 2.47/1.56 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax37,axiom,
% 2.47/1.56 ( c_trichotomous_or_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] :
% 2.47/1.56 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax38,axiom,
% 2.47/1.56 ( c_partialorder_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax39,axiom,
% 2.47/1.56 ( c_totalorder_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax40,axiom,
% 2.47/1.56 ( c_strictpartialorder_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax41,axiom,
% 2.47/1.56 ( c_stricttotalorder_i
% 2.47/1.56 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax42,axiom,
% 2.47/1.56 ( c_If_i
% 2.47/1.56 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 2.47/1.56 ( c_Eps_i
% 2.47/1.56 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax43,axiom,
% 2.47/1.56 ( c_exactly1of2
% 2.47/1.56 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax44,axiom,
% 2.47/1.56 ( c_exactly1of3
% 2.47/1.56 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax45,axiom,
% 2.47/1.56 ( c_nIn
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax46,axiom,
% 2.47/1.56 ( c_nSubq
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax47,axiom,
% 2.47/1.56 ( c_UPair
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 2.47/1.56 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax48,axiom,
% 2.47/1.56 ( c_Sing
% 2.47/1.56 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax49,axiom,
% 2.47/1.56 ( c_binunion
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax50,axiom,
% 2.47/1.56 ( c_SetAdjoin
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax51,axiom,
% 2.47/1.56 ( c_famunion
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i] :
% 2.47/1.56 ( c_Union
% 2.47/1.56 @ ( c_Repl @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax52,axiom,
% 2.47/1.56 ( c_Sep
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $o] :
% 2.47/1.56 ( c_If_i
% 2.47/1.56 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 2.47/1.56 @ ( c_Repl @ X0
% 2.47/1.56 @ ^ [X2: $i] :
% 2.47/1.56 ( ^ [X3: $i] :
% 2.47/1.56 ( c_If_i @ ( X1 @ X3 ) @ X3
% 2.47/1.56 @ ( c_Eps_i
% 2.47/1.56 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 2.47/1.56 @ X2 ) )
% 2.47/1.56 @ c_Empty ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax53,axiom,
% 2.47/1.56 ( c_ReplSep
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 2.47/1.56 ( c_Repl
% 2.47/1.56 @ ( c_Sep @ X0
% 2.47/1.56 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.47/1.56 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax54,axiom,
% 2.47/1.56 ( c_binintersect
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_Sep @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax55,axiom,
% 2.47/1.56 ( c_setminus
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_Sep @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax56,axiom,
% 2.47/1.56 ( c_inj
% 2.47/1.56 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.47/1.56 ( c_and
% 2.47/1.56 @ ! [X3: $i] :
% 2.47/1.56 ( ( c_In @ X3 @ X0 )
% 2.47/1.56 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 2.47/1.56 @ ! [X3: $i] :
% 2.47/1.56 ( ( c_In @ X3 @ X0 )
% 2.47/1.56 => ! [X4: $i] :
% 2.47/1.56 ( ( c_In @ X4 @ X0 )
% 2.47/1.56 => ( ( ( X2 @ X3 )
% 2.47/1.56 = ( X2 @ X4 ) )
% 2.47/1.56 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax57,axiom,
% 2.47/1.56 ( c_bij
% 2.47/1.56 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.47/1.56 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 2.47/1.56 @ ! [X3: $i] :
% 2.47/1.56 ( ( c_In @ X3 @ X1 )
% 2.47/1.56 => ? [X4: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X4 @ X0 )
% 2.47/1.56 @ ( ( X2 @ X4 )
% 2.47/1.56 = X3 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax58,axiom,
% 2.47/1.56 ( c_atleastp
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax59,axiom,
% 2.47/1.56 ( c_equip
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax60,axiom,
% 2.47/1.56 ( c_In_rec_poly_G_i
% 2.47/1.56 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 2.47/1.56 ! [X3: $i > $i > $o] :
% 2.47/1.56 ( ! [X4: $i,X5: $i > $i] :
% 2.47/1.56 ( ! [X6: $i] :
% 2.47/1.56 ( ( c_In @ X6 @ X4 )
% 2.47/1.56 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 2.47/1.56 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 2.47/1.56 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax61,axiom,
% 2.47/1.56 ( c_In_rec_poly_i
% 2.47/1.56 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 2.47/1.56 ( c_Eps_i
% 2.47/1.56 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax62,axiom,
% 2.47/1.56 ( c_ordsucc
% 2.47/1.56 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax63,axiom,
% 2.47/1.56 ( c_nat_p
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ! [X1: $i > $o] :
% 2.47/1.56 ( ( X1 @ c_Empty )
% 2.47/1.56 => ( ! [X2: $i] :
% 2.47/1.56 ( ( X1 @ X2 )
% 2.47/1.56 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 2.47/1.56 => ( X1 @ X0 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax64,axiom,
% 2.47/1.56 ( c_nat_primrec
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.47/1.56 ( c_In_rec_poly_i
% 2.47/1.56 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax65,axiom,
% 2.47/1.56 ( c_add_nat
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_nat_primrec @ X0
% 2.47/1.56 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 2.47/1.56 @ X1 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax66,axiom,
% 2.47/1.56 ( c_mul_nat
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_nat_primrec @ c_Empty
% 2.47/1.56 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 2.47/1.56 @ X1 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax67,axiom,
% 2.47/1.56 ( c_ordinal
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ( c_and @ ( c_TransSet @ X0 )
% 2.47/1.56 @ ! [X1: $i] :
% 2.47/1.56 ( ( c_In @ X1 @ X0 )
% 2.47/1.56 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax68,axiom,
% 2.47/1.56 ( c_V_
% 2.47/1.56 = ( c_In_rec_poly_i
% 2.47/1.56 @ ^ [X0: $i,X1: $i > $i] :
% 2.47/1.56 ( c_famunion @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax69,axiom,
% 2.47/1.56 ( c_Inj1
% 2.47/1.56 = ( c_In_rec_poly_i
% 2.47/1.56 @ ^ [X0: $i,X1: $i > $i] :
% 2.47/1.56 ( c_binunion @ ( c_Sing @ c_Empty )
% 2.47/1.56 @ ( c_Repl @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax70,axiom,
% 2.47/1.56 ( c_Inj0
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ( c_Repl @ X0
% 2.47/1.56 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax71,axiom,
% 2.47/1.56 ( c_Unj
% 2.47/1.56 = ( c_In_rec_poly_i
% 2.47/1.56 @ ^ [X0: $i,X1: $i > $i] :
% 2.47/1.56 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 2.47/1.56 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax72,axiom,
% 2.47/1.56 ( c_combine_funcs
% 2.47/1.56 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 2.47/1.56 ( c_If_i
% 2.47/1.56 @ ( X4
% 2.47/1.56 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 2.47/1.56 @ ( X2 @ ( c_Unj @ X4 ) )
% 2.47/1.56 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax73,axiom,
% 2.47/1.56 ( c_setsum
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_binunion
% 2.47/1.56 @ ( c_Repl @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 2.47/1.56 @ ( c_Repl @ X1
% 2.47/1.56 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax74,axiom,
% 2.47/1.56 ( c_proj0
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ( c_ReplSep @ X0
% 2.47/1.56 @ ^ [X1: $i] :
% 2.47/1.56 ? [X2: $i] :
% 2.47/1.56 ( ( c_Inj0 @ X2 )
% 2.47/1.56 = X1 )
% 2.47/1.56 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax75,axiom,
% 2.47/1.56 ( c_proj1
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ( c_ReplSep @ X0
% 2.47/1.56 @ ^ [X1: $i] :
% 2.47/1.56 ? [X2: $i] :
% 2.47/1.56 ( ( c_Inj1 @ X2 )
% 2.47/1.56 = X1 )
% 2.47/1.56 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax76,axiom,
% 2.47/1.56 ( c_binrep
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax77,axiom,
% 2.47/1.56 ( c_lam
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i] :
% 2.47/1.56 ( c_famunion @ X0
% 2.47/1.56 @ ^ [X2: $i] :
% 2.47/1.56 ( c_Repl @ ( X1 @ X2 )
% 2.47/1.56 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax78,axiom,
% 2.47/1.56 ( c_setprod
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_lam @ X0
% 2.47/1.56 @ ^ [X2: $i] : X1 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax79,axiom,
% 2.47/1.56 ( c_ap
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_ReplSep @ X0
% 2.47/1.56 @ ^ [X2: $i] :
% 2.47/1.56 ? [X3: $i] :
% 2.47/1.56 ( X2
% 2.47/1.56 = ( c_setsum @ X1 @ X3 ) )
% 2.47/1.56 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax80,axiom,
% 2.47/1.56 ( c_setsum_p
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 2.47/1.56 = X0 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax81,axiom,
% 2.47/1.56 ( c_tuple_p
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ! [X2: $i] :
% 2.47/1.56 ( ( c_In @ X2 @ X1 )
% 2.47/1.56 => ? [X3: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X3 @ X0 )
% 2.47/1.56 @ ? [X4: $i] :
% 2.47/1.56 ( X2
% 2.47/1.56 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax82,axiom,
% 2.47/1.56 ( c_Pi
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i] :
% 2.47/1.56 ( c_Sep
% 2.47/1.56 @ ( c_Power
% 2.47/1.56 @ ( c_lam @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 2.47/1.56 @ ^ [X2: $i] :
% 2.47/1.56 ! [X3: $i] :
% 2.47/1.56 ( ( c_In @ X3 @ X0 )
% 2.47/1.56 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax83,axiom,
% 2.47/1.56 ( c_setexp
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_Pi @ X1
% 2.47/1.56 @ ^ [X2: $i] : X0 ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax84,axiom,
% 2.47/1.56 ( c_Sep2
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 2.47/1.56 ( c_Sep
% 2.47/1.56 @ ( c_lam @ X0
% 2.47/1.56 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.47/1.56 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax85,axiom,
% 2.47/1.56 ( c_set_of_pairs
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ! [X1: $i] :
% 2.47/1.56 ( ( c_In @ X1 @ X0 )
% 2.47/1.56 => ? [X2: $i,X3: $i] :
% 2.47/1.56 ( X1
% 2.47/1.56 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 2.47/1.56 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax86,axiom,
% 2.47/1.56 ( c_lam2
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 2.47/1.56 ( c_lam @ X0
% 2.47/1.56 @ ^ [X3: $i] :
% 2.47/1.56 ( c_lam @ ( X1 @ X3 )
% 2.47/1.56 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax87,axiom,
% 2.47/1.56 ( c_PNoEq_
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.47/1.56 ! [X3: $i] :
% 2.47/1.56 ( ( c_In @ X3 @ X0 )
% 2.47/1.56 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax88,axiom,
% 2.47/1.56 ( c_PNoLt_
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.47/1.56 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax89,axiom,
% 2.47/1.56 ( c_PNoLt
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax90,axiom,
% 2.47/1.56 ( c_PNoLe
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax91,axiom,
% 2.47/1.56 ( c_PNo_downc
% 2.47/1.56 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.47/1.56 ? [X3: $i] :
% 2.47/1.56 ( c_and @ ( c_ordinal @ X3 )
% 2.47/1.56 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax92,axiom,
% 2.47/1.56 ( c_PNo_upc
% 2.47/1.56 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.47/1.56 ? [X3: $i] :
% 2.47/1.56 ( c_and @ ( c_ordinal @ X3 )
% 2.47/1.56 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax93,axiom,
% 2.47/1.56 ( c_SNoElts_
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ( c_binunion @ X0
% 2.47/1.56 @ ( c_Repl @ X0
% 2.47/1.56 @ ^ [X1: $i] :
% 2.47/1.56 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.47/1.56 @ X1 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax94,axiom,
% 2.47/1.56 ( c_SNo_
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 2.47/1.56 @ ! [X2: $i] :
% 2.47/1.56 ( ( c_In @ X2 @ X0 )
% 2.47/1.56 => ( c_exactly1of2
% 2.47/1.56 @ ( c_In
% 2.47/1.56 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.47/1.56 @ X2 )
% 2.47/1.56 @ X1 )
% 2.47/1.56 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax95,axiom,
% 2.47/1.56 ( c_PSNo
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $o] :
% 2.47/1.56 ( c_binunion
% 2.47/1.56 @ ( c_Sep @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 2.47/1.56 @ ( c_ReplSep @ X0
% 2.47/1.56 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 2.47/1.56 @ ^ [X2: $i] :
% 2.47/1.56 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.47/1.56 @ X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax96,axiom,
% 2.47/1.56 ( c_SNo
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax97,axiom,
% 2.47/1.56 ( c_SNoLev
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ( c_Eps_i
% 2.47/1.56 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax98,axiom,
% 2.47/1.56 ( c_SNoEq_
% 2.47/1.56 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.47/1.56 ( c_PNoEq_ @ X0
% 2.47/1.56 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 2.47/1.56 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax99,axiom,
% 2.47/1.56 ( c_SNoLt
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 2.47/1.56 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.47/1.56 @ ( c_SNoLev @ X1 )
% 2.47/1.56 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax100,axiom,
% 2.47/1.56 ( c_SNoLe
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 2.47/1.56 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.47/1.56 @ ( c_SNoLev @ X1 )
% 2.47/1.56 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax101,axiom,
% 2.47/1.56 ( c_binop_on
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.47/1.56 ! [X2: $i] :
% 2.47/1.56 ( ( c_In @ X2 @ X0 )
% 2.47/1.56 => ! [X3: $i] :
% 2.47/1.56 ( ( c_In @ X3 @ X0 )
% 2.47/1.56 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax102,axiom,
% 2.47/1.56 ( c_Loop
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 2.47/1.56 ( c_and
% 2.47/1.56 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 2.47/1.56 @ ! [X5: $i] :
% 2.47/1.56 ( ( c_In @ X5 @ X0 )
% 2.47/1.56 => ( c_and
% 2.47/1.56 @ ( ( X1 @ X4 @ X5 )
% 2.47/1.56 = X5 )
% 2.47/1.56 @ ( ( X1 @ X5 @ X4 )
% 2.47/1.56 = X5 ) ) ) )
% 2.47/1.56 @ ! [X5: $i] :
% 2.47/1.56 ( ( c_In @ X5 @ X0 )
% 2.47/1.56 => ! [X6: $i] :
% 2.47/1.56 ( ( c_In @ X6 @ X0 )
% 2.47/1.56 => ( c_and
% 2.47/1.56 @ ( c_and
% 2.47/1.56 @ ( c_and
% 2.47/1.56 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 2.47/1.56 = X6 )
% 2.47/1.56 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 2.47/1.56 = X6 ) )
% 2.47/1.56 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 2.47/1.56 = X5 ) )
% 2.47/1.56 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 2.47/1.56 = X5 ) ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax103,axiom,
% 2.47/1.56 ( c_Loop_with_defs
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.47/1.56 ( c_and
% 2.47/1.56 @ ( c_and
% 2.47/1.56 @ ( c_and
% 2.47/1.56 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 2.47/1.56 @ ! [X14: $i] :
% 2.47/1.56 ( ( c_In @ X14 @ X0 )
% 2.47/1.56 => ! [X15: $i] :
% 2.47/1.56 ( ( c_In @ X15 @ X0 )
% 2.47/1.56 => ( ( X5 @ X14 @ X15 )
% 2.47/1.56 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 2.47/1.56 @ ! [X14: $i] :
% 2.47/1.56 ( ( c_In @ X14 @ X0 )
% 2.47/1.56 => ! [X15: $i] :
% 2.47/1.56 ( ( c_In @ X15 @ X0 )
% 2.47/1.56 => ! [X16: $i] :
% 2.47/1.56 ( ( c_In @ X16 @ X0 )
% 2.47/1.56 => ( ( X6 @ X14 @ X15 @ X16 )
% 2.47/1.56 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 2.47/1.56 @ ! [X14: $i] :
% 2.47/1.56 ( ( c_In @ X14 @ X0 )
% 2.47/1.56 => ! [X15: $i] :
% 2.47/1.56 ( ( c_In @ X15 @ X0 )
% 2.47/1.56 => ( c_and
% 2.47/1.56 @ ( c_and
% 2.47/1.56 @ ( c_and
% 2.47/1.56 @ ( c_and
% 2.47/1.56 @ ( ( X7 @ X14 @ X15 )
% 2.47/1.56 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 2.47/1.56 @ ( ( X10 @ X14 @ X15 )
% 2.47/1.56 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 2.47/1.56 @ ( ( X11 @ X14 @ X15 )
% 2.47/1.56 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 2.47/1.56 @ ( ( X12 @ X14 @ X15 )
% 2.47/1.56 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 2.47/1.56 @ ( ( X13 @ X14 @ X15 )
% 2.47/1.56 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 2.47/1.56 @ ! [X14: $i] :
% 2.47/1.56 ( ( c_In @ X14 @ X0 )
% 2.47/1.56 => ! [X15: $i] :
% 2.47/1.56 ( ( c_In @ X15 @ X0 )
% 2.47/1.56 => ! [X16: $i] :
% 2.47/1.56 ( ( c_In @ X16 @ X0 )
% 2.47/1.56 => ( c_and
% 2.47/1.56 @ ( ( X8 @ X14 @ X15 @ X16 )
% 2.47/1.56 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 2.47/1.56 @ ( ( X9 @ X14 @ X15 @ X16 )
% 2.47/1.56 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax104,axiom,
% 2.47/1.56 ( c_Loop_with_defs_cex1
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.47/1.56 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.47/1.56 @ ? [X14: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X14 @ X0 )
% 2.47/1.56 @ ? [X15: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X15 @ X0 )
% 2.47/1.56 @ ? [X16: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X16 @ X0 )
% 2.47/1.56 @ ? [X17: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X17 @ X0 )
% 2.47/1.56 @ ( c_not
% 2.47/1.56 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 2.47/1.56 = X4 ) ) ) ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax105,axiom,
% 2.47/1.56 ( c_Loop_with_defs_cex2
% 2.47/1.56 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.47/1.56 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.47/1.56 @ ? [X14: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X14 @ X0 )
% 2.47/1.56 @ ? [X15: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X15 @ X0 )
% 2.47/1.56 @ ? [X16: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X16 @ X0 )
% 2.47/1.56 @ ? [X17: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X17 @ X0 )
% 2.47/1.56 @ ? [X18: $i] :
% 2.47/1.56 ( c_and @ ( c_In @ X18 @ X0 )
% 2.47/1.56 @ ( c_not
% 2.47/1.56 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 2.47/1.56 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax106,axiom,
% 2.47/1.56 ( c_combinator
% 2.47/1.56 = ( ^ [X0: $i] :
% 2.47/1.56 ! [X1: $i > $o] :
% 2.47/1.56 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 2.47/1.56 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 2.47/1.56 => ( ! [X2: $i,X3: $i] :
% 2.47/1.56 ( ( X1 @ X2 )
% 2.47/1.56 => ( ( X1 @ X3 )
% 2.47/1.56 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 2.47/1.56 => ( X1 @ X0 ) ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax107,axiom,
% 2.47/1.56 ( c_combinator_equiv
% 2.47/1.56 = ( ^ [X0: $i,X1: $i] :
% 2.47/1.56 ! [X2: $i > $i > $o] :
% 2.47/1.56 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 2.47/1.56 ( ( c_per_i @ X2 )
% 2.47/1.56 => ( ! [X6: $i] :
% 2.47/1.56 ( ( c_combinator @ X6 )
% 2.47/1.56 => ( X2 @ X6 @ X6 ) )
% 2.47/1.56 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.47/1.56 ( ( c_combinator @ X6 )
% 2.47/1.56 => ( ( c_combinator @ X7 )
% 2.47/1.56 => ( ( c_combinator @ X8 )
% 2.47/1.56 => ( ( c_combinator @ X9 )
% 2.47/1.56 => ( ( X2 @ X6 @ X8 )
% 2.47/1.56 => ( ( X2 @ X7 @ X9 )
% 2.47/1.56 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 2.47/1.56 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 2.47/1.56 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 2.47/1.56 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 2.47/1.56 @ ( c_Inj0 @ c_Empty )
% 2.47/1.56 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 2.47/1.56 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(ax108,axiom,
% 2.47/1.56 ( c_equip_mod
% 2.47/1.56 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.47/1.56 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 2.47/1.56
% 2.47/1.56 thf(conj,conjecture,
% 2.47/1.56 ( c_not
% 2.47/1.56 @ ! [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 ) > $i ) > ( $i > $i > $i ) > $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $o,X3: ( $i > $i ) > ( $i > $i ) > $o] :
% 2.47/1.56 ( ! [X4: ( ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: ( ( ( $i > $i ) > $i ) > $i > $i > $i ) > $i,X7: $i] :
% 2.47/1.56 ( ( c_In @ X7
% 2.47/1.56 @ ( X6
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i,X9: $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ X7 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 2.47/1.56 => ( X3
% 2.47/1.56 @ ^ [X8: $i] : X8
% 2.47/1.56 @ ^ [X8: $i] : ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
% 2.47/1.56 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 2.47/1.56 ( ( 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 )
% 2.47/1.56 => ( ( X3
% 2.47/1.56 @ ^ [X8: $i] : c_Empty
% 2.47/1.56 @ ^ [X8: $i] : c_Empty )
% 2.47/1.56 => ( X0
% 2.47/1.56 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ c_Empty )
% 2.47/1.56 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] :
% 2.47/1.56 ( X9
% 2.47/1.56 @ ^ [X11: $i] : c_Empty )
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i] : X5
% 2.47/1.56 @ c_Empty
% 2.47/1.56 @ ( c_Inj0 @ c_Empty ) ) ) )
% 2.47/1.56 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 2.47/1.56 ( ( c_In @ ( c_Inj1 @ X6 ) @ X7 )
% 2.47/1.56 => ( ( X0
% 2.47/1.56 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
% 2.47/1.56 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ X7 @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) )
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i] : c_Empty
% 2.47/1.56 @ ( c_setsum @ c_Empty @ ( c_setsum @ X7 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ X6 ) ) )
% 2.47/1.56 @ c_Empty )
% 2.47/1.56 => ( X2
% 2.47/1.56 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : X7
% 2.47/1.56 @ ( c_Inj1 @ ( c_setsum @ ( c_Inj0 @ X4 ) @ c_Empty ) )
% 2.47/1.56 @ ^ [X8: $i] : ( c_setsum @ ( c_setsum @ ( c_setsum @ X7 @ X6 ) @ X7 ) @ ( c_setsum @ c_Empty @ c_Empty ) )
% 2.47/1.56 @ c_Empty ) ) )
% 2.47/1.56 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 2.47/1.56 ( ( c_In @ ( c_setsum @ c_Empty @ X6 ) @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
% 2.47/1.56 => ( ( X2
% 2.47/1.56 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ X7 @ X5 )
% 2.47/1.56 @ c_Empty
% 2.47/1.56 @ ^ [X8: $i] : ( c_Inj0 @ ( c_setsum @ X5 @ c_Empty ) )
% 2.47/1.56 @ c_Empty )
% 2.47/1.56 => ( X0
% 2.47/1.56 @ ^ [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 ) )
% 2.47/1.56 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i] :
% 2.47/1.56 ( c_setsum
% 2.47/1.56 @ ( c_Inj1
% 2.47/1.56 @ ( X8
% 2.47/1.56 @ ^ [X9: $i] : X6
% 2.47/1.56 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
% 2.47/1.56 @ X7 )
% 2.47/1.56 @ c_Empty
% 2.47/1.56 @ ( 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 ) ) ) ) ) ) )
% 2.47/1.56 => ( ! [X4: $i,X5: $i,X6: $i,X7: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i > $i] :
% 2.47/1.56 ( ( c_In @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) )
% 2.47/1.56 @ ( c_Inj0
% 2.47/1.56 @ ( c_setsum
% 2.47/1.56 @ ( c_Inj0
% 2.47/1.56 @ ( X7
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
% 2.47/1.56 @ c_Empty
% 2.47/1.56 @ ^ [X8: $i] : c_Empty
% 2.47/1.56 @ c_Empty ) )
% 2.47/1.56 @ c_Empty ) ) )
% 2.47/1.56 => ( ( X0
% 2.47/1.56 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
% 2.47/1.56 @ ^ [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 ) ) ) )
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i] :
% 2.47/1.56 ( X8
% 2.47/1.56 @ ^ [X9: $i] :
% 2.47/1.56 ( c_setsum
% 2.47/1.56 @ ( X7
% 2.47/1.56 @ ^ [X10: ( $i > $i ) > $i > $i,X11: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
% 2.47/1.56 @ c_Empty
% 2.47/1.56 @ ^ [X10: $i] : ( c_Inj0 @ c_Empty )
% 2.47/1.56 @ X9 )
% 2.47/1.56 @ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
% 2.47/1.56 @ c_Empty )
% 2.47/1.56 @ ( c_setsum @ c_Empty
% 2.47/1.56 @ ( c_Inj1
% 2.47/1.56 @ ( c_setsum
% 2.47/1.56 @ ( X7
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i] : c_Empty
% 2.47/1.56 @ c_Empty
% 2.47/1.56 @ ^ [X8: $i] : c_Empty
% 2.47/1.56 @ c_Empty )
% 2.47/1.56 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 2.47/1.56 @ c_Empty )
% 2.47/1.56 => ( X1
% 2.47/1.56 @ ^ [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 ) )
% 2.47/1.56 @ ( c_Inj1 @ c_Empty ) ) ) )
% 2.47/1.56 => ( ! [X4: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i,X5: $i,X6: $i > $i,X7: ( $i > $i ) > $i] :
% 2.47/1.56 ( ( 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 ) ) ) )
% 2.47/1.56 @ ( c_Inj0
% 2.47/1.56 @ ( c_setsum @ c_Empty
% 2.47/1.56 @ ( X4
% 2.47/1.56 @ ^ [X8: $i,X9: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
% 2.47/1.56 @ ( c_setsum @ c_Empty @ c_Empty )
% 2.47/1.56 @ ( c_Inj0 @ c_Empty )
% 2.47/1.56 @ ( c_Inj0 @ c_Empty ) ) ) ) )
% 2.47/1.56 => ( ( X1
% 2.47/1.56 @ ^ [X8: $i > $i] : ( X6 @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 2.47/1.56 @ ( c_setsum
% 2.47/1.56 @ ( X7
% 2.47/1.56 @ ^ [X8: $i] : ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) )
% 2.47/1.56 @ ( c_Inj0 @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) )
% 2.47/1.56 => ( X1
% 2.47/1.56 @ ^ [X8: $i > $i] :
% 2.47/1.56 ( c_Inj1
% 2.47/1.56 @ ( c_setsum @ ( X8 @ ( c_setsum @ c_Empty @ c_Empty ) )
% 2.47/1.56 @ ( c_setsum @ ( c_Inj1 @ c_Empty )
% 2.47/1.56 @ ( X7
% 2.47/1.56 @ ^ [X9: $i] : c_Empty ) ) ) )
% 2.47/1.56 @ c_Empty ) ) )
% 2.47/1.56 => ( ! [X4: $i,X5: $i,X6: $i > $i,X7: $i] :
% 2.47/1.56 ( ( c_In @ X4 @ ( c_Inj0 @ c_Empty ) )
% 2.47/1.56 => ( ( X2
% 2.47/1.56 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i > $i] : ( c_setsum @ c_Empty @ X5 )
% 2.47/1.56 @ ( c_Inj0 @ X7 )
% 2.47/1.56 @ ^ [X8: $i] : ( c_setsum @ c_Empty @ X8 )
% 2.47/1.56 @ c_Empty )
% 2.47/1.56 => ( X0
% 2.47/1.56 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] : c_Empty
% 2.47/1.56 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : c_Empty
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i] : ( c_setsum @ ( c_Inj1 @ c_Empty ) @ X5 )
% 2.47/1.56 @ ( c_Inj0 @ c_Empty )
% 2.47/1.56 @ X7 ) ) )
% 2.47/1.56 => ( ! [X4: $i,X5: $i,X6: ( $i > $i ) > $i,X7: $i] :
% 2.47/1.56 ( ( X0
% 2.47/1.56 @ ^ [X8: ( ( $i > $i > $i ) > $i ) > $i,X9: $i > ( $i > $i ) > $i] :
% 2.47/1.56 ( X9
% 2.47/1.56 @ ( c_setsum
% 2.47/1.56 @ ( X8
% 2.47/1.56 @ ^ [X10: $i > $i > $i] : ( c_Inj0 @ c_Empty ) )
% 2.47/1.56 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
% 2.47/1.56 @ ^ [X10: $i] :
% 2.47/1.56 ( X9
% 2.47/1.56 @ ( X8
% 2.47/1.56 @ ^ [X11: $i > $i > $i] : c_Empty )
% 2.47/1.56 @ ^ [X11: $i] :
% 2.47/1.56 ( X9
% 2.47/1.56 @ ( X9 @ c_Empty
% 2.47/1.56 @ ^ [X12: $i] : c_Empty )
% 2.47/1.56 @ ^ [X12: $i] : c_Empty ) ) )
% 2.47/1.56 @ ^ [X8: $i,X9: ( $i > $i ) > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ X10 @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
% 2.47/1.56 @ ^ [X8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ X5 )
% 2.47/1.56 @ ( c_Inj0 @ X7 )
% 2.47/1.56 @ ( c_setsum @ c_Empty
% 2.47/1.56 @ ( c_setsum
% 2.47/1.56 @ ( c_setsum
% 2.47/1.56 @ ( X6
% 2.47/1.56 @ ^ [X8: $i] : c_Empty )
% 2.47/1.56 @ c_Empty )
% 2.47/1.56 @ ( c_setsum @ c_Empty @ X5 ) ) ) )
% 2.47/1.56 => ( 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 ) ) ) ) )
% 2.47/1.56 => c_False ) ) ) ) ) ) ) ) ) ).
% 2.47/1.56 ------------------------
% 2.47/1.59 % (32357)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/4Mi)
% 2.47/1.59 % (32360)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/2Mi)
% 2.47/1.59 % (32359)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/2Mi)
% 2.47/1.59 % (32358)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/27Mi)
% 2.47/1.59 % (32361)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/275Mi)
% 2.47/1.59 % (32356)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/183Mi)
% 2.47/1.59 % (32362)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/18Mi)
% 2.47/1.59 % (32359)Instruction limit reached!
% 2.47/1.59 % (32359)------------------------------
% 2.47/1.59 % (32359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.59 % (32359)Termination reason: Unknown
% 2.47/1.59 % (32359)Termination phase: shuffling
% 2.47/1.59
% 2.47/1.59 % (32359)Memory used [KB]: 1279
% 2.47/1.59 % (32359)Time elapsed: 0.003 s
% 2.47/1.59 % (32359)Instructions burned: 2 (million)
% 2.47/1.59 % (32359)------------------------------
% 2.47/1.59 % (32359)------------------------------
% 2.47/1.59 % (32360)Instruction limit reached!
% 2.47/1.59 % (32360)------------------------------
% 2.47/1.59 % (32360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.59 % (32360)Termination reason: Unknown
% 2.47/1.59 % (32360)Termination phase: shuffling
% 2.47/1.59
% 2.47/1.59 % (32360)Memory used [KB]: 1279
% 2.47/1.59 % (32360)Time elapsed: 0.003 s
% 2.47/1.59 % (32360)Instructions burned: 3 (million)
% 2.47/1.59 % (32360)------------------------------
% 2.47/1.59 % (32360)------------------------------
% 2.47/1.60 % (32357)Instruction limit reached!
% 2.47/1.60 % (32357)------------------------------
% 2.47/1.60 % (32357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.60 % (32357)Termination reason: Unknown
% 2.47/1.60 % (32357)Termination phase: shuffling
% 2.47/1.60
% 2.47/1.60 % (32357)Memory used [KB]: 1279
% 2.47/1.60 % (32357)Time elapsed: 0.004 s
% 2.47/1.60 % (32357)Instructions burned: 4 (million)
% 2.47/1.60 % (32357)------------------------------
% 2.47/1.60 % (32357)------------------------------
% 2.58/1.60 % (32362)Instruction limit reached!
% 2.58/1.60 % (32362)------------------------------
% 2.58/1.60 % (32362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.60 % (32362)Termination reason: Unknown
% 2.58/1.60 % (32362)Termination phase: shuffling
% 2.58/1.60
% 2.58/1.60 % (32362)Memory used [KB]: 1535
% 2.58/1.60 % (32362)Time elapsed: 0.010 s
% 2.58/1.60 % (32362)Instructions burned: 18 (million)
% 2.58/1.60 % (32362)------------------------------
% 2.58/1.60 % (32362)------------------------------
% 2.58/1.61 % (32358)Instruction limit reached!
% 2.58/1.61 % (32358)------------------------------
% 2.58/1.61 % (32358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (32358)Termination reason: Unknown
% 2.58/1.61 % (32358)Termination phase: Property scanning
% 2.58/1.61
% 2.58/1.61 % (32358)Memory used [KB]: 1535
% 2.58/1.61 % (32358)Time elapsed: 0.015 s
% 2.58/1.61 % (32358)Instructions burned: 28 (million)
% 2.58/1.61 % (32358)------------------------------
% 2.58/1.61 % (32358)------------------------------
% 2.58/1.61 % (32364)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/37Mi)
% 2.58/1.61 % (32363)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/3Mi)
% 2.58/1.61 % (32365)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/15Mi)
% 2.58/1.61 % (32363)Instruction limit reached!
% 2.58/1.61 % (32363)------------------------------
% 2.58/1.61 % (32363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (32363)Termination reason: Unknown
% 2.58/1.61 % (32363)Termination phase: shuffling
% 2.58/1.61
% 2.58/1.61 % (32363)Memory used [KB]: 1279
% 2.58/1.61 % (32363)Time elapsed: 0.004 s
% 2.58/1.61 % (32363)Instructions burned: 5 (million)
% 2.58/1.61 % (32363)------------------------------
% 2.58/1.61 % (32363)------------------------------
% 2.58/1.62 % (32366)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/3Mi)
% 2.58/1.62 % (32365)Instruction limit reached!
% 2.58/1.62 % (32365)------------------------------
% 2.58/1.62 % (32365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (32365)Termination reason: Unknown
% 2.58/1.62 % (32365)Termination phase: shuffling
% 2.58/1.62
% 2.58/1.62 % (32365)Memory used [KB]: 1535
% 2.58/1.62 % (32365)Time elapsed: 0.009 s
% 2.58/1.62 % (32365)Instructions burned: 16 (million)
% 2.58/1.62 % (32365)------------------------------
% 2.58/1.62 % (32365)------------------------------
% 2.58/1.62 % (32366)Instruction limit reached!
% 2.58/1.62 % (32366)------------------------------
% 2.58/1.62 % (32366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (32366)Termination reason: Unknown
% 2.58/1.62 % (32366)Termination phase: shuffling
% 2.58/1.62
% 2.58/1.62 % (32366)Memory used [KB]: 1279
% 2.58/1.62 % (32366)Time elapsed: 0.003 s
% 2.58/1.62 % (32366)Instructions burned: 3 (million)
% 2.58/1.62 % (32366)------------------------------
% 2.58/1.62 % (32366)------------------------------
% 2.58/1.62 % (32367)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/1041Mi)
% 2.58/1.63 % (32364)Instruction limit reached!
% 2.58/1.63 % (32364)------------------------------
% 2.58/1.63 % (32364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.63 % (32364)Termination reason: Unknown
% 2.58/1.63 % (32364)Termination phase: Property scanning
% 2.58/1.63
% 2.58/1.63 % (32364)Memory used [KB]: 1663
% 2.58/1.63 % (32364)Time elapsed: 0.019 s
% 2.58/1.63 % (32364)Instructions burned: 39 (million)
% 2.58/1.63 % (32364)------------------------------
% 2.58/1.63 % (32364)------------------------------
% 2.58/1.63 % (32368)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/7Mi)
% 2.58/1.63 % (32368)Instruction limit reached!
% 2.58/1.63 % (32368)------------------------------
% 2.58/1.63 % (32368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.63 % (32368)Termination reason: Unknown
% 2.58/1.63 % (32368)Termination phase: shuffling
% 2.58/1.63
% 2.58/1.63 % (32368)Memory used [KB]: 1279
% 2.58/1.63 % (32368)Time elapsed: 0.005 s
% 2.58/1.63 % (32368)Instructions burned: 7 (million)
% 2.58/1.63 % (32368)------------------------------
% 2.58/1.63 % (32368)------------------------------
% 2.58/1.64 % (32369)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/16Mi)
% 2.58/1.64 % (32370)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/3Mi)
% 2.58/1.64 % (32370)Instruction limit reached!
% 2.58/1.64 % (32370)------------------------------
% 2.58/1.64 % (32370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.64 % (32370)Termination reason: Unknown
% 2.58/1.64 % (32370)Termination phase: shuffling
% 2.58/1.64
% 2.58/1.64 % (32370)Memory used [KB]: 1279
% 2.58/1.64 % (32370)Time elapsed: 0.003 s
% 2.58/1.64 % (32370)Instructions burned: 3 (million)
% 2.58/1.64 % (32370)------------------------------
% 2.58/1.64 % (32370)------------------------------
% 2.58/1.64 % (32369)Instruction limit reached!
% 2.58/1.64 % (32369)------------------------------
% 2.58/1.64 % (32369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.64 % (32369)Termination reason: Unknown
% 2.58/1.64 % (32369)Termination phase: shuffling
% 2.58/1.64
% 2.58/1.64 % (32369)Memory used [KB]: 1535
% 2.58/1.64 % (32369)Time elapsed: 0.009 s
% 2.58/1.64 % (32369)Instructions burned: 17 (million)
% 2.58/1.64 % (32369)------------------------------
% 2.58/1.64 % (32369)------------------------------
% 2.58/1.64 % (32371)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/3Mi)
% 2.58/1.65 % (32371)Instruction limit reached!
% 2.58/1.65 % (32371)------------------------------
% 2.58/1.65 % (32371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.65 % (32371)Termination reason: Unknown
% 2.58/1.65 % (32371)Termination phase: shuffling
% 2.58/1.65
% 2.58/1.65 % (32371)Memory used [KB]: 1279
% 2.58/1.65 % (32371)Time elapsed: 0.003 s
% 2.58/1.65 % (32371)Instructions burned: 3 (million)
% 2.58/1.65 % (32371)------------------------------
% 2.58/1.65 % (32371)------------------------------
% 2.58/1.65 % (32372)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/7Mi)
% 2.58/1.65 % (32372)Instruction limit reached!
% 2.58/1.65 % (32372)------------------------------
% 2.58/1.65 % (32372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.65 % (32372)Termination reason: Unknown
% 2.58/1.65 % (32372)Termination phase: shuffling
% 2.58/1.65
% 2.58/1.65 % (32372)Memory used [KB]: 1279
% 2.58/1.65 % (32372)Time elapsed: 0.005 s
% 2.58/1.65 % (32372)Instructions burned: 7 (million)
% 2.58/1.65 % (32372)------------------------------
% 2.58/1.65 % (32372)------------------------------
% 2.58/1.65 % (32373)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/3Mi)
% 2.58/1.65 % (32373)Instruction limit reached!
% 2.58/1.65 % (32373)------------------------------
% 2.58/1.65 % (32373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.65 % (32373)Termination reason: Unknown
% 2.58/1.65 % (32373)Termination phase: shuffling
% 2.58/1.65
% 2.58/1.65 % (32373)Memory used [KB]: 1279
% 2.58/1.65 % (32373)Time elapsed: 0.003 s
% 2.58/1.65 % (32373)Instructions burned: 3 (million)
% 2.58/1.65 % (32373)------------------------------
% 2.58/1.65 % (32373)------------------------------
% 2.58/1.66 % (32374)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/4Mi)
% 2.58/1.66 % (32374)Instruction limit reached!
% 2.58/1.66 % (32374)------------------------------
% 2.58/1.66 % (32374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.66 % (32374)Termination reason: Unknown
% 2.58/1.66 % (32374)Termination phase: shuffling
% 2.58/1.66
% 2.58/1.66 % (32374)Memory used [KB]: 1279
% 2.58/1.66 % (32374)Time elapsed: 0.004 s
% 2.58/1.66 % (32374)Instructions burned: 6 (million)
% 2.58/1.66 % (32374)------------------------------
% 2.58/1.66 % (32374)------------------------------
% 2.58/1.66 % (32375)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/18Mi)
% 2.58/1.67 % (32356)Instruction limit reached!
% 2.58/1.67 % (32356)------------------------------
% 2.58/1.67 % (32356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.67 % (32356)Termination reason: Unknown
% 2.58/1.67 % (32356)Termination phase: Property scanning
% 2.58/1.67
% 2.58/1.67 % (32356)Memory used [KB]: 1918
% 2.58/1.67 % (32356)Time elapsed: 0.077 s
% 2.58/1.67 % (32356)Instructions burned: 184 (million)
% 2.58/1.67 % (32356)------------------------------
% 2.58/1.67 % (32356)------------------------------
% 2.58/1.67 % (32376)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/710Mi)
% 2.58/1.67 % (32375)Instruction limit reached!
% 2.58/1.67 % (32375)------------------------------
% 2.58/1.67 % (32375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.67 % (32377)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/6Mi)
% 2.58/1.67 % (32375)Termination reason: Unknown
% 2.58/1.67 % (32375)Termination phase: shuffling
% 2.58/1.67
% 2.58/1.67 % (32375)Memory used [KB]: 1535
% 2.58/1.67 % (32375)Time elapsed: 0.010 s
% 2.58/1.67 % (32375)Instructions burned: 19 (million)
% 2.58/1.67 % (32375)------------------------------
% 2.58/1.67 % (32375)------------------------------
% 2.58/1.67 % (32377)Instruction limit reached!
% 2.58/1.67 % (32377)------------------------------
% 2.58/1.67 % (32377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.67 % (32377)Termination reason: Unknown
% 2.58/1.67 % (32377)Termination phase: shuffling
% 2.58/1.67
% 2.58/1.67 % (32377)Memory used [KB]: 1279
% 2.58/1.67 % (32377)Time elapsed: 0.004 s
% 2.58/1.67 % (32377)Instructions burned: 6 (million)
% 2.58/1.67 % (32377)------------------------------
% 2.58/1.67 % (32377)------------------------------
% 2.58/1.68 % (32378)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/902Mi)
% 2.58/1.69 % (32379)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/21Mi)
% 2.58/1.69 % (32380)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/5Mi)
% 2.58/1.69 % (32380)Instruction limit reached!
% 2.58/1.69 % (32380)------------------------------
% 2.58/1.69 % (32380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.69 % (32381)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_32257 for (2999ds/6Mi)
% 2.58/1.69 % (32380)Termination reason: Unknown
% 2.58/1.69 % (32380)Termination phase: shuffling
% 2.58/1.69
% 2.58/1.69 % (32380)Memory used [KB]: 1279
% 2.58/1.69 % (32380)Time elapsed: 0.004 s
% 2.58/1.69 % (32380)Instructions burned: 6 (million)
% 2.58/1.69 % (32380)------------------------------
% 2.58/1.69 % (32380)------------------------------
% 2.58/1.69 % (32381)Instruction limit reached!
% 2.58/1.69 % (32381)------------------------------
% 2.58/1.69 % (32381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.69 % (32381)Termination reason: Unknown
% 2.58/1.69 % (32381)Termination phase: shuffling
% 2.58/1.69
% 2.58/1.69 % (32381)Memory used [KB]: 1279
% 2.58/1.69 % (32381)Time elapsed: 0.004 s
% 2.58/1.69 % (32381)Instructions burned: 6 (million)
% 2.58/1.69 % (32381)------------------------------
% 2.58/1.69 % (32381)------------------------------
% 2.58/1.69 % (32379)Instruction limit reached!
% 2.58/1.69 % (32379)------------------------------
% 2.58/1.69 % (32379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.69 % (32379)Termination reason: Unknown
% 2.58/1.69 % (32379)Termination phase: shuffling
% 2.58/1.69
% 2.58/1.69 % (32379)Memory used [KB]: 1535
% 2.58/1.69 % (32379)Time elapsed: 0.011 s
% 2.58/1.69 % (32379)Instructions burned: 21 (million)
% 2.58/1.69 % (32379)------------------------------
% 2.58/1.69 % (32379)------------------------------
% 2.58/1.71 % (32382)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/377Mi)
% 2.58/1.71 % (32383)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/779Mi)
% 2.58/1.71 % (32361)Instruction limit reached!
% 2.58/1.71 % (32361)------------------------------
% 2.58/1.71 % (32361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.71 % (32361)Termination reason: Unknown
% 2.58/1.71 % (32361)Termination phase: Saturation
% 2.58/1.71
% 2.58/1.71 % (32361)Memory used [KB]: 6524
% 2.58/1.71 % (32361)Time elapsed: 0.118 s
% 2.58/1.71 % (32361)Instructions burned: 276 (million)
% 2.58/1.71 % (32361)------------------------------
% 2.58/1.71 % (32361)------------------------------
% 2.58/1.71 % (32384)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/19Mi)
% 2.58/1.72 % (32378)Refutation not found, incomplete strategy
% 2.58/1.72 % (32378)------------------------------
% 2.58/1.72 % (32378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.72 % (32378)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.72
% 2.58/1.72
% 2.58/1.72 % (32378)Memory used [KB]: 6396
% 2.58/1.72 % (32378)Time elapsed: 0.039 s
% 2.58/1.72 % (32378)Instructions burned: 83 (million)
% 2.58/1.72 % (32378)------------------------------
% 2.58/1.72 % (32378)------------------------------
% 2.58/1.72 % (32384)Instruction limit reached!
% 2.58/1.72 % (32384)------------------------------
% 2.58/1.72 % (32384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.72 % (32384)Termination reason: Unknown
% 2.58/1.72 % (32384)Termination phase: shuffling
% 2.58/1.72
% 2.58/1.72 % (32384)Memory used [KB]: 1535
% 2.58/1.72 % (32384)Time elapsed: 0.010 s
% 2.58/1.72 % (32384)Instructions burned: 19 (million)
% 2.58/1.72 % (32384)------------------------------
% 2.58/1.72 % (32384)------------------------------
% 2.58/1.73 % (32385)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/879Mi)
% 2.58/1.73 % (32386)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/17Mi)
% 2.58/1.74 % (32387)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/3Mi)
% 2.58/1.74 % (32387)Instruction limit reached!
% 2.58/1.74 % (32387)------------------------------
% 2.58/1.74 % (32387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.74 % (32387)Termination reason: Unknown
% 2.58/1.74 % (32387)Termination phase: shuffling
% 2.58/1.74
% 2.58/1.74 % (32387)Memory used [KB]: 1279
% 2.58/1.74 % (32387)Time elapsed: 0.003 s
% 2.58/1.74 % (32387)Instructions burned: 3 (million)
% 2.58/1.74 % (32387)------------------------------
% 2.58/1.74 % (32387)------------------------------
% 2.58/1.74 % (32386)Instruction limit reached!
% 2.58/1.74 % (32386)------------------------------
% 2.58/1.74 % (32386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.74 % (32386)Termination reason: Unknown
% 2.58/1.74 % (32386)Termination phase: shuffling
% 2.58/1.74
% 2.58/1.74 % (32386)Memory used [KB]: 1535
% 2.58/1.74 % (32386)Time elapsed: 0.009 s
% 2.58/1.74 % (32386)Instructions burned: 17 (million)
% 2.58/1.74 % (32386)------------------------------
% 2.58/1.74 % (32386)------------------------------
% 2.58/1.75 % (32388)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/30Mi)
% 2.58/1.76 % (32389)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32257 for (2998ds/127Mi)
% 2.58/1.77 % (32388)Instruction limit reached!
% 2.58/1.77 % (32388)------------------------------
% 2.58/1.77 % (32388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.77 % (32388)Termination reason: Unknown
% 2.58/1.77 % (32388)Termination phase: Property scanning
% 2.58/1.77
% 2.58/1.77 % (32388)Memory used [KB]: 1535
% 2.58/1.77 % (32388)Time elapsed: 0.015 s
% 2.58/1.77 % (32388)Instructions burned: 30 (million)
% 2.58/1.77 % (32388)------------------------------
% 2.58/1.77 % (32388)------------------------------
% 2.58/1.78 % (32390)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32257 for (2997ds/100Mi)
% 2.58/1.81 % (32389)Instruction limit reached!
% 2.58/1.81 % (32389)------------------------------
% 2.58/1.81 % (32389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.81 % (32389)Termination reason: Unknown
% 2.58/1.81 % (32389)Termination phase: Property scanning
% 2.58/1.81
% 2.58/1.81 % (32389)Memory used [KB]: 1918
% 2.58/1.81 % (32389)Time elapsed: 0.052 s
% 2.58/1.81 % (32389)Instructions burned: 129 (million)
% 2.58/1.81 % (32389)------------------------------
% 2.58/1.81 % (32389)------------------------------
% 2.58/1.82 % (32390)Instruction limit reached!
% 2.58/1.82 % (32390)------------------------------
% 2.58/1.82 % (32390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.82 % (32390)Termination reason: Unknown
% 2.58/1.82 % (32390)Termination phase: Property scanning
% 2.58/1.82
% 2.58/1.82 % (32390)Memory used [KB]: 1918
% 2.58/1.82 % (32390)Time elapsed: 0.040 s
% 2.58/1.82 % (32390)Instructions burned: 101 (million)
% 2.58/1.82 % (32390)------------------------------
% 2.58/1.82 % (32390)------------------------------
% 2.58/1.82 % (32391)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_32257 for (2997ds/3Mi)
% 2.58/1.82 % (32391)Instruction limit reached!
% 2.58/1.82 % (32391)------------------------------
% 2.58/1.82 % (32391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.82 % (32391)Termination reason: Unknown
% 2.58/1.82 % (32391)Termination phase: shuffling
% 2.58/1.82
% 2.58/1.82 % (32391)Memory used [KB]: 1279
% 2.58/1.82 % (32391)Time elapsed: 0.003 s
% 2.58/1.82 % (32391)Instructions burned: 3 (million)
% 2.58/1.82 % (32391)------------------------------
% 2.58/1.82 % (32391)------------------------------
% 2.58/1.84 % (32392)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_32257 for (2997ds/20Mi)
% 2.58/1.84 % (32393)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_32257 for (2997ds/86Mi)
% 2.58/1.85 % (32392)Instruction limit reached!
% 2.58/1.85 % (32392)------------------------------
% 2.58/1.85 % (32392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.85 % (32392)Termination reason: Unknown
% 2.58/1.85 % (32392)Termination phase: shuffling
% 2.58/1.85
% 2.58/1.85 % (32392)Memory used [KB]: 1535
% 2.58/1.85 % (32392)Time elapsed: 0.011 s
% 2.58/1.85 % (32392)Instructions burned: 20 (million)
% 2.58/1.85 % (32392)------------------------------
% 2.58/1.85 % (32392)------------------------------
% 2.58/1.86 % (32382)Instruction limit reached!
% 2.58/1.86 % (32382)------------------------------
% 2.58/1.86 % (32382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.86 % (32382)Termination reason: Unknown
% 2.58/1.86 % (32382)Termination phase: Saturation
% 2.58/1.86
% 2.58/1.86 % (32382)Memory used [KB]: 6396
% 2.58/1.86 % (32382)Time elapsed: 0.154 s
% 2.58/1.86 % (32382)Instructions burned: 378 (million)
% 2.58/1.86 % (32382)------------------------------
% 2.58/1.86 % (32382)------------------------------
% 2.58/1.86 % (32394)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_32257 for (2997ds/107Mi)
% 2.58/1.87 % (32393)Instruction limit reached!
% 2.58/1.87 % (32393)------------------------------
% 2.58/1.87 % (32393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.87 % (32393)Termination reason: Unknown
% 2.58/1.87 % (32393)Termination phase: Function definition elimination
% 2.58/1.87
% 2.58/1.87 % (32393)Memory used [KB]: 1918
% 2.58/1.87 % (32393)Time elapsed: 0.035 s
% 2.58/1.87 % (32393)Instructions burned: 86 (million)
% 2.58/1.87 % (32393)------------------------------
% 2.58/1.87 % (32393)------------------------------
% 2.58/1.87 % (32395)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_32257 for (2997ds/39Mi)
% 2.58/1.89 % (32396)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_32257 for (2996ds/448Mi)
% 2.58/1.89 % (32395)Instruction limit reached!
% 2.58/1.89 % (32395)------------------------------
% 2.58/1.89 % (32395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.89 % (32395)Termination reason: Unknown
% 2.58/1.89 % (32395)Termination phase: Property scanning
% 2.58/1.89
% 2.58/1.89 % (32395)Memory used [KB]: 1663
% 2.58/1.89 % (32395)Time elapsed: 0.019 s
% 2.58/1.89 % (32395)Instructions burned: 39 (million)
% 2.58/1.89 % (32395)------------------------------
% 2.58/1.89 % (32395)------------------------------
% 2.58/1.90 % (32394)Instruction limit reached!
% 2.58/1.90 % (32394)------------------------------
% 2.58/1.90 % (32394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.90 % (32394)Termination reason: Unknown
% 2.58/1.90 % (32394)Termination phase: Property scanning
% 2.58/1.90
% 2.58/1.90 % (32394)Memory used [KB]: 1918
% 2.58/1.90 % (32394)Time elapsed: 0.044 s
% 2.58/1.90 % (32394)Instructions burned: 108 (million)
% 2.58/1.90 % (32394)------------------------------
% 2.58/1.90 % (32394)------------------------------
% 2.58/1.91 % (32397)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_32257 for (2996ds/46Mi)
% 2.58/1.92 % (32398)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_32257 for (2996ds/98Mi)
% 2.58/1.93 % (32397)Instruction limit reached!
% 2.58/1.93 % (32397)------------------------------
% 2.58/1.93 % (32397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.93 % (32397)Termination reason: Unknown
% 2.58/1.93 % (32397)Termination phase: Property scanning
% 2.58/1.93
% 2.58/1.93 % (32397)Memory used [KB]: 1663
% 2.58/1.93 % (32397)Time elapsed: 0.022 s
% 2.58/1.93 % (32397)Instructions burned: 47 (million)
% 2.58/1.93 % (32397)------------------------------
% 2.58/1.93 % (32397)------------------------------
% 2.58/1.94 % (32399)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_32257 for (2996ds/507Mi)
% 2.58/1.96 % (32376)Instruction limit reached!
% 2.58/1.96 % (32376)------------------------------
% 2.58/1.96 % (32376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.96 % (32376)Termination reason: Unknown
% 2.58/1.96 % (32376)Termination phase: Saturation
% 2.58/1.96
% 2.58/1.96 % (32376)Memory used [KB]: 6524
% 2.58/1.96 % (32376)Time elapsed: 0.290 s
% 2.58/1.96 % (32376)Instructions burned: 711 (million)
% 2.58/1.96 % (32376)------------------------------
% 2.58/1.96 % (32376)------------------------------
% 2.58/1.96 % (32398)Instruction limit reached!
% 2.58/1.96 % (32398)------------------------------
% 2.58/1.96 % (32398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.96 % (32398)Termination reason: Unknown
% 2.58/1.96 % (32398)Termination phase: Property scanning
% 2.58/1.96
% 2.58/1.96 % (32398)Memory used [KB]: 1918
% 2.58/1.96 % (32398)Time elapsed: 0.039 s
% 2.58/1.96 % (32398)Instructions burned: 99 (million)
% 2.58/1.96 % (32398)------------------------------
% 2.58/1.96 % (32398)------------------------------
% 2.58/1.97 % (32400)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_32257 for (2996ds/149Mi)
% 2.58/1.97 % (32401)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32257 for (2996ds/39Mi)
% 2.58/1.99 % (32401)Instruction limit reached!
% 2.58/1.99 % (32401)------------------------------
% 2.58/1.99 % (32401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.99 % (32401)Termination reason: Unknown
% 2.58/1.99 % (32401)Termination phase: Property scanning
% 2.58/1.99
% 2.58/1.99 % (32401)Memory used [KB]: 1663
% 2.58/1.99 % (32401)Time elapsed: 0.019 s
% 2.58/1.99 % (32401)Instructions burned: 39 (million)
% 2.58/1.99 % (32401)------------------------------
% 2.58/1.99 % (32401)------------------------------
% 2.58/2.00 % (32383)Instruction limit reached!
% 2.58/2.00 % (32383)------------------------------
% 2.58/2.00 % (32383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/2.00 % (32383)Termination reason: Unknown
% 2.58/2.00 % (32383)Termination phase: Saturation
% 2.58/2.00
% 2.58/2.00 % (32383)Memory used [KB]: 6780
% 2.58/2.00 % (32383)Time elapsed: 0.292 s
% 2.58/2.00 % (32383)Instructions burned: 779 (million)
% 2.58/2.00 % (32383)------------------------------
% 2.58/2.00 % (32383)------------------------------
% 2.58/2.01 % (32402)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/6Mi)
% 2.58/2.01 % (32402)Instruction limit reached!
% 2.58/2.01 % (32402)------------------------------
% 2.58/2.01 % (32402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/2.01 % (32402)Termination reason: Unknown
% 2.58/2.01 % (32402)Termination phase: shuffling
% 2.58/2.01
% 2.58/2.01 % (32402)Memory used [KB]: 1279
% 2.58/2.01 % (32402)Time elapsed: 0.005 s
% 2.58/2.01 % (32402)Instructions burned: 7 (million)
% 2.58/2.01 % (32402)------------------------------
% 2.58/2.01 % (32402)------------------------------
% 2.58/2.01 % (32367)Instruction limit reached!
% 2.58/2.01 % (32367)------------------------------
% 2.58/2.01 % (32367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/2.01 % (32367)Termination reason: Unknown
% 2.58/2.01 % (32367)Termination phase: Saturation
% 2.58/2.01
% 2.58/2.01 % (32367)Memory used [KB]: 7036
% 2.58/2.01 % (32367)Time elapsed: 0.392 s
% 2.58/2.01 % (32367)Instructions burned: 1041 (million)
% 2.58/2.01 % (32367)------------------------------
% 2.58/2.01 % (32367)------------------------------
% 2.58/2.02 % (32403)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/1087Mi)
% 5.64/2.03 % (32404)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/47Mi)
% 5.64/2.03 % (32405)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/44Mi)
% 5.64/2.03 % (32400)Instruction limit reached!
% 5.64/2.03 % (32400)------------------------------
% 5.64/2.03 % (32400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.03 % (32400)Termination reason: Unknown
% 5.64/2.03 % (32400)Termination phase: Twee Goal Transformation
% 5.64/2.03
% 5.64/2.03 % (32400)Memory used [KB]: 2046
% 5.64/2.03 % (32400)Time elapsed: 0.063 s
% 5.64/2.03 % (32400)Instructions burned: 149 (million)
% 5.64/2.03 % (32400)------------------------------
% 5.64/2.03 % (32400)------------------------------
% 5.64/2.05 % (32404)Instruction limit reached!
% 5.64/2.05 % (32404)------------------------------
% 5.64/2.05 % (32404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.05 % (32404)Termination reason: Unknown
% 5.64/2.05 % (32404)Termination phase: Function definition elimination
% 5.64/2.05
% 5.64/2.05 % (32404)Memory used [KB]: 1663
% 5.64/2.05 % (32404)Time elapsed: 0.023 s
% 5.64/2.05 % (32404)Instructions burned: 48 (million)
% 5.64/2.05 % (32404)------------------------------
% 5.64/2.05 % (32404)------------------------------
% 5.64/2.05 % (32405)Instruction limit reached!
% 5.64/2.05 % (32405)------------------------------
% 5.64/2.05 % (32405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.05 % (32405)Termination reason: Unknown
% 5.64/2.05 % (32405)Termination phase: Function definition elimination
% 5.64/2.05
% 5.64/2.05 % (32405)Memory used [KB]: 1663
% 5.64/2.05 % (32405)Time elapsed: 0.021 s
% 5.64/2.05 % (32405)Instructions burned: 44 (million)
% 5.64/2.05 % (32405)------------------------------
% 5.64/2.05 % (32405)------------------------------
% 5.64/2.05 % (32406)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/432Mi)
% 5.64/2.05 % (32385)Instruction limit reached!
% 5.64/2.05 % (32385)------------------------------
% 5.64/2.05 % (32385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.05 % (32385)Termination reason: Unknown
% 5.64/2.05 % (32385)Termination phase: Saturation
% 5.64/2.05
% 5.64/2.05 % (32385)Memory used [KB]: 6524
% 5.64/2.05 % (32385)Time elapsed: 0.329 s
% 5.64/2.05 % (32385)Instructions burned: 880 (million)
% 5.64/2.05 % (32385)------------------------------
% 5.64/2.05 % (32385)------------------------------
% 5.64/2.07 % (32407)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/62Mi)
% 5.64/2.07 % (32408)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/31Mi)
% 5.64/2.07 % (32396)Instruction limit reached!
% 5.64/2.07 % (32396)------------------------------
% 5.64/2.07 % (32396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.07 % (32396)Termination reason: Unknown
% 5.64/2.07 % (32396)Termination phase: Saturation
% 5.64/2.07
% 5.64/2.07 % (32396)Memory used [KB]: 6396
% 5.64/2.07 % (32396)Time elapsed: 0.178 s
% 5.64/2.07 % (32396)Instructions burned: 449 (million)
% 5.64/2.07 % (32396)------------------------------
% 5.64/2.07 % (32396)------------------------------
% 5.64/2.07 % (32409)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/96Mi)
% 5.64/2.08 % (32408)Instruction limit reached!
% 5.64/2.08 % (32408)------------------------------
% 5.64/2.08 % (32408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.08 % (32408)Termination reason: Unknown
% 5.64/2.08 % (32408)Termination phase: Property scanning
% 5.64/2.08
% 5.64/2.08 % (32408)Memory used [KB]: 1535
% 5.64/2.08 % (32408)Time elapsed: 0.016 s
% 5.64/2.08 % (32408)Instructions burned: 32 (million)
% 5.64/2.08 % (32408)------------------------------
% 5.64/2.08 % (32408)------------------------------
% 5.64/2.08 % (32410)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_32257 for (2995ds/453Mi)
% 5.64/2.09 % (32407)Instruction limit reached!
% 5.64/2.09 % (32407)------------------------------
% 5.64/2.09 % (32407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.09 % (32407)Termination reason: Unknown
% 5.64/2.09 % (32407)Termination phase: Function definition elimination
% 5.64/2.09
% 5.64/2.09 % (32407)Memory used [KB]: 1791
% 5.64/2.09 % (32407)Time elapsed: 0.028 s
% 5.64/2.09 % (32407)Instructions burned: 64 (million)
% 5.64/2.09 % (32407)------------------------------
% 5.64/2.09 % (32407)------------------------------
% 5.64/2.10 % (32411)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/71Mi)
% 5.64/2.11 % (32409)Instruction limit reached!
% 5.64/2.11 % (32409)------------------------------
% 5.64/2.11 % (32409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.11 % (32409)Termination reason: Unknown
% 5.64/2.11 % (32409)Termination phase: Property scanning
% 5.64/2.11
% 5.64/2.11 % (32409)Memory used [KB]: 1918
% 5.64/2.11 % (32409)Time elapsed: 0.039 s
% 5.64/2.11 % (32409)Instructions burned: 97 (million)
% 5.64/2.11 % (32409)------------------------------
% 5.64/2.11 % (32409)------------------------------
% 5.64/2.11 % (32412)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/83Mi)
% 5.64/2.12 % (32413)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/11Mi)
% 5.64/2.13 % (32411)Instruction limit reached!
% 5.64/2.13 % (32411)------------------------------
% 5.64/2.13 % (32411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.13 % (32411)Termination reason: Unknown
% 5.64/2.13 % (32411)Termination phase: Function definition elimination
% 5.64/2.13
% 5.64/2.13 % (32411)Memory used [KB]: 1918
% 5.64/2.13 % (32411)Time elapsed: 0.031 s
% 5.64/2.13 % (32411)Instructions burned: 73 (million)
% 5.64/2.13 % (32411)------------------------------
% 5.64/2.13 % (32411)------------------------------
% 6.07/2.13 % (32413)Instruction limit reached!
% 6.07/2.13 % (32413)------------------------------
% 6.07/2.13 % (32413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.13 % (32413)Termination reason: Unknown
% 6.07/2.13 % (32413)Termination phase: shuffling
% 6.07/2.13
% 6.07/2.13 % (32413)Memory used [KB]: 1407
% 6.07/2.13 % (32413)Time elapsed: 0.007 s
% 6.07/2.13 % (32413)Instructions burned: 11 (million)
% 6.07/2.13 % (32413)------------------------------
% 6.07/2.13 % (32413)------------------------------
% 6.07/2.14 % (32414)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/41Mi)
% 6.07/2.14 % (32412)Instruction limit reached!
% 6.07/2.14 % (32412)------------------------------
% 6.07/2.14 % (32412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.14 % (32412)Termination reason: Unknown
% 6.07/2.14 % (32412)Termination phase: Saturation
% 6.07/2.14
% 6.07/2.14 % (32412)Memory used [KB]: 6268
% 6.07/2.14 % (32412)Time elapsed: 0.037 s
% 6.07/2.14 % (32412)Instructions burned: 84 (million)
% 6.07/2.14 % (32412)------------------------------
% 6.07/2.14 % (32412)------------------------------
% 6.07/2.14 % (32399)Instruction limit reached!
% 6.07/2.14 % (32399)------------------------------
% 6.07/2.14 % (32399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.14 % (32399)Termination reason: Unknown
% 6.07/2.14 % (32399)Termination phase: Saturation
% 6.07/2.14
% 6.07/2.14 % (32399)Memory used [KB]: 6780
% 6.07/2.14 % (32399)Time elapsed: 0.201 s
% 6.07/2.14 % (32399)Instructions burned: 508 (million)
% 6.07/2.14 % (32399)------------------------------
% 6.07/2.14 % (32399)------------------------------
% 6.07/2.15 % (32415)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/6Mi)
% 6.07/2.15 % (32415)Instruction limit reached!
% 6.07/2.15 % (32415)------------------------------
% 6.07/2.15 % (32415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.15 % (32415)Termination reason: Unknown
% 6.07/2.15 % (32415)Termination phase: shuffling
% 6.07/2.15
% 6.07/2.15 % (32415)Memory used [KB]: 1279
% 6.07/2.15 % (32415)Time elapsed: 0.005 s
% 6.07/2.15 % (32415)Instructions burned: 7 (million)
% 6.07/2.15 % (32415)------------------------------
% 6.07/2.15 % (32415)------------------------------
% 6.07/2.16 % (32416)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/150Mi)
% 6.07/2.16 % (32417)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/343Mi)
% 6.07/2.16 % (32414)Instruction limit reached!
% 6.07/2.16 % (32414)------------------------------
% 6.07/2.16 % (32414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.16 % (32414)Termination reason: Unknown
% 6.07/2.16 % (32414)Termination phase: Property scanning
% 6.07/2.16
% 6.07/2.16 % (32414)Memory used [KB]: 1663
% 6.07/2.16 % (32414)Time elapsed: 0.020 s
% 6.07/2.16 % (32414)Instructions burned: 42 (million)
% 6.07/2.16 % (32414)------------------------------
% 6.07/2.16 % (32414)------------------------------
% 6.07/2.16 % (32418)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_32257 for (2994ds/109Mi)
% 6.07/2.18 % (32419)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_32257 for (2993ds/253Mi)
% 6.23/2.21 % (32418)Instruction limit reached!
% 6.23/2.21 % (32418)------------------------------
% 6.23/2.21 % (32418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.21 % (32418)Termination reason: Unknown
% 6.23/2.21 % (32418)Termination phase: Property scanning
% 6.23/2.21
% 6.23/2.21 % (32418)Memory used [KB]: 1918
% 6.23/2.21 % (32418)Time elapsed: 0.044 s
% 6.23/2.21 % (32418)Instructions burned: 109 (million)
% 6.23/2.21 % (32418)------------------------------
% 6.23/2.21 % (32418)------------------------------
% 6.23/2.22 % (32416)Instruction limit reached!
% 6.23/2.22 % (32416)------------------------------
% 6.23/2.22 % (32416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.22 % (32416)Termination reason: Unknown
% 6.23/2.22 % (32416)Termination phase: Property scanning
% 6.23/2.22
% 6.23/2.22 % (32416)Memory used [KB]: 1918
% 6.23/2.22 % (32416)Time elapsed: 0.062 s
% 6.23/2.22 % (32416)Instructions burned: 152 (million)
% 6.23/2.22 % (32416)------------------------------
% 6.23/2.22 % (32416)------------------------------
% 6.23/2.22 % (32406)Instruction limit reached!
% 6.23/2.22 % (32406)------------------------------
% 6.23/2.22 % (32406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.22 % (32406)Termination reason: Unknown
% 6.23/2.22 % (32406)Termination phase: Saturation
% 6.23/2.22
% 6.23/2.22 % (32406)Memory used [KB]: 2046
% 6.23/2.22 % (32406)Time elapsed: 0.173 s
% 6.23/2.22 % (32406)Instructions burned: 434 (million)
% 6.23/2.22 % (32406)------------------------------
% 6.23/2.22 % (32406)------------------------------
% 6.23/2.22 % (32420)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32257 for (2993ds/140Mi)
% 6.23/2.24 % (32421)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_32257 for (2993ds/614Mi)
% 6.23/2.24 % (32422)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_32257 for (2993ds/202Mi)
% 6.23/2.26 % (32410)Instruction limit reached!
% 6.23/2.26 % (32410)------------------------------
% 6.23/2.26 % (32410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.26 % (32410)Termination reason: Unknown
% 6.23/2.26 % (32410)Termination phase: Saturation
% 6.23/2.26
% 6.23/2.26 % (32410)Memory used [KB]: 6524
% 6.23/2.26 % (32410)Time elapsed: 0.181 s
% 6.23/2.26 % (32410)Instructions burned: 455 (million)
% 6.23/2.26 % (32410)------------------------------
% 6.23/2.26 % (32410)------------------------------
% 6.23/2.27 % (32422)Refutation not found, incomplete strategy
% 6.23/2.27 % (32422)------------------------------
% 6.23/2.27 % (32422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.27 % (32422)Termination reason: Refutation not found, incomplete strategy
% 6.23/2.27
% 6.23/2.27
% 6.23/2.27 % (32422)Memory used [KB]: 6140
% 6.23/2.27 % (32422)Time elapsed: 0.028 s
% 6.23/2.27 % (32422)Instructions burned: 59 (million)
% 6.23/2.27 % (32422)------------------------------
% 6.23/2.27 % (32422)------------------------------
% 6.23/2.28 % (32423)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_32257 for (2993ds/339Mi)
% 6.23/2.28 % (32424)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_32257 for (2992ds/283Mi)
% 6.23/2.28 % (32419)Instruction limit reached!
% 6.23/2.28 % (32419)------------------------------
% 6.23/2.28 % (32419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.28 % (32419)Termination reason: Unknown
% 6.23/2.28 % (32419)Termination phase: Saturation
% 6.23/2.28
% 6.23/2.28 % (32419)Memory used [KB]: 6396
% 6.23/2.28 % (32419)Time elapsed: 0.110 s
% 6.23/2.28 % (32419)Instructions burned: 254 (million)
% 6.23/2.28 % (32419)------------------------------
% 6.23/2.28 % (32419)------------------------------
% 6.23/2.29 % (32420)Instruction limit reached!
% 6.23/2.29 % (32420)------------------------------
% 6.23/2.29 % (32420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.29 % (32420)Termination reason: Unknown
% 6.23/2.29 % (32420)Termination phase: Saturation
% 6.23/2.29
% 6.23/2.29 % (32420)Memory used [KB]: 6652
% 6.23/2.29 % (32420)Time elapsed: 0.064 s
% 6.23/2.29 % (32420)Instructions burned: 140 (million)
% 6.23/2.29 % (32420)------------------------------
% 6.23/2.29 % (32420)------------------------------
% 6.23/2.29 % (32417)Instruction limit reached!
% 6.23/2.29 % (32417)------------------------------
% 6.23/2.29 % (32417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.29 % (32417)Termination reason: Unknown
% 6.23/2.29 % (32417)Termination phase: Saturation
% 6.23/2.29
% 6.23/2.29 % (32417)Memory used [KB]: 6396
% 6.23/2.29 % (32417)Time elapsed: 0.137 s
% 6.23/2.29 % (32417)Instructions burned: 344 (million)
% 6.23/2.29 % (32417)------------------------------
% 6.23/2.29 % (32417)------------------------------
% 7.15/2.30 % (32425)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32257 for (2992ds/134Mi)
% 7.15/2.30 % (32426)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32257 for (2992ds/298Mi)
% 7.15/2.31 % (32427)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32257 for (2992ds/192Mi)
% 7.15/2.35 % (32425)Instruction limit reached!
% 7.15/2.35 % (32425)------------------------------
% 7.15/2.35 % (32425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.15/2.35 % (32425)Termination reason: Unknown
% 7.15/2.35 % (32425)Termination phase: Property scanning
% 7.15/2.35
% 7.15/2.35 % (32425)Memory used [KB]: 1918
% 7.15/2.35 % (32425)Time elapsed: 0.056 s
% 7.15/2.35 % (32425)Instructions burned: 135 (million)
% 7.15/2.35 % (32425)------------------------------
% 7.15/2.35 % (32425)------------------------------
% 7.15/2.37 % (32428)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_32257 for (2992ds/258Mi)
% 7.15/2.39 % (32427)Instruction limit reached!
% 7.15/2.39 % (32427)------------------------------
% 7.15/2.39 % (32427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.15/2.39 % (32427)Termination reason: Unknown
% 7.15/2.39 % (32427)Termination phase: Property scanning
% 7.15/2.39
% 7.15/2.39 % (32427)Memory used [KB]: 1918
% 7.15/2.39 % (32427)Time elapsed: 0.079 s
% 7.15/2.39 % (32427)Instructions burned: 192 (million)
% 7.15/2.39 % (32427)------------------------------
% 7.15/2.39 % (32427)------------------------------
% 7.31/2.40 % (32424)Instruction limit reached!
% 7.31/2.40 % (32424)------------------------------
% 7.31/2.40 % (32424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.40 % (32424)Termination reason: Unknown
% 7.31/2.40 % (32424)Termination phase: Property scanning
% 7.31/2.40
% 7.31/2.40 % (32424)Memory used [KB]: 1918
% 7.31/2.40 % (32424)Time elapsed: 0.118 s
% 7.31/2.40 % (32424)Instructions burned: 284 (million)
% 7.31/2.40 % (32424)------------------------------
% 7.31/2.40 % (32424)------------------------------
% 7.31/2.40 % (32429)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_32257 for (2991ds/90Mi)
% 7.31/2.41 % (32430)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_32257 for (2991ds/231Mi)
% 7.31/2.42 % (32423)Instruction limit reached!
% 7.31/2.42 % (32423)------------------------------
% 7.31/2.42 % (32423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.42 % (32423)Termination reason: Unknown
% 7.31/2.42 % (32423)Termination phase: Saturation
% 7.31/2.42
% 7.31/2.42 % (32423)Memory used [KB]: 6524
% 7.31/2.42 % (32423)Time elapsed: 0.145 s
% 7.31/2.42 % (32423)Instructions burned: 339 (million)
% 7.31/2.42 % (32423)------------------------------
% 7.31/2.42 % (32423)------------------------------
% 7.31/2.43 % (32426)Instruction limit reached!
% 7.31/2.43 % (32426)------------------------------
% 7.31/2.43 % (32426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.43 % (32426)Termination reason: Unknown
% 7.31/2.43 % (32426)Termination phase: Property scanning
% 7.31/2.43
% 7.31/2.43 % (32426)Memory used [KB]: 1918
% 7.31/2.43 % (32426)Time elapsed: 0.125 s
% 7.31/2.43 % (32426)Instructions burned: 299 (million)
% 7.31/2.43 % (32426)------------------------------
% 7.31/2.43 % (32426)------------------------------
% 7.31/2.44 % (32431)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_32257 for (2991ds/458Mi)
% 7.31/2.44 % (32429)Instruction limit reached!
% 7.31/2.44 % (32429)------------------------------
% 7.31/2.44 % (32429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.44 % (32429)Termination reason: Unknown
% 7.31/2.44 % (32429)Termination phase: Function definition elimination
% 7.31/2.44
% 7.31/2.44 % (32429)Memory used [KB]: 1918
% 7.31/2.44 % (32429)Time elapsed: 0.037 s
% 7.31/2.44 % (32429)Instructions burned: 92 (million)
% 7.31/2.44 % (32429)------------------------------
% 7.31/2.44 % (32429)------------------------------
% 7.31/2.44 % (32432)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32257 for (2991ds/31Mi)
% 7.31/2.45 % (32403)Instruction limit reached!
% 7.31/2.45 % (32403)------------------------------
% 7.31/2.45 % (32403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.45 % (32403)Termination reason: Unknown
% 7.31/2.45 % (32403)Termination phase: Saturation
% 7.31/2.45
% 7.31/2.45 % (32403)Memory used [KB]: 6524
% 7.31/2.45 % (32403)Time elapsed: 0.434 s
% 7.31/2.45 % (32403)Instructions burned: 1087 (million)
% 7.31/2.45 % (32403)------------------------------
% 7.31/2.45 % (32403)------------------------------
% 7.31/2.46 % (32432)Instruction limit reached!
% 7.31/2.46 % (32432)------------------------------
% 7.31/2.46 % (32432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.46 % (32432)Termination reason: Unknown
% 7.31/2.46 % (32432)Termination phase: Property scanning
% 7.31/2.46
% 7.31/2.46 % (32432)Memory used [KB]: 1535
% 7.31/2.46 % (32432)Time elapsed: 0.016 s
% 7.31/2.46 % (32432)Instructions burned: 32 (million)
% 7.31/2.46 % (32432)------------------------------
% 7.31/2.46 % (32432)------------------------------
% 7.31/2.46 % (32433)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_32257 for (2991ds/297Mi)
% 7.31/2.47 % (32434)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_32257 for (2991ds/987Mi)
% 7.31/2.47 % (32435)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_32257 for (2991ds/182Mi)
% 7.31/2.48 % (32421)Instruction limit reached!
% 7.31/2.48 % (32421)------------------------------
% 7.31/2.48 % (32421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.48 % (32421)Termination reason: Unknown
% 7.31/2.48 % (32421)Termination phase: Saturation
% 7.31/2.48
% 7.31/2.48 % (32421)Memory used [KB]: 6780
% 7.31/2.48 % (32421)Time elapsed: 0.243 s
% 7.31/2.48 % (32421)Instructions burned: 615 (million)
% 7.31/2.48 % (32421)------------------------------
% 7.31/2.48 % (32421)------------------------------
% 7.31/2.48 % (32428)Instruction limit reached!
% 7.31/2.48 % (32428)------------------------------
% 7.31/2.48 % (32428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.48 % (32428)Termination reason: Unknown
% 7.31/2.48 % (32428)Termination phase: Property scanning
% 7.31/2.48
% 7.31/2.48 % (32428)Memory used [KB]: 1918
% 7.31/2.48 % (32428)Time elapsed: 0.108 s
% 7.31/2.48 % (32428)Instructions burned: 258 (million)
% 7.31/2.48 % (32428)------------------------------
% 7.31/2.48 % (32428)------------------------------
% 7.31/2.49 % (32436)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_32257 for (2990ds/182Mi)
% 7.31/2.49 % (32437)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_32257 for (2990ds/154Mi)
% 8.65/2.51 % (32430)Instruction limit reached!
% 8.65/2.51 % (32430)------------------------------
% 8.65/2.51 % (32430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.51 % (32430)Termination reason: Unknown
% 8.65/2.51 % (32430)Termination phase: Twee Goal Transformation
% 8.65/2.51
% 8.65/2.51 % (32430)Memory used [KB]: 2174
% 8.65/2.51 % (32430)Time elapsed: 0.100 s
% 8.65/2.51 % (32430)Instructions burned: 231 (million)
% 8.65/2.51 % (32430)------------------------------
% 8.65/2.51 % (32430)------------------------------
% 8.65/2.53 % (32438)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_32257 for (2990ds/79Mi)
% 8.65/2.55 % (32435)Instruction limit reached!
% 8.65/2.55 % (32435)------------------------------
% 8.65/2.55 % (32435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.55 % (32435)Termination reason: Unknown
% 8.65/2.55 % (32435)Termination phase: Property scanning
% 8.65/2.55
% 8.65/2.55 % (32435)Memory used [KB]: 1918
% 8.65/2.55 % (32435)Time elapsed: 0.075 s
% 8.65/2.55 % (32435)Instructions burned: 182 (million)
% 8.65/2.55 % (32435)------------------------------
% 8.65/2.55 % (32435)------------------------------
% 8.65/2.56 % (32437)Instruction limit reached!
% 8.65/2.56 % (32437)------------------------------
% 8.65/2.56 % (32437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.56 % (32437)Termination reason: Unknown
% 8.65/2.56 % (32437)Termination phase: Property scanning
% 8.65/2.56
% 8.65/2.56 % (32437)Memory used [KB]: 1918
% 8.65/2.56 % (32437)Time elapsed: 0.063 s
% 8.65/2.56 % (32437)Instructions burned: 154 (million)
% 8.65/2.56 % (32437)------------------------------
% 8.65/2.56 % (32437)------------------------------
% 8.65/2.56 % (32438)Instruction limit reached!
% 8.65/2.56 % (32438)------------------------------
% 8.65/2.56 % (32438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.56 % (32438)Termination reason: Unknown
% 8.65/2.56 % (32438)Termination phase: Function definition elimination
% 8.65/2.56
% 8.65/2.56 % (32438)Memory used [KB]: 1918
% 8.65/2.56 % (32438)Time elapsed: 0.034 s
% 8.65/2.56 % (32438)Instructions burned: 81 (million)
% 8.65/2.56 % (32438)------------------------------
% 8.65/2.56 % (32438)------------------------------
% 8.65/2.56 % (32439)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_32257 for (2990ds/216Mi)
% 8.65/2.57 % (32440)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_32257 for (2990ds/114Mi)
% 8.65/2.57 % (32436)Instruction limit reached!
% 8.65/2.57 % (32436)------------------------------
% 8.65/2.57 % (32436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.57 % (32436)Termination reason: Unknown
% 8.65/2.57 % (32436)Termination phase: Saturation
% 8.65/2.57
% 8.65/2.57 % (32436)Memory used [KB]: 6524
% 8.65/2.57 % (32436)Time elapsed: 0.083 s
% 8.65/2.57 % (32436)Instructions burned: 182 (million)
% 8.65/2.57 % (32436)------------------------------
% 8.65/2.57 % (32436)------------------------------
% 8.65/2.58 % (32441)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_32257 for (2990ds/922Mi)
% 8.65/2.58 % (32433)Instruction limit reached!
% 8.65/2.58 % (32433)------------------------------
% 8.65/2.58 % (32433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.58 % (32433)Termination reason: Unknown
% 8.65/2.58 % (32433)Termination phase: Saturation
% 8.65/2.58
% 8.65/2.58 % (32433)Memory used [KB]: 6524
% 8.65/2.58 % (32433)Time elapsed: 0.127 s
% 8.65/2.58 % (32433)Instructions burned: 298 (million)
% 8.65/2.58 % (32433)------------------------------
% 8.65/2.58 % (32433)------------------------------
% 8.65/2.59 % (32442)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/182Mi)
% 9.22/2.60 % (32443)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/164Mi)
% 9.22/2.62 % (32440)Instruction limit reached!
% 9.22/2.62 % (32440)------------------------------
% 9.22/2.62 % (32440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.62 % (32440)Termination reason: Unknown
% 9.22/2.62 % (32440)Termination phase: Property scanning
% 9.22/2.62
% 9.22/2.62 % (32440)Memory used [KB]: 1918
% 9.22/2.62 % (32440)Time elapsed: 0.046 s
% 9.22/2.62 % (32440)Instructions burned: 114 (million)
% 9.22/2.62 % (32440)------------------------------
% 9.22/2.62 % (32440)------------------------------
% 9.22/2.62 % (32431)Instruction limit reached!
% 9.22/2.62 % (32431)------------------------------
% 9.22/2.62 % (32431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.62 % (32431)Termination reason: Unknown
% 9.22/2.62 % (32431)Termination phase: Saturation
% 9.22/2.62
% 9.22/2.62 % (32431)Memory used [KB]: 6524
% 9.22/2.62 % (32431)Time elapsed: 0.183 s
% 9.22/2.62 % (32431)Instructions burned: 458 (million)
% 9.22/2.62 % (32431)------------------------------
% 9.22/2.62 % (32431)------------------------------
% 9.22/2.63 % (32444)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/50Mi)
% 9.22/2.63 % (32445)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/368Mi)
% 9.22/2.65 % (32439)Instruction limit reached!
% 9.22/2.65 % (32439)------------------------------
% 9.22/2.65 % (32439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.65 % (32439)Termination reason: Unknown
% 9.22/2.65 % (32439)Termination phase: Saturation
% 9.22/2.65
% 9.22/2.65 % (32439)Memory used [KB]: 6396
% 9.22/2.65 % (32439)Time elapsed: 0.088 s
% 9.22/2.65 % (32439)Instructions burned: 216 (million)
% 9.22/2.65 % (32439)------------------------------
% 9.22/2.65 % (32439)------------------------------
% 9.22/2.65 % (32444)Instruction limit reached!
% 9.22/2.65 % (32444)------------------------------
% 9.22/2.65 % (32444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.65 % (32444)Termination reason: Unknown
% 9.22/2.65 % (32444)Termination phase: Function definition elimination
% 9.22/2.65
% 9.22/2.65 % (32444)Memory used [KB]: 1663
% 9.22/2.65 % (32444)Time elapsed: 0.024 s
% 9.22/2.65 % (32444)Instructions burned: 52 (million)
% 9.22/2.65 % (32444)------------------------------
% 9.22/2.65 % (32444)------------------------------
% 9.22/2.66 % (32446)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/1021Mi)
% 9.22/2.66 % (32442)Instruction limit reached!
% 9.22/2.66 % (32442)------------------------------
% 9.22/2.66 % (32442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.66 % (32442)Termination reason: Unknown
% 9.22/2.66 % (32442)Termination phase: Property scanning
% 9.22/2.66
% 9.22/2.66 % (32442)Memory used [KB]: 1918
% 9.22/2.66 % (32442)Time elapsed: 0.075 s
% 9.22/2.66 % (32442)Instructions burned: 183 (million)
% 9.22/2.66 % (32442)------------------------------
% 9.22/2.66 % (32442)------------------------------
% 9.22/2.67 % (32443)Instruction limit reached!
% 9.22/2.67 % (32443)------------------------------
% 9.22/2.67 % (32443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.67 % (32443)Termination reason: Unknown
% 9.22/2.67 % (32443)Termination phase: Saturation
% 9.22/2.67
% 9.22/2.67 % (32443)Memory used [KB]: 1918
% 9.22/2.67 % (32443)Time elapsed: 0.071 s
% 9.22/2.67 % (32443)Instructions burned: 165 (million)
% 9.22/2.67 % (32443)------------------------------
% 9.22/2.67 % (32443)------------------------------
% 9.22/2.67 % (32447)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/267Mi)
% 9.22/2.68 % (32448)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/204Mi)
% 9.22/2.68 % (32449)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_32257 for (2989ds/26Mi)
% 9.22/2.70 % (32449)Instruction limit reached!
% 9.22/2.70 % (32449)------------------------------
% 9.22/2.70 % (32449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.70 % (32449)Termination reason: Unknown
% 9.22/2.70 % (32449)Termination phase: Property scanning
% 9.22/2.70
% 9.22/2.70 % (32449)Memory used [KB]: 1535
% 9.22/2.70 % (32449)Time elapsed: 0.014 s
% 9.22/2.70 % (32449)Instructions burned: 28 (million)
% 9.22/2.70 % (32449)------------------------------
% 9.22/2.70 % (32449)------------------------------
% 9.79/2.71 % (32450)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_32257 for (2988ds/53Mi)
% 9.79/2.74 % (32450)Instruction limit reached!
% 9.79/2.74 % (32450)------------------------------
% 9.79/2.74 % (32450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.74 % (32450)Termination reason: Unknown
% 9.79/2.74 % (32450)Termination phase: Function definition elimination
% 9.79/2.74
% 9.79/2.74 % (32450)Memory used [KB]: 1663
% 9.79/2.74 % (32450)Time elapsed: 0.025 s
% 9.79/2.74 % (32450)Instructions burned: 53 (million)
% 9.79/2.74 % (32450)------------------------------
% 9.79/2.74 % (32450)------------------------------
% 9.79/2.75 % (32451)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_32257 for (2988ds/4436Mi)
% 9.79/2.76 % (32448)Instruction limit reached!
% 9.79/2.76 % (32448)------------------------------
% 9.79/2.76 % (32448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.76 % (32448)Termination reason: Unknown
% 9.79/2.76 % (32448)Termination phase: Property scanning
% 9.79/2.76
% 9.79/2.76 % (32448)Memory used [KB]: 1918
% 9.79/2.76 % (32448)Time elapsed: 0.085 s
% 9.79/2.76 % (32448)Instructions burned: 205 (million)
% 9.79/2.76 % (32448)------------------------------
% 9.79/2.76 % (32448)------------------------------
% 9.79/2.78 % (32447)Instruction limit reached!
% 9.79/2.78 % (32447)------------------------------
% 9.79/2.78 % (32447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.78 % (32447)Termination reason: Unknown
% 9.79/2.78 % (32447)Termination phase: Property scanning
% 9.79/2.78
% 9.79/2.78 % (32447)Memory used [KB]: 1918
% 9.79/2.78 % (32447)Time elapsed: 0.111 s
% 9.79/2.78 % (32447)Instructions burned: 267 (million)
% 9.79/2.78 % (32447)------------------------------
% 9.79/2.78 % (32447)------------------------------
% 9.79/2.78 % (32452)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_32257 for (2988ds/1539Mi)
% 9.79/2.78 % (32445)Instruction limit reached!
% 9.79/2.78 % (32445)------------------------------
% 9.79/2.78 % (32445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.78 % (32445)Termination reason: Unknown
% 9.79/2.78 % (32445)Termination phase: Saturation
% 9.79/2.78
% 9.79/2.78 % (32445)Memory used [KB]: 6524
% 9.79/2.78 % (32445)Time elapsed: 0.151 s
% 9.79/2.78 % (32445)Instructions burned: 370 (million)
% 9.79/2.78 % (32445)------------------------------
% 9.79/2.78 % (32445)------------------------------
% 10.25/2.80 % (32453)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_32257 for (2987ds/408Mi)
% 10.25/2.80 % (32454)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_32257 for (2987ds/5205Mi)
% 10.25/2.84 % (32434)Instruction limit reached!
% 10.25/2.84 % (32434)------------------------------
% 10.25/2.84 % (32434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.25/2.84 % (32434)Termination reason: Unknown
% 10.25/2.84 % (32434)Termination phase: Saturation
% 10.25/2.84
% 10.25/2.84 % (32434)Memory used [KB]: 7036
% 10.25/2.84 % (32434)Time elapsed: 0.378 s
% 10.25/2.84 % (32434)Instructions burned: 989 (million)
% 10.25/2.84 % (32434)------------------------------
% 10.25/2.84 % (32434)------------------------------
% 10.25/2.86 % (32455)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_32257 for (2987ds/1913Mi)
% 10.64/2.93 % (32441)Instruction limit reached!
% 10.64/2.93 % (32441)------------------------------
% 10.64/2.93 % (32441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.93 % (32441)Termination reason: Unknown
% 10.64/2.93 % (32441)Termination phase: Saturation
% 10.64/2.93
% 10.64/2.93 % (32441)Memory used [KB]: 7036
% 10.64/2.93 % (32441)Time elapsed: 0.351 s
% 10.64/2.93 % (32441)Instructions burned: 922 (million)
% 10.64/2.93 % (32441)------------------------------
% 10.64/2.93 % (32441)------------------------------
% 10.64/2.94 % (32456)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_32257 for (2986ds/4350Mi)
% 10.64/2.98 % (32453)Instruction limit reached!
% 10.64/2.98 % (32453)------------------------------
% 10.64/2.98 % (32453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.98 % (32453)Termination reason: Unknown
% 10.64/2.98 % (32453)Termination phase: Saturation
% 10.64/2.98
% 10.64/2.98 % (32453)Memory used [KB]: 7036
% 10.64/2.98 % (32453)Time elapsed: 0.185 s
% 10.64/2.98 % (32453)Instructions burned: 408 (million)
% 10.64/2.98 % (32453)------------------------------
% 10.64/2.98 % (32453)------------------------------
% 10.64/3.00 % (32457)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_32257 for (2986ds/68Mi)
% 10.64/3.03 % (32457)Instruction limit reached!
% 10.64/3.03 % (32457)------------------------------
% 10.64/3.03 % (32457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/3.03 % (32457)Termination reason: Unknown
% 10.64/3.03 % (32457)Termination phase: Function definition elimination
% 10.64/3.03
% 10.64/3.03 % (32457)Memory used [KB]: 1791
% 10.64/3.03 % (32457)Time elapsed: 0.031 s
% 10.64/3.03 % (32457)Instructions burned: 69 (million)
% 10.64/3.03 % (32457)------------------------------
% 10.64/3.03 % (32457)------------------------------
% 12.59/3.04 % (32458)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_32257 for (2985ds/358Mi)
% 12.59/3.05 % (32446)Instruction limit reached!
% 12.59/3.05 % (32446)------------------------------
% 12.59/3.05 % (32446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.59/3.05 % (32446)Termination reason: Unknown
% 12.59/3.05 % (32446)Termination phase: Saturation
% 12.59/3.05
% 12.59/3.05 % (32446)Memory used [KB]: 7036
% 12.59/3.05 % (32446)Time elapsed: 0.390 s
% 12.59/3.05 % (32446)Instructions burned: 1022 (million)
% 12.59/3.05 % (32446)------------------------------
% 12.59/3.05 % (32446)------------------------------
% 12.59/3.07 % (32459)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32257 for (2985ds/31Mi)
% 12.59/3.08 % (32459)Instruction limit reached!
% 12.59/3.08 % (32459)------------------------------
% 12.59/3.08 % (32459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.59/3.08 % (32459)Termination reason: Unknown
% 12.59/3.08 % (32459)Termination phase: Property scanning
% 12.59/3.08
% 12.59/3.08 % (32459)Memory used [KB]: 1535
% 12.59/3.08 % (32459)Time elapsed: 0.016 s
% 12.59/3.08 % (32459)Instructions burned: 32 (million)
% 12.59/3.08 % (32459)------------------------------
% 12.59/3.08 % (32459)------------------------------
% 12.59/3.10 % (32460)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_32257 for (2984ds/279Mi)
% 13.22/3.19 % (32458)Instruction limit reached!
% 13.22/3.19 % (32458)------------------------------
% 13.22/3.19 % (32458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.19 % (32458)Termination reason: Unknown
% 13.22/3.19 % (32458)Termination phase: Saturation
% 13.22/3.19
% 13.22/3.19 % (32458)Memory used [KB]: 6524
% 13.22/3.19 % (32458)Time elapsed: 0.147 s
% 13.22/3.19 % (32458)Instructions burned: 358 (million)
% 13.22/3.19 % (32458)------------------------------
% 13.22/3.19 % (32458)------------------------------
% 13.73/3.20 % (32461)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_32257 for (2983ds/258Mi)
% 13.73/3.22 % (32460)Instruction limit reached!
% 13.73/3.22 % (32460)------------------------------
% 13.73/3.22 % (32460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.22 % (32460)Termination reason: Unknown
% 13.73/3.22 % (32460)Termination phase: Saturation
% 13.73/3.22
% 13.73/3.22 % (32460)Memory used [KB]: 6524
% 13.73/3.22 % (32460)Time elapsed: 0.120 s
% 13.73/3.22 % (32460)Instructions burned: 279 (million)
% 13.73/3.22 % (32460)------------------------------
% 13.73/3.22 % (32460)------------------------------
% 13.73/3.23 % (32462)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_32257 for (2983ds/26Mi)
% 13.73/3.25 % (32462)Instruction limit reached!
% 13.73/3.25 % (32462)------------------------------
% 13.73/3.25 % (32462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.25 % (32462)Termination reason: Unknown
% 13.73/3.25 % (32462)Termination phase: Property scanning
% 13.73/3.25
% 13.73/3.25 % (32462)Memory used [KB]: 1535
% 13.73/3.25 % (32462)Time elapsed: 0.014 s
% 13.73/3.25 % (32462)Instructions burned: 26 (million)
% 13.73/3.25 % (32462)------------------------------
% 13.73/3.25 % (32462)------------------------------
% 13.73/3.27 % (32463)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_32257 for (2983ds/995Mi)
% 14.40/3.32 % (32461)Instruction limit reached!
% 14.40/3.32 % (32461)------------------------------
% 14.40/3.32 % (32461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.40/3.32 % (32461)Termination reason: Unknown
% 14.40/3.32 % (32461)Termination phase: Saturation
% 14.40/3.32
% 14.40/3.32 % (32461)Memory used [KB]: 6908
% 14.40/3.32 % (32461)Time elapsed: 0.131 s
% 14.40/3.32 % (32461)Instructions burned: 259 (million)
% 14.40/3.32 % (32461)------------------------------
% 14.40/3.32 % (32461)------------------------------
% 14.40/3.33 % (32464)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_32257 for (2982ds/373Mi)
% 14.40/3.34 % (32452)Instruction limit reached!
% 14.40/3.34 % (32452)------------------------------
% 14.40/3.34 % (32452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.40/3.34 % (32452)Termination reason: Unknown
% 14.40/3.34 % (32452)Termination phase: Saturation
% 14.40/3.34
% 14.40/3.34 % (32452)Memory used [KB]: 7036
% 14.40/3.34 % (32452)Time elapsed: 0.562 s
% 14.40/3.34 % (32452)Instructions burned: 1539 (million)
% 14.40/3.34 % (32452)------------------------------
% 14.40/3.34 % (32452)------------------------------
% 14.40/3.36 % (32465)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_32257 for (2982ds/253Mi)
% 14.98/3.46 % (32465)Instruction limit reached!
% 14.98/3.46 % (32465)------------------------------
% 14.98/3.46 % (32465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.98/3.46 % (32465)Termination reason: Unknown
% 14.98/3.46 % (32465)Termination phase: Property scanning
% 14.98/3.46
% 14.98/3.46 % (32465)Memory used [KB]: 1918
% 14.98/3.46 % (32465)Time elapsed: 0.106 s
% 14.98/3.46 % (32465)Instructions burned: 254 (million)
% 14.98/3.46 % (32465)------------------------------
% 14.98/3.46 % (32465)------------------------------
% 14.98/3.48 % (32466)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_32257 for (2981ds/832Mi)
% 14.98/3.48 % (32464)Instruction limit reached!
% 14.98/3.48 % (32464)------------------------------
% 14.98/3.48 % (32464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.98/3.48 % (32464)Termination reason: Unknown
% 14.98/3.48 % (32464)Termination phase: Saturation
% 14.98/3.48
% 14.98/3.48 % (32464)Memory used [KB]: 6396
% 14.98/3.48 % (32464)Time elapsed: 0.152 s
% 14.98/3.48 % (32464)Instructions burned: 374 (million)
% 14.98/3.48 % (32464)------------------------------
% 14.98/3.48 % (32464)------------------------------
% 15.67/3.50 % (32467)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_32257 for (2980ds/668Mi)
% 15.67/3.51 % (32466)Refutation not found, incomplete strategy
% 15.67/3.51 % (32466)------------------------------
% 15.67/3.51 % (32466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.67/3.51 % (32466)Termination reason: Refutation not found, incomplete strategy
% 15.67/3.51
% 15.67/3.51
% 15.67/3.51 % (32466)Memory used [KB]: 6268
% 15.67/3.51 % (32466)Time elapsed: 0.032 s
% 15.67/3.51 % (32466)Instructions burned: 66 (million)
% 15.67/3.51 % (32466)------------------------------
% 15.67/3.51 % (32466)------------------------------
% 15.67/3.53 % (32468)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_32257 for (2980ds/40Mi)
% 15.67/3.54 % (32468)Instruction limit reached!
% 15.67/3.54 % (32468)------------------------------
% 15.67/3.54 % (32468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.67/3.54 % (32468)Termination reason: Unknown
% 15.67/3.54 % (32468)Termination phase: Property scanning
% 15.67/3.54
% 15.67/3.54 % (32468)Memory used [KB]: 1663
% 15.67/3.54 % (32468)Time elapsed: 0.020 s
% 15.67/3.54 % (32468)Instructions burned: 41 (million)
% 15.67/3.54 % (32468)------------------------------
% 15.67/3.54 % (32468)------------------------------
% 15.67/3.55 % (32455)Instruction limit reached!
% 15.67/3.55 % (32455)------------------------------
% 15.67/3.55 % (32455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.67/3.55 % (32455)Termination reason: Unknown
% 15.67/3.55 % (32455)Termination phase: Saturation
% 15.67/3.55
% 15.67/3.55 % (32455)Memory used [KB]: 2558
% 15.67/3.55 % (32455)Time elapsed: 0.694 s
% 15.67/3.55 % (32455)Instructions burned: 1914 (million)
% 15.67/3.55 % (32455)------------------------------
% 15.67/3.55 % (32455)------------------------------
% 15.67/3.56 % (32469)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_32257 for (2980ds/294Mi)
% 15.67/3.57 % (32470)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_32257 for (2980ds/187Mi)
% 16.10/3.61 % (32463)Instruction limit reached!
% 16.10/3.61 % (32463)------------------------------
% 16.10/3.61 % (32463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.10/3.61 % (32463)Termination reason: Unknown
% 16.10/3.61 % (32463)Termination phase: Saturation
% 16.10/3.61
% 16.10/3.61 % (32463)Memory used [KB]: 7036
% 16.10/3.61 % (32463)Time elapsed: 0.337 s
% 16.10/3.61 % (32463)Instructions burned: 996 (million)
% 16.10/3.61 % (32463)------------------------------
% 16.10/3.61 % (32463)------------------------------
% 16.10/3.62 % (32471)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_32257 for (2979ds/371Mi)
% 16.10/3.64 % (32470)Instruction limit reached!
% 16.10/3.64 % (32470)------------------------------
% 16.10/3.64 % (32470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.10/3.64 % (32470)Termination reason: Unknown
% 16.10/3.64 % (32470)Termination phase: Property scanning
% 16.10/3.64
% 16.10/3.64 % (32470)Memory used [KB]: 1918
% 16.10/3.64 % (32470)Time elapsed: 0.078 s
% 16.10/3.64 % (32470)Instructions burned: 188 (million)
% 16.10/3.64 % (32470)------------------------------
% 16.10/3.64 % (32470)------------------------------
% 16.10/3.66 % (32472)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_32257 for (2979ds/1827Mi)
% 16.10/3.68 % (32469)Instruction limit reached!
% 16.10/3.68 % (32469)------------------------------
% 16.10/3.68 % (32469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.10/3.68 % (32469)Termination reason: Unknown
% 16.10/3.68 % (32469)Termination phase: Saturation
% 16.10/3.68
% 16.10/3.68 % (32469)Memory used [KB]: 6524
% 16.10/3.68 % (32469)Time elapsed: 0.122 s
% 16.10/3.68 % (32469)Instructions burned: 294 (million)
% 16.10/3.68 % (32469)------------------------------
% 16.10/3.68 % (32469)------------------------------
% 16.98/3.70 % (32473)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_32257 for (2978ds/70Mi)
% 16.98/3.73 % (32473)Instruction limit reached!
% 16.98/3.73 % (32473)------------------------------
% 16.98/3.73 % (32473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/3.73 % (32473)Termination reason: Unknown
% 16.98/3.73 % (32473)Termination phase: Function definition elimination
% 16.98/3.73
% 16.98/3.73 % (32473)Memory used [KB]: 1791
% 16.98/3.73 % (32473)Time elapsed: 0.031 s
% 16.98/3.73 % (32473)Instructions burned: 72 (million)
% 16.98/3.73 % (32473)------------------------------
% 16.98/3.73 % (32473)------------------------------
% 16.98/3.74 % (32474)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_32257 for (2978ds/316Mi)
% 16.98/3.76 % (32467)Instruction limit reached!
% 16.98/3.76 % (32467)------------------------------
% 16.98/3.76 % (32467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/3.76 % (32467)Termination reason: Unknown
% 16.98/3.76 % (32467)Termination phase: Saturation
% 16.98/3.76
% 16.98/3.76 % (32467)Memory used [KB]: 11257
% 16.98/3.76 % (32467)Time elapsed: 0.261 s
% 16.98/3.76 % (32467)Instructions burned: 669 (million)
% 16.98/3.76 % (32467)------------------------------
% 16.98/3.76 % (32467)------------------------------
% 16.98/3.77 % (32471)Instruction limit reached!
% 16.98/3.77 % (32471)------------------------------
% 16.98/3.77 % (32471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/3.77 % (32471)Termination reason: Unknown
% 16.98/3.77 % (32471)Termination phase: Saturation
% 16.98/3.77
% 16.98/3.77 % (32471)Memory used [KB]: 6396
% 16.98/3.77 % (32471)Time elapsed: 0.149 s
% 16.98/3.77 % (32471)Instructions burned: 373 (million)
% 16.98/3.77 % (32471)------------------------------
% 16.98/3.77 % (32471)------------------------------
% 16.98/3.78 % (32475)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_32257 for (2978ds/932Mi)
% 16.98/3.79 % (32476)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_32257 for (2977ds/4714Mi)
% 17.76/3.87 % (32474)Instruction limit reached!
% 17.76/3.87 % (32474)------------------------------
% 17.76/3.87 % (32474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/3.87 % (32474)Termination reason: Unknown
% 17.76/3.87 % (32474)Termination phase: Saturation
% 17.76/3.87
% 17.76/3.87 % (32474)Memory used [KB]: 6396
% 17.76/3.87 % (32474)Time elapsed: 0.132 s
% 17.76/3.87 % (32474)Instructions burned: 316 (million)
% 17.76/3.87 % (32474)------------------------------
% 17.76/3.87 % (32474)------------------------------
% 17.76/3.89 % (32477)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_32257 for (2976ds/8250Mi)
% 20.32/4.13 % (32475)Instruction limit reached!
% 20.32/4.13 % (32475)------------------------------
% 20.32/4.13 % (32475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.13 % (32475)Termination reason: Unknown
% 20.32/4.13 % (32475)Termination phase: Saturation
% 20.32/4.13
% 20.32/4.13 % (32475)Memory used [KB]: 7036
% 20.32/4.13 % (32475)Time elapsed: 0.355 s
% 20.32/4.13 % (32475)Instructions burned: 933 (million)
% 20.32/4.13 % (32475)------------------------------
% 20.32/4.13 % (32475)------------------------------
% 20.32/4.15 % (32478)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_32257 for (2974ds/770Mi)
% 20.32/4.19 % (32478)Refutation not found, incomplete strategy
% 20.32/4.19 % (32478)------------------------------
% 20.32/4.19 % (32478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.19 % (32478)Termination reason: Refutation not found, incomplete strategy
% 20.32/4.19
% 20.32/4.19
% 20.32/4.19 % (32478)Memory used [KB]: 6396
% 20.32/4.19 % (32478)Time elapsed: 0.049 s
% 20.32/4.19 % (32478)Instructions burned: 105 (million)
% 20.32/4.19 % (32478)------------------------------
% 20.32/4.19 % (32478)------------------------------
% 20.82/4.21 % (32479)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_32257 for (2973ds/794Mi)
% 22.62/4.50 % (32472)Instruction limit reached!
% 22.62/4.50 % (32472)------------------------------
% 22.62/4.50 % (32472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.62/4.50 % (32472)Termination reason: Unknown
% 22.62/4.50 % (32472)Termination phase: Saturation
% 22.62/4.50
% 22.62/4.50 % (32472)Memory used [KB]: 10234
% 22.62/4.50 % (32472)Time elapsed: 0.845 s
% 22.62/4.50 % (32472)Instructions burned: 1827 (million)
% 22.62/4.50 % (32472)------------------------------
% 22.62/4.50 % (32472)------------------------------
% 22.62/4.51 % (32479)Instruction limit reached!
% 22.62/4.51 % (32479)------------------------------
% 22.62/4.51 % (32479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.62/4.51 % (32479)Termination reason: Unknown
% 22.62/4.51 % (32479)Termination phase: Saturation
% 22.62/4.51
% 22.62/4.51 % (32479)Memory used [KB]: 2430
% 22.62/4.51 % (32479)Time elapsed: 0.305 s
% 22.62/4.51 % (32479)Instructions burned: 794 (million)
% 22.62/4.51 % (32479)------------------------------
% 22.62/4.51 % (32479)------------------------------
% 22.62/4.52 % (32480)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_32257 for (2970ds/464Mi)
% 22.62/4.53 % (32481)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_32257 for (2970ds/1376Mi)
% 22.62/4.60 % (32451)Instruction limit reached!
% 22.62/4.60 % (32451)------------------------------
% 22.62/4.60 % (32451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.62/4.60 % (32451)Termination reason: Unknown
% 22.62/4.60 % (32451)Termination phase: Saturation
% 22.62/4.60
% 22.62/4.60 % (32451)Memory used [KB]: 7547
% 22.62/4.60 % (32451)Time elapsed: 1.836 s
% 22.62/4.60 % (32451)Instructions burned: 4437 (million)
% 23.45/4.60 % (32451)------------------------------
% 23.45/4.60 % (32451)------------------------------
% 23.45/4.61 % (32482)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_32257 for (2969ds/906Mi)
% 23.86/4.71 % (32480)Instruction limit reached!
% 23.86/4.71 % (32480)------------------------------
% 23.86/4.71 % (32480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.86/4.71 % (32480)Termination reason: Unknown
% 23.86/4.71 % (32480)Termination phase: Saturation
% 23.86/4.71
% 23.86/4.71 % (32480)Memory used [KB]: 6908
% 23.86/4.71 % (32480)Time elapsed: 0.187 s
% 23.86/4.71 % (32480)Instructions burned: 464 (million)
% 23.86/4.71 % (32480)------------------------------
% 23.86/4.71 % (32480)------------------------------
% 23.86/4.71 % (32454)Instruction limit reached!
% 23.86/4.71 % (32454)------------------------------
% 23.86/4.71 % (32454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.86/4.71 % (32454)Termination reason: Unknown
% 23.86/4.71 % (32454)Termination phase: Saturation
% 23.86/4.71
% 23.86/4.71 % (32454)Memory used [KB]: 8315
% 23.86/4.71 % (32454)Time elapsed: 1.911 s
% 23.86/4.71 % (32454)Instructions burned: 5205 (million)
% 23.86/4.71 % (32454)------------------------------
% 23.86/4.71 % (32454)------------------------------
% 23.86/4.72 % (32483)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_32257 for (2968ds/434Mi)
% 23.86/4.73 % (32484)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_32257 for (2968ds/865Mi)
% 23.86/4.75 % (32456)Instruction limit reached!
% 23.86/4.75 % (32456)------------------------------
% 23.86/4.75 % (32456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.86/4.75 % (32456)Termination reason: Unknown
% 23.86/4.75 % (32456)Termination phase: Saturation
% 23.86/4.75
% 23.86/4.75 % (32456)Memory used [KB]: 7547
% 23.86/4.75 % (32456)Time elapsed: 1.809 s
% 23.86/4.75 % (32456)Instructions burned: 4350 (million)
% 23.86/4.75 % (32456)------------------------------
% 23.86/4.75 % (32456)------------------------------
% 23.86/4.77 % (32485)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_32257 for (2968ds/593Mi)
% 24.55/4.91 % (32483)Instruction limit reached!
% 24.55/4.91 % (32483)------------------------------
% 24.55/4.91 % (32483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.55/4.92 % (32483)Termination reason: Unknown
% 24.55/4.92 % (32483)Termination phase: Saturation
% 24.55/4.92
% 24.55/4.92 % (32483)Memory used [KB]: 6780
% 24.55/4.92 % (32483)Time elapsed: 0.195 s
% 24.55/4.92 % (32483)Instructions burned: 435 (million)
% 24.55/4.92 % (32483)------------------------------
% 24.55/4.92 % (32483)------------------------------
% 24.55/4.93 % (32486)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_32257 for (2966ds/443Mi)
% 24.55/4.96 % (32482)Instruction limit reached!
% 24.55/4.96 % (32482)------------------------------
% 24.55/4.96 % (32482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.55/4.96 % (32482)Termination reason: Unknown
% 24.55/4.96 % (32482)Termination phase: Saturation
% 24.55/4.96
% 24.55/4.96 % (32482)Memory used [KB]: 7164
% 24.55/4.96 % (32482)Time elapsed: 0.348 s
% 24.55/4.96 % (32482)Instructions burned: 907 (million)
% 24.55/4.96 % (32482)------------------------------
% 24.55/4.96 % (32482)------------------------------
% 24.55/4.98 % (32487)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_32257 for (2966ds/594Mi)
% 24.55/5.00 % (32485)Instruction limit reached!
% 24.55/5.00 % (32485)------------------------------
% 24.55/5.00 % (32485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.55/5.00 % (32485)Termination reason: Unknown
% 24.55/5.00 % (32485)Termination phase: Saturation
% 24.55/5.00
% 24.55/5.00 % (32485)Memory used [KB]: 6780
% 24.55/5.00 % (32485)Time elapsed: 0.231 s
% 24.55/5.00 % (32485)Instructions burned: 594 (million)
% 24.55/5.00 % (32485)------------------------------
% 24.55/5.00 % (32485)------------------------------
% 24.55/5.01 % (32488)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_32257 for (2965ds/327Mi)
% 26.59/5.04 % (32481)Instruction limit reached!
% 26.59/5.04 % (32481)------------------------------
% 26.59/5.04 % (32481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.59/5.04 % (32481)Termination reason: Unknown
% 26.59/5.04 % (32481)Termination phase: Saturation
% 26.59/5.04
% 26.59/5.04 % (32481)Memory used [KB]: 7036
% 26.59/5.04 % (32481)Time elapsed: 0.514 s
% 26.59/5.04 % (32481)Instructions burned: 1376 (million)
% 26.59/5.04 % (32481)------------------------------
% 26.59/5.04 % (32481)------------------------------
% 26.59/5.06 % (32489)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_32257 for (2965ds/5411Mi)
% 26.59/5.10 % (32484)Instruction limit reached!
% 26.59/5.10 % (32484)------------------------------
% 26.59/5.10 % (32484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.59/5.10 % (32484)Termination reason: Unknown
% 26.59/5.10 % (32484)Termination phase: Saturation
% 26.59/5.10
% 26.59/5.10 % (32484)Memory used [KB]: 7164
% 26.59/5.10 % (32484)Time elapsed: 0.378 s
% 26.59/5.10 % (32484)Instructions burned: 865 (million)
% 26.59/5.10 % (32484)------------------------------
% 26.59/5.10 % (32484)------------------------------
% 26.59/5.11 % (32486)Instruction limit reached!
% 26.59/5.11 % (32486)------------------------------
% 26.59/5.11 % (32486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.59/5.11 % (32486)Termination reason: Unknown
% 26.59/5.11 % (32486)Termination phase: Saturation
% 26.59/5.11
% 26.59/5.11 % (32486)Memory used [KB]: 6524
% 26.59/5.11 % (32486)Time elapsed: 0.179 s
% 26.59/5.11 % (32486)Instructions burned: 444 (million)
% 26.59/5.11 % (32486)------------------------------
% 26.59/5.11 % (32486)------------------------------
% 26.59/5.12 % (32490)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_32257 for (2964ds/1762Mi)
% 26.59/5.13 % (32491)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_32257 for (2964ds/96Mi)
% 27.09/5.16 % (32491)Instruction limit reached!
% 27.09/5.16 % (32491)------------------------------
% 27.09/5.16 % (32491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.09/5.16 % (32491)Termination reason: Unknown
% 27.09/5.16 % (32491)Termination phase: Property scanning
% 27.09/5.16
% 27.09/5.16 % (32491)Memory used [KB]: 1918
% 27.09/5.16 % (32491)Time elapsed: 0.039 s
% 27.09/5.16 % (32491)Instructions burned: 98 (million)
% 27.09/5.16 % (32491)------------------------------
% 27.09/5.16 % (32491)------------------------------
% 27.09/5.17 % (32488)Instruction limit reached!
% 27.09/5.17 % (32488)------------------------------
% 27.09/5.17 % (32488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.09/5.17 % (32488)Termination reason: Unknown
% 27.09/5.17 % (32488)Termination phase: Saturation
% 27.09/5.17
% 27.09/5.17 % (32488)Memory used [KB]: 7547
% 27.09/5.17 % (32488)Time elapsed: 0.161 s
% 27.09/5.17 % (32488)Instructions burned: 327 (million)
% 27.09/5.17 % (32488)------------------------------
% 27.09/5.17 % (32488)------------------------------
% 27.09/5.18 % (32492)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_32257 for (2964ds/503Mi)
% 27.09/5.19 % (32493)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_32257 for (2964ds/90Mi)
% 27.52/5.21 % (32487)Instruction limit reached!
% 27.52/5.21 % (32487)------------------------------
% 27.52/5.21 % (32487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.21 % (32487)Termination reason: Unknown
% 27.52/5.21 % (32487)Termination phase: Saturation
% 27.52/5.21
% 27.52/5.21 % (32487)Memory used [KB]: 6780
% 27.52/5.21 % (32487)Time elapsed: 0.239 s
% 27.52/5.21 % (32487)Instructions burned: 596 (million)
% 27.52/5.22 % (32487)------------------------------
% 27.52/5.22 % (32487)------------------------------
% 27.52/5.22 % (32493)Instruction limit reached!
% 27.52/5.22 % (32493)------------------------------
% 27.52/5.22 % (32493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.22 % (32493)Termination reason: Unknown
% 27.52/5.22 % (32493)Termination phase: Function definition elimination
% 27.52/5.22
% 27.52/5.22 % (32493)Memory used [KB]: 1918
% 27.52/5.22 % (32493)Time elapsed: 0.037 s
% 27.52/5.22 % (32493)Instructions burned: 90 (million)
% 27.52/5.22 % (32493)------------------------------
% 27.52/5.22 % (32493)------------------------------
% 27.52/5.23 % (32494)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_32257 for (2963ds/593Mi)
% 27.52/5.24 % (32495)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_32257 for (2963ds/1512Mi)
% 27.52/5.28 % (32495)Refutation not found, incomplete strategy
% 27.52/5.28 % (32495)------------------------------
% 27.52/5.28 % (32495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.28 % (32495)Termination reason: Refutation not found, incomplete strategy
% 27.52/5.28
% 27.52/5.28
% 27.52/5.28 % (32495)Memory used [KB]: 6268
% 27.52/5.28 % (32495)Time elapsed: 0.062 s
% 27.52/5.28 % (32495)Instructions burned: 83 (million)
% 27.52/5.28 % (32495)------------------------------
% 27.52/5.28 % (32495)------------------------------
% 27.86/5.30 % (32496)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_32257 for (2962ds/569Mi)
% 27.86/5.39 % (32492)Instruction limit reached!
% 27.86/5.39 % (32492)------------------------------
% 27.86/5.39 % (32492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.86/5.39 % (32492)Termination reason: Unknown
% 27.86/5.39 % (32492)Termination phase: Saturation
% 27.86/5.39
% 27.86/5.39 % (32492)Memory used [KB]: 6908
% 27.86/5.39 % (32492)Time elapsed: 0.215 s
% 27.86/5.39 % (32492)Instructions burned: 504 (million)
% 27.86/5.39 % (32492)------------------------------
% 27.86/5.39 % (32492)------------------------------
% 28.30/5.41 % (32497)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_32257 for (2961ds/501Mi)
% 28.30/5.46 % (32494)Instruction limit reached!
% 28.30/5.46 % (32494)------------------------------
% 28.30/5.46 % (32494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.46 % (32494)Termination reason: Unknown
% 28.30/5.46 % (32494)Termination phase: Saturation
% 28.30/5.46
% 28.30/5.46 % (32494)Memory used [KB]: 6780
% 28.30/5.46 % (32494)Time elapsed: 0.234 s
% 28.30/5.46 % (32494)Instructions burned: 595 (million)
% 28.30/5.46 % (32494)------------------------------
% 28.30/5.46 % (32494)------------------------------
% 28.30/5.48 % (32498)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_32257 for (2961ds/562Mi)
% 28.74/5.50 % (32476)Instruction limit reached!
% 28.74/5.50 % (32476)------------------------------
% 28.74/5.50 % (32476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.74/5.50 % (32476)Termination reason: Unknown
% 28.74/5.50 % (32476)Termination phase: Saturation
% 28.74/5.50
% 28.74/5.50 % (32476)Memory used [KB]: 7803
% 28.74/5.50 % (32476)Time elapsed: 1.715 s
% 28.74/5.50 % (32476)Instructions burned: 4716 (million)
% 28.74/5.50 % (32476)------------------------------
% 28.74/5.50 % (32476)------------------------------
% 28.74/5.52 % (32499)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_32257 for (2960ds/406Mi)
% 28.74/5.52 % (32496)Instruction limit reached!
% 28.74/5.52 % (32496)------------------------------
% 28.74/5.52 % (32496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.74/5.52 % (32496)Termination reason: Unknown
% 28.74/5.52 % (32496)Termination phase: Saturation
% 28.74/5.52
% 28.74/5.52 % (32496)Memory used [KB]: 6780
% 28.74/5.52 % (32496)Time elapsed: 0.223 s
% 28.74/5.52 % (32496)Instructions burned: 570 (million)
% 28.74/5.52 % (32496)------------------------------
% 28.74/5.52 % (32496)------------------------------
% 28.74/5.54 % (32500)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_32257 for (2960ds/582Mi)
% 29.09/5.61 % (32497)Instruction limit reached!
% 29.09/5.61 % (32497)------------------------------
% 29.09/5.61 % (32497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/5.61 % (32497)Termination reason: Unknown
% 29.09/5.61 % (32497)Termination phase: Saturation
% 29.09/5.61
% 29.09/5.61 % (32497)Memory used [KB]: 6780
% 29.09/5.61 % (32497)Time elapsed: 0.202 s
% 29.09/5.61 % (32497)Instructions burned: 501 (million)
% 29.09/5.61 % (32497)------------------------------
% 29.09/5.61 % (32497)------------------------------
% 29.09/5.63 % (32501)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_32257 for (2959ds/456Mi)
% 29.42/5.70 % (32498)Instruction limit reached!
% 29.42/5.70 % (32498)------------------------------
% 29.42/5.70 % (32498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.70 % (32498)Termination reason: Unknown
% 29.42/5.70 % (32498)Termination phase: Saturation
% 29.42/5.70
% 29.42/5.70 % (32498)Memory used [KB]: 6780
% 29.42/5.70 % (32498)Time elapsed: 0.225 s
% 29.42/5.70 % (32498)Instructions burned: 562 (million)
% 29.42/5.70 % (32498)------------------------------
% 29.42/5.70 % (32498)------------------------------
% 29.42/5.72 % (32502)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_32257 for (2958ds/393Mi)
% 29.42/5.72 % (32499)Instruction limit reached!
% 29.42/5.72 % (32499)------------------------------
% 29.42/5.72 % (32499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.72 % (32499)Termination reason: Unknown
% 29.42/5.72 % (32499)Termination phase: Saturation
% 29.42/5.72
% 29.42/5.72 % (32499)Memory used [KB]: 7803
% 29.42/5.72 % (32499)Time elapsed: 0.210 s
% 29.42/5.72 % (32499)Instructions burned: 407 (million)
% 29.42/5.72 % (32499)------------------------------
% 29.42/5.72 % (32499)------------------------------
% 29.42/5.74 % (32503)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_32257 for (2958ds/1335Mi)
% 29.42/5.75 % (32490)Instruction limit reached!
% 29.42/5.75 % (32490)------------------------------
% 29.42/5.75 % (32490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.75 % (32490)Termination reason: Unknown
% 29.42/5.75 % (32490)Termination phase: Saturation
% 29.42/5.75
% 29.42/5.75 % (32490)Memory used [KB]: 7803
% 29.42/5.75 % (32490)Time elapsed: 0.635 s
% 29.42/5.75 % (32490)Instructions burned: 1762 (million)
% 29.42/5.75 % (32490)------------------------------
% 29.42/5.75 % (32490)------------------------------
% 29.42/5.76 % (32500)Instruction limit reached!
% 29.42/5.76 % (32500)------------------------------
% 29.42/5.76 % (32500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.76 % (32500)Termination reason: Unknown
% 29.42/5.76 % (32500)Termination phase: Saturation
% 29.42/5.76
% 29.42/5.76 % (32500)Memory used [KB]: 6780
% 29.42/5.76 % (32500)Time elapsed: 0.230 s
% 29.42/5.76 % (32500)Instructions burned: 583 (million)
% 29.42/5.76 % (32500)------------------------------
% 29.42/5.76 % (32500)------------------------------
% 29.42/5.77 % (32504)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_32257 for (2958ds/3373Mi)
% 29.42/5.78 % (32505)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_32257 for (2957ds/474Mi)
% 30.87/5.81 % (32501)Instruction limit reached!
% 30.87/5.81 % (32501)------------------------------
% 30.87/5.81 % (32501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.87/5.81 % (32501)Termination reason: Unknown
% 30.87/5.81 % (32501)Termination phase: Saturation
% 30.87/5.81
% 30.87/5.81 % (32501)Memory used [KB]: 6524
% 30.87/5.81 % (32501)Time elapsed: 0.184 s
% 30.87/5.81 % (32501)Instructions burned: 458 (million)
% 30.87/5.81 % (32501)------------------------------
% 30.87/5.81 % (32501)------------------------------
% 30.87/5.83 % (32506)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_32257 for (2957ds/157Mi)
% 30.87/5.89 % (32506)Instruction limit reached!
% 30.87/5.89 % (32506)------------------------------
% 30.87/5.89 % (32506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.87/5.89 % (32506)Termination reason: Unknown
% 30.87/5.89 % (32506)Termination phase: Property scanning
% 30.87/5.89
% 30.87/5.89 % (32506)Memory used [KB]: 1918
% 30.87/5.89 % (32506)Time elapsed: 0.065 s
% 30.87/5.89 % (32506)Instructions burned: 159 (million)
% 30.87/5.89 % (32506)------------------------------
% 30.87/5.89 % (32506)------------------------------
% 31.24/5.90 % (32502)Instruction limit reached!
% 31.24/5.90 % (32502)------------------------------
% 31.24/5.90 % (32502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/5.90 % (32502)Termination reason: Unknown
% 31.24/5.90 % (32502)Termination phase: Saturation
% 31.24/5.90
% 31.24/5.90 % (32502)Memory used [KB]: 7036
% 31.24/5.90 % (32502)Time elapsed: 0.181 s
% 31.24/5.90 % (32502)Instructions burned: 394 (million)
% 31.24/5.90 % (32502)------------------------------
% 31.24/5.90 % (32502)------------------------------
% 31.24/5.91 % (32507)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_32257 for (2956ds/590Mi)
% 31.24/5.92 % (32508)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_32257 for (2956ds/104Mi)
% 31.24/5.96 % (32508)Instruction limit reached!
% 31.24/5.96 % (32508)------------------------------
% 31.24/5.96 % (32508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/5.96 % (32508)Termination reason: Unknown
% 31.24/5.96 % (32508)Termination phase: Property scanning
% 31.24/5.96
% 31.24/5.96 % (32508)Memory used [KB]: 1918
% 31.24/5.96 % (32508)Time elapsed: 0.043 s
% 31.24/5.96 % (32508)Instructions burned: 105 (million)
% 31.24/5.96 % (32508)------------------------------
% 31.24/5.96 % (32508)------------------------------
% 31.24/5.97 % (32505)Instruction limit reached!
% 31.24/5.97 % (32505)------------------------------
% 31.24/5.97 % (32505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/5.97 % (32505)Termination reason: Unknown
% 31.24/5.97 % (32505)Termination phase: Saturation
% 31.24/5.97
% 31.24/5.97 % (32505)Memory used [KB]: 6780
% 31.24/5.97 % (32505)Time elapsed: 0.189 s
% 31.24/5.97 % (32505)Instructions burned: 475 (million)
% 31.24/5.97 % (32505)------------------------------
% 31.24/5.97 % (32505)------------------------------
% 31.24/5.98 % (32509)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_32257 for (2956ds/414Mi)
% 31.24/5.98 % (32510)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_32257 for (2955ds/715Mi)
% 34.31/6.14 % (32509)Instruction limit reached!
% 34.31/6.14 % (32509)------------------------------
% 34.31/6.14 % (32509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.31/6.14 % (32509)Termination reason: Unknown
% 34.31/6.14 % (32509)Termination phase: Saturation
% 34.31/6.14
% 34.31/6.14 % (32509)Memory used [KB]: 6396
% 34.31/6.14 % (32509)Time elapsed: 0.166 s
% 34.31/6.14 % (32509)Instructions burned: 415 (million)
% 34.31/6.14 % (32509)------------------------------
% 34.31/6.14 % (32509)------------------------------
% 34.31/6.16 % (32511)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_32257 for (2954ds/961Mi)
% 34.31/6.17 % (32507)Instruction limit reached!
% 34.31/6.17 % (32507)------------------------------
% 34.31/6.17 % (32507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.31/6.17 % (32507)Termination reason: Unknown
% 34.31/6.17 % (32507)Termination phase: Saturation
% 34.31/6.17
% 34.31/6.17 % (32507)Memory used [KB]: 7675
% 34.31/6.17 % (32507)Time elapsed: 0.268 s
% 34.31/6.17 % (32507)Instructions burned: 591 (million)
% 34.31/6.17 % (32507)------------------------------
% 34.31/6.17 % (32507)------------------------------
% 34.31/6.19 % (32512)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_32257 for (2953ds/1213Mi)
% 34.74/6.27 % (32510)Instruction limit reached!
% 34.74/6.27 % (32510)------------------------------
% 34.74/6.27 % (32510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.74/6.27 % (32510)Termination reason: Unknown
% 34.74/6.27 % (32510)Termination phase: Saturation
% 34.74/6.27
% 34.74/6.27 % (32510)Memory used [KB]: 2430
% 34.74/6.27 % (32510)Time elapsed: 0.283 s
% 34.74/6.27 % (32510)Instructions burned: 716 (million)
% 34.74/6.27 % (32510)------------------------------
% 34.74/6.27 % (32510)------------------------------
% 34.74/6.28 % (32513)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_32257 for (2953ds/1979Mi)
% 34.74/6.28 % (32503)Instruction limit reached!
% 34.74/6.28 % (32503)------------------------------
% 34.74/6.28 % (32503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.74/6.28 % (32503)Termination reason: Unknown
% 34.74/6.28 % (32503)Termination phase: Saturation
% 34.74/6.28
% 34.74/6.28 % (32503)Memory used [KB]: 6652
% 34.74/6.28 % (32503)Time elapsed: 0.546 s
% 34.74/6.28 % (32503)Instructions burned: 1337 (million)
% 34.74/6.28 % (32503)------------------------------
% 34.74/6.28 % (32503)------------------------------
% 35.23/6.30 % (32514)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_32257 for (2952ds/481Mi)
% 35.53/6.48 % (32514)Instruction limit reached!
% 35.53/6.48 % (32514)------------------------------
% 35.53/6.48 % (32514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.53/6.48 % (32514)Termination reason: Unknown
% 35.53/6.48 % (32514)Termination phase: Saturation
% 35.53/6.48
% 35.53/6.48 % (32514)Memory used [KB]: 6524
% 35.53/6.48 % (32514)Time elapsed: 0.179 s
% 35.53/6.48 % (32514)Instructions burned: 483 (million)
% 35.53/6.48 % (32514)------------------------------
% 35.53/6.48 % (32514)------------------------------
% 35.53/6.49 % (32515)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_32257 for (2950ds/783Mi)
% 36.02/6.51 % (32511)Instruction limit reached!
% 36.02/6.51 % (32511)------------------------------
% 36.02/6.51 % (32511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.02/6.51 % (32511)Termination reason: Unknown
% 36.02/6.51 % (32511)Termination phase: Saturation
% 36.02/6.51
% 36.02/6.51 % (32511)Memory used [KB]: 7036
% 36.02/6.51 % (32511)Time elapsed: 0.357 s
% 36.02/6.51 % (32511)Instructions burned: 964 (million)
% 36.02/6.51 % (32511)------------------------------
% 36.02/6.51 % (32511)------------------------------
% 36.02/6.52 % (32516)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_32257 for (2950ds/432Mi)
% 36.68/6.63 % (32516)Instruction limit reached!
% 36.68/6.63 % (32516)------------------------------
% 36.68/6.63 % (32516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.68/6.63 % (32516)Termination reason: Unknown
% 36.68/6.63 % (32516)Termination phase: Saturation
% 36.68/6.63
% 36.68/6.63 % (32516)Memory used [KB]: 6524
% 36.68/6.63 % (32516)Time elapsed: 0.111 s
% 36.68/6.63 % (32516)Instructions burned: 433 (million)
% 36.68/6.63 % (32516)------------------------------
% 36.68/6.63 % (32516)------------------------------
% 36.68/6.64 % (32517)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_32257 for (2949ds/1670Mi)
% 36.68/6.68 % (32512)Instruction limit reached!
% 36.68/6.68 % (32512)------------------------------
% 36.68/6.68 % (32512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.68/6.68 % (32512)Termination reason: Unknown
% 36.68/6.68 % (32512)Termination phase: Saturation
% 36.68/6.68
% 36.68/6.68 % (32512)Memory used [KB]: 8955
% 36.68/6.68 % (32512)Time elapsed: 0.489 s
% 36.68/6.68 % (32512)Instructions burned: 1215 (million)
% 36.68/6.68 % (32512)------------------------------
% 36.68/6.68 % (32512)------------------------------
% 36.68/6.69 % (32518)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_32257 for (2948ds/90Mi)
% 37.61/6.71 % (32518)Instruction limit reached!
% 37.61/6.71 % (32518)------------------------------
% 37.61/6.71 % (32518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.61/6.71 % (32518)Termination reason: Unknown
% 37.61/6.71 % (32518)Termination phase: Function definition elimination
% 37.61/6.71
% 37.61/6.71 % (32518)Memory used [KB]: 1918
% 37.61/6.71 % (32518)Time elapsed: 0.023 s
% 37.61/6.71 % (32518)Instructions burned: 90 (million)
% 37.61/6.71 % (32518)------------------------------
% 37.61/6.71 % (32518)------------------------------
% 37.61/6.71 % (32515)Instruction limit reached!
% 37.61/6.71 % (32515)------------------------------
% 37.61/6.71 % (32515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.61/6.71 % (32515)Termination reason: Unknown
% 37.61/6.71 % (32515)Termination phase: Saturation
% 37.61/6.71
% 37.61/6.71 % (32515)Memory used [KB]: 8315
% 37.61/6.71 % (32515)Time elapsed: 0.225 s
% 37.61/6.71 % (32515)Instructions burned: 785 (million)
% 37.61/6.71 % (32515)------------------------------
% 37.61/6.71 % (32515)------------------------------
% 37.61/6.72 % (32519)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_32257 for (2948ds/346Mi)
% 37.61/6.72 % (32520)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_32257 for (2948ds/401Mi)
% 38.17/6.80 % (32519)Instruction limit reached!
% 38.17/6.80 % (32519)------------------------------
% 38.17/6.80 % (32519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.80 % (32519)Termination reason: Unknown
% 38.17/6.80 % (32519)Termination phase: Saturation
% 38.17/6.80
% 38.17/6.80 % (32519)Memory used [KB]: 6396
% 38.17/6.80 % (32519)Time elapsed: 0.082 s
% 38.17/6.80 % (32519)Instructions burned: 350 (million)
% 38.17/6.80 % (32519)------------------------------
% 38.17/6.80 % (32519)------------------------------
% 38.17/6.81 % (32528)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_32257 for (2947ds/6454Mi)
% 38.17/6.81 % (32520)Instruction limit reached!
% 38.17/6.81 % (32520)------------------------------
% 38.17/6.81 % (32520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.81 % (32520)Termination reason: Unknown
% 38.17/6.81 % (32520)Termination phase: Saturation
% 38.17/6.81
% 38.17/6.81 % (32520)Memory used [KB]: 6396
% 38.17/6.81 % (32520)Time elapsed: 0.094 s
% 38.17/6.81 % (32520)Instructions burned: 403 (million)
% 38.17/6.81 % (32520)------------------------------
% 38.17/6.81 % (32520)------------------------------
% 38.17/6.82 % (32504)Instruction limit reached!
% 38.17/6.82 % (32504)------------------------------
% 38.17/6.82 % (32504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.82 % (32504)Termination reason: Unknown
% 38.17/6.82 % (32504)Termination phase: Saturation
% 38.17/6.82
% 38.17/6.82 % (32504)Memory used [KB]: 7164
% 38.17/6.82 % (32504)Time elapsed: 1.051 s
% 38.17/6.82 % (32504)Instructions burned: 3374 (million)
% 38.17/6.82 % (32504)------------------------------
% 38.17/6.82 % (32504)------------------------------
% 38.17/6.82 % (32536)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_32257 for (2947ds/283Mi)
% 38.17/6.83 % (32538)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_32257 for (2947ds/865Mi)
% 38.17/6.85 % (32513)Instruction limit reached!
% 38.17/6.85 % (32513)------------------------------
% 38.17/6.85 % (32513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.85 % (32513)Termination reason: Unknown
% 38.17/6.85 % (32513)Termination phase: Saturation
% 38.17/6.85
% 38.17/6.85 % (32513)Memory used [KB]: 7036
% 38.17/6.85 % (32513)Time elapsed: 0.573 s
% 38.17/6.85 % (32513)Instructions burned: 1980 (million)
% 38.17/6.85 % (32513)------------------------------
% 38.17/6.85 % (32513)------------------------------
% 38.17/6.86 % (32551)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_32257 for (2947ds/4528Mi)
% 38.17/6.88 % (32551)Refutation not found, incomplete strategy
% 38.17/6.88 % (32551)------------------------------
% 38.17/6.88 % (32551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.88 % (32551)Termination reason: Refutation not found, incomplete strategy
% 38.17/6.88
% 38.17/6.88
% 38.17/6.88 % (32551)Memory used [KB]: 1918
% 38.17/6.88 % (32551)Time elapsed: 0.022 s
% 38.17/6.88 % (32551)Instructions burned: 77 (million)
% 38.17/6.88 % (32551)------------------------------
% 38.17/6.88 % (32551)------------------------------
% 38.17/6.89 % (32536)Instruction limit reached!
% 38.17/6.89 % (32536)------------------------------
% 38.17/6.89 % (32536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.89 % (32536)Termination reason: Unknown
% 38.17/6.89 % (32536)Termination phase: Property scanning
% 38.17/6.89
% 38.17/6.89 % (32536)Memory used [KB]: 1918
% 38.17/6.89 % (32536)Time elapsed: 0.068 s
% 38.17/6.89 % (32536)Instructions burned: 286 (million)
% 38.17/6.89 % (32536)------------------------------
% 38.17/6.89 % (32536)------------------------------
% 38.17/6.89 % (32565)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_32257 for (2946ds/1001Mi)
% 39.28/6.90 % (32569)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_32257 for (2946ds/102Mi)
% 39.28/6.92 % (32569)Instruction limit reached!
% 39.28/6.92 % (32569)------------------------------
% 39.28/6.92 % (32569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.28/6.92 % (32569)Termination reason: Unknown
% 39.28/6.92 % (32569)Termination phase: Property scanning
% 39.28/6.92
% 39.28/6.92 % (32569)Memory used [KB]: 1918
% 39.28/6.92 % (32569)Time elapsed: 0.025 s
% 39.28/6.92 % (32569)Instructions burned: 104 (million)
% 39.28/6.92 % (32569)------------------------------
% 39.28/6.92 % (32569)------------------------------
% 39.28/6.93 % (32583)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_32257 for (2946ds/952Mi)
% 39.28/6.99 % (32489)Instruction limit reached!
% 39.28/6.99 % (32489)------------------------------
% 39.28/6.99 % (32489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.28/6.99 % (32489)Termination reason: Unknown
% 39.28/6.99 % (32489)Termination phase: Saturation
% 39.28/6.99
% 39.28/6.99 % (32489)Memory used [KB]: 10106
% 39.28/6.99 % (32489)Time elapsed: 1.936 s
% 39.28/6.99 % (32489)Instructions burned: 5412 (million)
% 39.28/6.99 % (32489)------------------------------
% 39.28/6.99 % (32489)------------------------------
% 39.28/7.00 % (32614)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_32257 for (2945ds/578Mi)
% 40.52/7.04 % (32517)Instruction limit reached!
% 40.52/7.04 % (32517)------------------------------
% 40.52/7.04 % (32517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.52/7.04 % (32517)Termination reason: Unknown
% 40.52/7.04 % (32517)Termination phase: Saturation
% 40.52/7.04
% 40.52/7.04 % (32517)Memory used [KB]: 8059
% 40.52/7.04 % (32517)Time elapsed: 0.394 s
% 40.52/7.04 % (32517)Instructions burned: 1673 (million)
% 40.52/7.04 % (32517)------------------------------
% 40.52/7.04 % (32517)------------------------------
% 40.52/7.04 % (32637)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_32257 for (2945ds/643Mi)
% 40.52/7.06 % (32538)Instruction limit reached!
% 40.52/7.06 % (32538)------------------------------
% 40.52/7.06 % (32538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.52/7.06 % (32538)Termination reason: Unknown
% 40.52/7.06 % (32538)Termination phase: Saturation
% 40.52/7.06
% 40.52/7.06 % (32538)Memory used [KB]: 7036
% 40.52/7.06 % (32538)Time elapsed: 0.235 s
% 40.52/7.06 % (32538)Instructions burned: 868 (million)
% 40.52/7.06 % (32538)------------------------------
% 40.52/7.06 % (32538)------------------------------
% 40.52/7.07 % (32649)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_32257 for (2945ds/865Mi)
% 41.11/7.13 % (32565)Instruction limit reached!
% 41.11/7.13 % (32565)------------------------------
% 41.11/7.13 % (32565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.11/7.13 % (32565)Termination reason: Unknown
% 41.11/7.13 % (32565)Termination phase: Saturation
% 41.11/7.13
% 41.11/7.13 % (32565)Memory used [KB]: 7036
% 41.11/7.13 % (32565)Time elapsed: 0.234 s
% 41.11/7.13 % (32565)Instructions burned: 1002 (million)
% 41.11/7.13 % (32565)------------------------------
% 41.11/7.13 % (32565)------------------------------
% 41.11/7.14 % (32677)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_32257 for (2944ds/1174Mi)
% 41.11/7.16 % (32583)Instruction limit reached!
% 41.11/7.16 % (32583)------------------------------
% 41.11/7.16 % (32583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.11/7.16 % (32583)Termination reason: Unknown
% 41.11/7.16 % (32583)Termination phase: Saturation
% 41.11/7.16
% 41.11/7.16 % (32583)Memory used [KB]: 7036
% 41.11/7.16 % (32583)Time elapsed: 0.223 s
% 41.11/7.16 % (32583)Instructions burned: 953 (million)
% 41.11/7.16 % (32583)------------------------------
% 41.11/7.16 % (32583)------------------------------
% 41.11/7.17 % (32688)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_32257 for (2944ds/644Mi)
% 41.11/7.18 % (32614)Instruction limit reached!
% 41.11/7.18 % (32614)------------------------------
% 41.11/7.18 % (32614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.11/7.18 % (32614)Termination reason: Unknown
% 41.11/7.18 % (32614)Termination phase: Saturation
% 41.11/7.18
% 41.11/7.18 % (32614)Memory used [KB]: 7036
% 41.11/7.18 % (32614)Time elapsed: 0.178 s
% 41.11/7.18 % (32614)Instructions burned: 581 (million)
% 41.11/7.18 % (32614)------------------------------
% 41.11/7.18 % (32614)------------------------------
% 41.11/7.19 % (32698)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_32257 for (2943ds/1201Mi)
% 41.11/7.19 % (32637)Instruction limit reached!
% 41.11/7.19 % (32637)------------------------------
% 41.11/7.19 % (32637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.11/7.19 % (32637)Termination reason: Unknown
% 41.11/7.19 % (32637)Termination phase: Saturation
% 41.11/7.19
% 41.11/7.19 % (32637)Memory used [KB]: 6780
% 41.11/7.19 % (32637)Time elapsed: 0.151 s
% 41.11/7.19 % (32637)Instructions burned: 646 (million)
% 41.11/7.19 % (32637)------------------------------
% 41.11/7.19 % (32637)------------------------------
% 41.59/7.20 % (32703)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_32257 for (2943ds/1046Mi)
% 41.59/7.24 % (32477)Instruction limit reached!
% 41.59/7.24 % (32477)------------------------------
% 41.59/7.24 % (32477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.59/7.24 % (32477)Termination reason: Unknown
% 41.59/7.24 % (32477)Termination phase: Saturation
% 41.59/7.24
% 41.59/7.24 % (32477)Memory used [KB]: 20084
% 41.59/7.24 % (32477)Time elapsed: 3.354 s
% 41.59/7.24 % (32477)Instructions burned: 8253 (million)
% 41.59/7.24 % (32477)------------------------------
% 41.59/7.24 % (32477)------------------------------
% 41.59/7.25 % (32716)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_32257 for (2943ds/222Mi)
% 41.59/7.28 % (32649)Instruction limit reached!
% 41.59/7.28 % (32649)------------------------------
% 41.59/7.28 % (32649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.59/7.28 % (32649)Termination reason: Unknown
% 41.59/7.28 % (32649)Termination phase: Saturation
% 41.59/7.28
% 41.59/7.28 % (32649)Memory used [KB]: 6908
% 41.59/7.28 % (32649)Time elapsed: 0.206 s
% 41.59/7.28 % (32649)Instructions burned: 865 (million)
% 41.59/7.28 % (32649)------------------------------
% 41.59/7.28 % (32649)------------------------------
% 41.59/7.29 % (32723)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_32257 for (2943ds/68Mi)
% 41.96/7.30 % (32723)Instruction limit reached!
% 41.96/7.30 % (32723)------------------------------
% 41.96/7.30 % (32723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.96/7.30 % (32723)Termination reason: Unknown
% 41.96/7.30 % (32723)Termination phase: Function definition elimination
% 41.96/7.30
% 41.96/7.30 % (32723)Memory used [KB]: 1791
% 41.96/7.30 % (32723)Time elapsed: 0.019 s
% 41.96/7.30 % (32723)Instructions burned: 70 (million)
% 41.96/7.30 % (32723)------------------------------
% 41.96/7.30 % (32723)------------------------------
% 41.96/7.30 % (32716)Instruction limit reached!
% 41.96/7.30 % (32716)------------------------------
% 41.96/7.30 % (32716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.96/7.30 % (32716)Termination reason: Unknown
% 41.96/7.30 % (32716)Termination phase: Property scanning
% 41.96/7.30
% 41.96/7.30 % (32716)Memory used [KB]: 1918
% 41.96/7.30 % (32716)Time elapsed: 0.053 s
% 41.96/7.30 % (32716)Instructions burned: 223 (million)
% 41.96/7.30 % (32716)------------------------------
% 41.96/7.30 % (32716)------------------------------
% 41.96/7.31 % (32735)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_32257 for (2942ds/454Mi)
% 41.96/7.31 % (32736)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_32257 for (2942ds/360Mi)
% 41.96/7.32 % (32688)Instruction limit reached!
% 41.96/7.32 % (32688)------------------------------
% 41.96/7.32 % (32688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.96/7.32 % (32688)Termination reason: Unknown
% 41.96/7.32 % (32688)Termination phase: Saturation
% 41.96/7.32
% 41.96/7.32 % (32688)Memory used [KB]: 6908
% 41.96/7.32 % (32688)Time elapsed: 0.154 s
% 41.96/7.32 % (32688)Instructions burned: 644 (million)
% 41.96/7.32 % (32688)------------------------------
% 41.96/7.32 % (32688)------------------------------
% 41.96/7.33 % (32747)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_32257 for (2942ds/157Mi)
% 41.96/7.37 % (32747)Instruction limit reached!
% 41.96/7.37 % (32747)------------------------------
% 41.96/7.37 % (32747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.96/7.37 % (32747)Termination reason: Unknown
% 41.96/7.37 % (32747)Termination phase: Property scanning
% 41.96/7.37
% 41.96/7.37 % (32747)Memory used [KB]: 1918
% 41.96/7.37 % (32747)Time elapsed: 0.040 s
% 41.96/7.37 % (32747)Instructions burned: 160 (million)
% 41.96/7.37 % (32747)------------------------------
% 41.96/7.37 % (32747)------------------------------
% 41.96/7.38 % (300)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_32257 for (2941ds/5061Mi)
% 42.37/7.40 % (32736)Instruction limit reached!
% 42.37/7.40 % (32736)------------------------------
% 42.37/7.40 % (32736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.37/7.40 % (32736)Termination reason: Unknown
% 42.37/7.40 % (32736)Termination phase: Saturation
% 42.37/7.40
% 42.37/7.40 % (32736)Memory used [KB]: 6396
% 42.37/7.40 % (32736)Time elapsed: 0.086 s
% 42.37/7.40 % (32736)Instructions burned: 362 (million)
% 42.37/7.40 % (32736)------------------------------
% 42.37/7.40 % (32736)------------------------------
% 42.37/7.41 % (302)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_32257 for (2941ds/2401Mi)
% 42.37/7.41 % (32677)Instruction limit reached!
% 42.37/7.41 % (32677)------------------------------
% 42.37/7.41 % (32677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.37/7.41 % (32677)Termination reason: Unknown
% 42.37/7.41 % (32677)Termination phase: Saturation
% 42.37/7.41
% 42.37/7.41 % (32677)Memory used [KB]: 7164
% 42.37/7.41 % (32677)Time elapsed: 0.276 s
% 42.37/7.41 % (32677)Instructions burned: 1176 (million)
% 42.37/7.41 % (32677)------------------------------
% 42.37/7.41 % (32677)------------------------------
% 42.37/7.42 % (32735)Instruction limit reached!
% 42.37/7.42 % (32735)------------------------------
% 42.37/7.42 % (32735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.37/7.42 % (32735)Termination reason: Unknown
% 42.37/7.42 % (32735)Termination phase: Saturation
% 42.37/7.42
% 42.37/7.42 % (32735)Memory used [KB]: 11001
% 42.37/7.42 % (32735)Time elapsed: 0.108 s
% 42.37/7.42 % (32735)Instructions burned: 454 (million)
% 42.37/7.42 % (32735)------------------------------
% 42.37/7.42 % (32735)------------------------------
% 42.37/7.42 % (303)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_32257 for (2941ds/5798Mi)
% 42.37/7.43 % (304)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_32257 for (2941ds/346Mi)
% 42.37/7.45 % (32703)Instruction limit reached!
% 42.37/7.45 % (32703)------------------------------
% 42.37/7.45 % (32703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.37/7.45 % (32703)Termination reason: Unknown
% 42.37/7.45 % (32703)Termination phase: Saturation
% 42.37/7.45
% 42.37/7.45 % (32703)Memory used [KB]: 7036
% 42.37/7.45 % (32703)Time elapsed: 0.246 s
% 42.37/7.45 % (32703)Instructions burned: 1047 (million)
% 42.37/7.45 % (32703)------------------------------
% 42.37/7.45 % (32703)------------------------------
% 42.37/7.46 % (305)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_32257 for (2941ds/1321Mi)
% 42.37/7.48 % (305)Refutation not found, incomplete strategy
% 42.37/7.48 % (305)------------------------------
% 42.37/7.48 % (305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.37/7.48 % (305)Termination reason: Refutation not found, incomplete strategy
% 42.37/7.48
% 42.37/7.48
% 42.37/7.48 % (305)Memory used [KB]: 1918
% 42.37/7.48 % (305)Time elapsed: 0.024 s
% 42.37/7.48 % (305)Instructions burned: 83 (million)
% 42.37/7.48 % (305)------------------------------
% 42.37/7.48 % (305)------------------------------
% 42.37/7.49 % (306)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_32257 for (2940ds/1312Mi)
% 43.25/7.51 % (304)Instruction limit reached!
% 43.25/7.51 % (304)------------------------------
% 43.25/7.51 % (304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.25/7.51 % (304)Termination reason: Unknown
% 43.25/7.51 % (304)Termination phase: Saturation
% 43.25/7.51
% 43.25/7.51 % (304)Memory used [KB]: 6396
% 43.25/7.51 % (304)Time elapsed: 0.081 s
% 43.25/7.51 % (304)Instructions burned: 349 (million)
% 43.25/7.51 % (304)------------------------------
% 43.25/7.51 % (304)------------------------------
% 43.25/7.52 % (307)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_32257 for (2940ds/672Mi)
% 43.25/7.55 % (32698)Instruction limit reached!
% 43.25/7.55 % (32698)------------------------------
% 43.25/7.55 % (32698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.25/7.55 % (32698)Termination reason: Unknown
% 43.25/7.55 % (32698)Termination phase: Saturation
% 43.25/7.55
% 43.25/7.55 % (32698)Memory used [KB]: 9978
% 43.25/7.55 % (32698)Time elapsed: 0.357 s
% 43.25/7.55 % (32698)Instructions burned: 1201 (million)
% 43.25/7.55 % (32698)------------------------------
% 43.25/7.55 % (32698)------------------------------
% 43.25/7.56 % (308)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_32257 for (2940ds/1897Mi)
% 43.91/7.71 % (307)Instruction limit reached!
% 43.91/7.71 % (307)------------------------------
% 43.91/7.71 % (307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.91/7.71 % (307)Termination reason: Unknown
% 43.91/7.71 % (307)Termination phase: Saturation
% 43.91/7.71
% 43.91/7.71 % (307)Memory used [KB]: 7803
% 43.91/7.71 % (307)Time elapsed: 0.189 s
% 43.91/7.71 % (307)Instructions burned: 673 (million)
% 43.91/7.71 % (307)------------------------------
% 43.91/7.71 % (307)------------------------------
% 43.91/7.72 % (309)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_32257 for (2938ds/1202Mi)
% 44.20/7.80 % (306)Instruction limit reached!
% 44.20/7.80 % (306)------------------------------
% 44.20/7.80 % (306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.20/7.80 % (306)Termination reason: Unknown
% 44.20/7.80 % (306)Termination phase: Saturation
% 44.20/7.80
% 44.20/7.80 % (306)Memory used [KB]: 7036
% 44.20/7.80 % (306)Time elapsed: 0.307 s
% 44.20/7.80 % (306)Instructions burned: 1314 (million)
% 44.20/7.80 % (306)------------------------------
% 44.20/7.80 % (306)------------------------------
% 44.20/7.81 % (310)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_32257 for (2937ds/1493Mi)
% 44.63/7.95 % (302)Instruction limit reached!
% 44.63/7.95 % (302)------------------------------
% 44.63/7.95 % (302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.63/7.95 % (302)Termination reason: Unknown
% 44.63/7.95 % (302)Termination phase: Saturation
% 44.63/7.95
% 44.63/7.95 % (302)Memory used [KB]: 2558
% 44.63/7.95 % (302)Time elapsed: 0.545 s
% 44.63/7.95 % (302)Instructions burned: 2402 (million)
% 44.63/7.95 % (302)------------------------------
% 44.63/7.95 % (302)------------------------------
% 44.63/7.96 % (311)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_32257 for (2936ds/7679Mi)
% 47.53/8.03 % (308)Instruction limit reached!
% 47.53/8.03 % (308)------------------------------
% 47.53/8.03 % (308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.53/8.03 % (308)Termination reason: Unknown
% 47.53/8.03 % (308)Termination phase: Saturation
% 47.53/8.03
% 47.53/8.03 % (308)Memory used [KB]: 7547
% 47.53/8.03 % (308)Time elapsed: 0.479 s
% 47.53/8.03 % (308)Instructions burned: 1899 (million)
% 47.53/8.03 % (308)------------------------------
% 47.53/8.03 % (308)------------------------------
% 47.53/8.04 % (312)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_32257 for (2935ds/340Mi)
% 47.53/8.06 % (309)Instruction limit reached!
% 47.53/8.06 % (309)------------------------------
% 47.53/8.06 % (309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.53/8.06 % (309)Termination reason: Unknown
% 47.53/8.06 % (309)Termination phase: Saturation
% 47.53/8.06
% 47.53/8.06 % (309)Memory used [KB]: 3070
% 47.53/8.06 % (309)Time elapsed: 0.341 s
% 47.53/8.06 % (309)Instructions burned: 1203 (million)
% 47.53/8.06 % (309)------------------------------
% 47.53/8.06 % (309)------------------------------
% 47.53/8.07 % (313)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_32257 for (2935ds/3672Mi)
% 48.18/8.13 % (312)Instruction limit reached!
% 48.18/8.13 % (312)------------------------------
% 48.18/8.13 % (312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.18/8.13 % (312)Termination reason: Unknown
% 48.18/8.13 % (312)Termination phase: Saturation
% 48.18/8.13
% 48.18/8.13 % (312)Memory used [KB]: 6396
% 48.18/8.13 % (312)Time elapsed: 0.083 s
% 48.18/8.13 % (312)Instructions burned: 340 (million)
% 48.18/8.13 % (312)------------------------------
% 48.18/8.13 % (312)------------------------------
% 48.18/8.14 % (314)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_32257 for (2934ds/1535Mi)
% 48.18/8.17 % (310)First to succeed.
% 48.64/8.23 % (310)Refutation found. Thanks to Tanya!
% 48.64/8.23 % SZS status Theorem for DTF2THF_32257
% 48.64/8.23 % SZS output start Proof for DTF2THF_32257
% 48.64/8.23 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i).
% 48.64/8.23 thf(func_def_3, type, c_not: $o > $o).
% 48.64/8.23 thf(func_def_4, type, c_and: $o > $o > $o).
% 48.64/8.23 thf(func_def_5, type, c_or: $o > $o > $o).
% 48.64/8.23 thf(func_def_6, type, c_iff: $o > $o > $o).
% 48.64/8.23 thf(func_def_7, type, c_In: $i > $i > $o).
% 48.64/8.23 thf(func_def_8, type, c_Subq: $i > $i > $o).
% 48.64/8.23 thf(func_def_10, type, c_Union: $i > $i).
% 48.64/8.23 thf(func_def_11, type, c_Power: $i > $i).
% 48.64/8.23 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i).
% 48.64/8.23 thf(func_def_13, type, c_TransSet: $i > $o).
% 48.64/8.23 thf(func_def_14, type, c_atleast2: $i > $o).
% 48.64/8.23 thf(func_def_15, type, c_atleast3: $i > $o).
% 48.64/8.23 thf(func_def_16, type, c_atleast4: $i > $o).
% 48.64/8.23 thf(func_def_17, type, c_atleast5: $i > $o).
% 48.64/8.23 thf(func_def_18, type, c_atleast6: $i > $o).
% 48.64/8.23 thf(func_def_19, type, c_exactly2: $i > $o).
% 48.64/8.23 thf(func_def_20, type, c_exactly3: $i > $o).
% 48.64/8.23 thf(func_def_21, type, c_exactly4: $i > $o).
% 48.64/8.23 thf(func_def_22, type, c_exactly5: $i > $o).
% 48.64/8.23 thf(func_def_23, type, c_exu_i: ($i > $o) > $o).
% 48.64/8.23 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o).
% 48.64/8.23 thf(func_def_37, type, c_If_i: $o > $i > $i > $i).
% 48.64/8.23 thf(func_def_38, type, c_exactly1of2: $o > $o > $o).
% 48.64/8.23 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o).
% 48.64/8.23 thf(func_def_40, type, c_nIn: $i > $i > $o).
% 48.64/8.23 thf(func_def_41, type, c_nSubq: $i > $i > $o).
% 48.64/8.23 thf(func_def_42, type, c_UPair: $i > $i > $i).
% 48.64/8.23 thf(func_def_43, type, c_Sing: $i > $i).
% 48.64/8.23 thf(func_def_44, type, c_binunion: $i > $i > $i).
% 48.64/8.23 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i).
% 48.64/8.23 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i).
% 48.64/8.23 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i).
% 48.64/8.23 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i).
% 48.64/8.23 thf(func_def_49, type, c_binintersect: $i > $i > $i).
% 48.64/8.23 thf(func_def_50, type, c_setminus: $i > $i > $i).
% 48.64/8.23 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o).
% 48.64/8.23 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o).
% 48.64/8.23 thf(func_def_53, type, c_atleastp: $i > $i > $o).
% 48.64/8.23 thf(func_def_54, type, c_equip: $i > $i > $o).
% 48.64/8.23 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o).
% 48.64/8.23 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i).
% 48.64/8.23 thf(func_def_57, type, c_ordsucc: $i > $i).
% 48.64/8.23 thf(func_def_58, type, c_nat_p: $i > $o).
% 48.64/8.23 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i).
% 48.64/8.23 thf(func_def_60, type, c_add_nat: $i > $i > $i).
% 48.64/8.23 thf(func_def_61, type, c_mul_nat: $i > $i > $i).
% 48.64/8.23 thf(func_def_62, type, c_ordinal: $i > $o).
% 48.64/8.23 thf(func_def_63, type, c_V_: $i > $i).
% 48.64/8.23 thf(func_def_64, type, c_Inj1: $i > $i).
% 48.64/8.23 thf(func_def_65, type, c_Inj0: $i > $i).
% 48.64/8.23 thf(func_def_66, type, c_Unj: $i > $i).
% 48.64/8.23 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i).
% 48.64/8.23 thf(func_def_68, type, c_setsum: $i > $i > $i).
% 48.64/8.23 thf(func_def_69, type, c_proj0: $i > $i).
% 48.64/8.23 thf(func_def_70, type, c_proj1: $i > $i).
% 48.64/8.23 thf(func_def_71, type, c_binrep: $i > $i > $i).
% 48.64/8.23 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i).
% 48.64/8.23 thf(func_def_73, type, c_setprod: $i > $i > $i).
% 48.64/8.23 thf(func_def_74, type, c_ap: $i > $i > $i).
% 48.64/8.23 thf(func_def_75, type, c_setsum_p: $i > $o).
% 48.64/8.23 thf(func_def_76, type, c_tuple_p: $i > $i > $o).
% 48.64/8.23 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i).
% 48.64/8.23 thf(func_def_78, type, c_setexp: $i > $i > $i).
% 48.64/8.23 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i).
% 48.64/8.23 thf(func_def_80, type, c_set_of_pairs: $i > $o).
% 48.64/8.23 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i).
% 48.64/8.23 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o).
% 48.64/8.23 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o).
% 48.64/8.23 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o).
% 48.64/8.23 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o).
% 48.64/8.23 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 48.64/8.23 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 48.64/8.23 thf(func_def_88, type, c_SNoElts_: $i > $i).
% 48.64/8.23 thf(func_def_89, type, c_SNo_: $i > $i > $o).
% 48.64/8.23 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i).
% 48.64/8.23 thf(func_def_91, type, c_SNo: $i > $o).
% 48.64/8.23 thf(func_def_92, type, c_SNoLev: $i > $i).
% 48.64/8.23 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o).
% 48.64/8.23 thf(func_def_94, type, c_SNoLt: $i > $i > $o).
% 48.64/8.23 thf(func_def_95, type, c_SNoLe: $i > $i > $o).
% 48.64/8.23 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o).
% 48.64/8.23 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o).
% 48.64/8.23 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).
% 48.64/8.23 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).
% 48.64/8.23 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).
% 48.64/8.23 thf(func_def_101, type, c_combinator: $i > $o).
% 48.64/8.23 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o).
% 48.64/8.23 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o).
% 48.64/8.23 thf(func_def_133, type, ph1: !>[X0: $tType]:(X0)).
% 48.64/8.23 thf(func_def_135, type, sK3: ((($i > $i) > $i) > $i > $o) > ($i > $i) > $i).
% 48.64/8.23 thf(func_def_136, type, sK4: ((($i > $i) > $i) > $i > $o) > $i > $i).
% 48.64/8.23 thf(func_def_137, type, sK5: ((((($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) > $i).
% 48.64/8.23 thf(func_def_138, type, sK6: (($i > $i) > ($i > $i) > $o) > ((($i > $i) > $i) > $i > $i > $i) > $i).
% 48.64/8.23 thf(func_def_139, type, sK7: (($i > $i) > ($i > $i) > $o) > $i).
% 48.64/8.23 thf(func_def_140, type, sK8: (($i > $i) > ($i > $i) > $o) > $i).
% 48.64/8.23 thf(func_def_141, type, sK9: ((($i > $i) > $i) > $i > $o) > ($i > ($i > $i) > $i) > $i > $i > $i > $i).
% 48.64/8.23 thf(func_def_142, type, sK10: ((((($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 > $i) > $i) > $i > $o) > ((($i > $i) > $i > $i) > ($i > $i) > $i) > $i > ($i > $i) > $i > $i).
% 48.64/8.23 thf(func_def_143, type, sK11: ((((($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) > $i > ($i > $i) > $i > $o) > $i).
% 48.64/8.23 thf(func_def_144, type, sK12: ((((($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) > $i) > ($i > $i > $i) > $i > $i) > $i) > $i > ($i > $i) > $i > $o) > $i).
% 48.64/8.23 thf(func_def_145, type, sK13: ((((($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) > $i > ($i > $i) > $i > $o) > $i).
% 48.64/8.23 thf(func_def_146, type, sK14: ((((($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 > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i) > $i > ($i > $i) > $i > $o) > $i).
% 48.64/8.23 thf(func_def_147, type, sK15: ((((($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) > $i > ($i > $i) > $i > $o) > $i).
% 48.64/8.23 thf(func_def_148, type, sK16: ((((($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) > $i > ($i > $i) > $i > $o) > $i).
% 48.64/8.23 thf(func_def_149, type, sK17: ((((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o) > $i).
% 48.64/8.23 thf(func_def_150, type, sK18: ((((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o) > $i).
% 48.64/8.23 thf(func_def_151, type, sK19: ((((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o) > $i).
% 48.64/8.23 thf(func_def_152, type, sK20: ((((($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) > $i).
% 48.64/8.23 thf(func_def_153, type, sK21: ((((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o) > $i).
% 48.64/8.23 thf(func_def_154, type, sK22: ((((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o) > $i).
% 48.64/8.23 thf(func_def_155, type, sK23: ((((($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).
% 48.64/8.23 thf(f768,plain,(
% 48.64/8.23 $false),
% 48.64/8.23 inference(avatar_sat_refutation,[status(thm)],[f351,f526,f550,f609,f652,f702,f732,f741,f762])).
% 48.64/8.23 thf(f762,plain,(
% 48.64/8.23 ~spl0_7),
% 48.64/8.23 inference(avatar_contradiction_clause,[status(thm)],[f761])).
% 48.64/8.23 thf(f761,plain,(
% 48.64/8.23 $false | ~spl0_7),
% 48.64/8.23 inference(trivial_inequality_removal,[status(thm)],[f760])).
% 48.64/8.23 thf(f760,plain,(
% 48.64/8.23 ($true = $false) | ~spl0_7),
% 48.64/8.23 inference(duplicate_literal_removal,[status(thm)],[f759])).
% 48.64/8.23 thf(f759,plain,(
% 48.64/8.23 ($true = $false) | ($true = $false) | ~spl0_7),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f747])).
% 48.64/8.23 thf(f747,plain,(
% 48.64/8.23 ($false = ((^[Y0 : ($i > $i) > $i]: ((^[Y1 : $i]: ($true)))) @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y0 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK3 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i]: ($true)))) @ (^[Y1 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty)) | ($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1))) @ (c_Inj1 @ c_Empty))) | ~spl0_7),
% 48.64/8.23 inference(primitive_instantiation,[status(thm)],[f578])).
% 48.64/8.23 thf(f578,plain,(
% 48.64/8.23 ( ! [X4 : (($i > $i) > $i) > $i > $o] : (($false = (X4 @ (^[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))) | ((X4 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y0 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty) = $false)) ) | ~spl0_7),
% 48.64/8.23 inference(avatar_component_clause,[status(thm)],[f577])).
% 48.64/8.23 thf(f577,definition,(
% 48.64/8.23 spl0_7 <=> ! [X4 : (($i > $i) > $i) > $i > $o] : (($false = (X4 @ (^[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))) | ((X4 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y0 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty) = $false))),
% 48.64/8.23 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 48.64/8.23 thf(f741,plain,(
% 48.64/8.23 spl0_7 | ~spl0_10),
% 48.64/8.23 inference(avatar_split_clause,[status(thm)],[f739,f607,f577])).
% 48.64/8.23 thf(f607,definition,(
% 48.64/8.23 spl0_10 <=> ! [X4 : (($i > $i) > $i) > $i > $o] : (($false = (X4 @ (^[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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1))) @ (c_Inj1 @ c_Empty))) | ((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false))),
% 48.64/8.23 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 48.64/8.23 thf(f739,plain,(
% 48.64/8.23 ( ! [X4 : (($i > $i) > $i) > $i > $o] : (((X4 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y0 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty) = $false) | ($false = (X4 @ (^[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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1))) @ (c_Inj1 @ c_Empty)))) ) | ~spl0_10),
% 48.64/8.23 inference(binary_proxy_clausification,[status(thm)],[f737])).
% 48.64/8.23 thf(f737,plain,(
% 48.64/8.23 ( ! [X4 : (($i > $i) > $i) > $i > $o] : (($false = ((X4 @ (^[Y0 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y0 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y0 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))) | ($false = (X4 @ (^[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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1))) @ (c_Inj1 @ c_Empty)))) ) | ~spl0_10),
% 48.64/8.23 inference(binary_proxy_clausification,[status(thm)],[f736])).
% 48.64/8.23 thf(f736,plain,(
% 48.64/8.23 ( ! [X4 : (($i > $i) > $i) > $i > $o] : (($false = (X4 @ (^[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 = ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (sK9 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y0 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y0 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y0 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) ) | ~spl0_10),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f735])).
% 48.64/8.23 thf(f735,plain,(
% 48.64/8.23 ( ! [X4 : (($i > $i) > $i) > $i > $o] : (($false = (X4 @ (^[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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1))) @ (c_Inj1 @ c_Empty))) | (((^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty)))) @ (sK9 @ X4)) = $false)) ) | ~spl0_10),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f608])).
% 48.64/8.23 thf(f608,plain,(
% 48.64/8.23 ( ! [X4 : (($i > $i) > $i) > $i > $o] : (((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ($false = (X4 @ (^[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)))) ) | ~spl0_10),
% 48.64/8.23 inference(avatar_component_clause,[status(thm)],[f607])).
% 48.64/8.23 thf(f732,plain,(
% 48.64/8.23 ~spl0_12),
% 48.64/8.23 inference(avatar_contradiction_clause,[status(thm)],[f731])).
% 48.64/8.23 thf(f731,plain,(
% 48.64/8.23 $false | ~spl0_12),
% 48.64/8.23 inference(trivial_inequality_removal,[status(thm)],[f730])).
% 48.64/8.23 thf(f730,plain,(
% 48.64/8.23 ($true = $false) | ~spl0_12),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f729])).
% 48.64/8.23 thf(f729,plain,(
% 48.64/8.23 ($false = ((^[Y0 : $i]: ($true)) @ sK26)) | ~spl0_12),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f728])).
% 48.64/8.23 thf(f728,plain,(
% 48.64/8.23 ((!! @ $i @ (^[Y0 : $i]: ($true))) = $false) | ~spl0_12),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f727])).
% 48.64/8.23 thf(f727,plain,(
% 48.64/8.23 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true)))) @ sK25) = $false) | ~spl0_12),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f726])).
% 48.64/8.23 thf(f726,plain,(
% 48.64/8.23 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true)))))) | ~spl0_12),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f725])).
% 48.64/8.23 thf(f725,plain,(
% 48.64/8.23 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ($true)))))) @ sK24) = $false) | ~spl0_12),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f651])).
% 48.64/8.23 thf(f651,plain,(
% 48.64/8.23 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ($true)))))))) | ~spl0_12),
% 48.64/8.23 inference(avatar_component_clause,[status(thm)],[f649])).
% 48.64/8.23 thf(f649,definition,(
% 48.64/8.23 spl0_12 <=> ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ($true))))))))),
% 48.64/8.23 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 48.64/8.23 thf(f702,plain,(
% 48.64/8.23 spl0_12 | ~spl0_11),
% 48.64/8.23 inference(avatar_split_clause,[status(thm)],[f699,f646,f649])).
% 48.64/8.23 thf(f646,definition,(
% 48.64/8.23 spl0_11 <=> ! [X3 : (((($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false))),
% 48.64/8.23 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 48.64/8.23 thf(f699,plain,(
% 48.64/8.23 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ($true)))))))) | ~spl0_11),
% 48.64/8.23 inference(boolean_simplification,[status(thm)],[f698])).
% 48.64/8.23 thf(f698,plain,(
% 48.64/8.23 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => $true))))))) = $false) | ~spl0_11),
% 48.64/8.23 inference(boolean_simplification,[status(thm)],[f697])).
% 48.64/8.23 thf(f697,plain,(
% 48.64/8.23 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ $false)))))))) = $false) | ~spl0_11),
% 48.64/8.23 inference(trivial_inequality_removal,[status(thm)],[f696])).
% 48.64/8.23 thf(f696,plain,(
% 48.64/8.23 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ $false)))))))) = $false) | ($true = $false) | ~spl0_11),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f689])).
% 48.64/8.23 thf(f689,plain,(
% 48.64/8.23 ($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 > $i]: (c_Inj1 @ (sK19 @ (^[Y1 : ((($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 @ (sK18 @ (^[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 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (sK20 @ (^[Y0 : ((($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 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (sK19 @ (^[Y0 : ((($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]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ ((^[Y3 : ((($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 > $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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false) | ~spl0_11),
% 48.64/8.23 inference(primitive_instantiation,[status(thm)],[f675])).
% 48.64/8.23 thf(f675,plain,(
% 48.64/8.23 ( ! [X3 : (((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o] : (((X3 @ (^[Y0 : (($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 @ (sK19 @ X3))) @ (c_Repl @ (sK18 @ X3) @ 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 @ (sK20 @ X3 @ (^[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 @ (sK19 @ X3) @ c_Inj1)) @ c_Inj1)) @ c_Inj1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(binary_proxy_clausification,[status(thm)],[f673])).
% 48.64/8.23 thf(f673,plain,(
% 48.64/8.23 ( ! [X3 : (((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o] : ((((X3 @ (^[Y0 : (($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 @ (sK19 @ X3))) @ (c_Repl @ (sK18 @ X3) @ 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 @ (sK20 @ X3 @ (^[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 @ (sK19 @ X3) @ c_Inj1)) @ c_Inj1)) @ c_Inj1))) => (c_In @ (sK17 @ X3) @ (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) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f672])).
% 48.64/8.23 thf(f672,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false) | (((^[Y0 : ($i > $i) > $i]: ((X3 @ (^[Y1 : (($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 @ (sK19 @ X3))) @ (c_Repl @ (sK18 @ X3) @ 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 @ (Y0 @ (^[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 @ (sK19 @ X3) @ c_Inj1)) @ c_Inj1)) @ c_Inj1))) => (c_In @ (sK17 @ X3) @ (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))))) @ (sK20 @ X3)) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f671])).
% 48.64/8.23 thf(f671,plain,(
% 48.64/8.23 ( ! [X3 : (((($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) > $i) @ (^[Y0 : ($i > $i) > $i]: ((X3 @ (^[Y1 : (($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 @ (sK19 @ X3))) @ (c_Repl @ (sK18 @ X3) @ 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 @ (Y0 @ (^[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 @ (sK19 @ X3) @ c_Inj1)) @ c_Inj1)) @ c_Inj1))) => (c_In @ (sK17 @ X3) @ (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]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f670])).
% 48.64/8.23 thf(f670,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false) | ($false = ((^[Y0 : $i]: (!! @ (($i > $i) > $i) @ (^[Y1 : ($i > $i) > $i]: ((X3 @ (^[Y2 : (($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 @ (sK18 @ X3) @ 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 @ (Y1 @ (^[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 @ (sK17 @ X3) @ (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 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) @ c_Inj1))))))) @ (sK19 @ X3)))) ) | ~spl0_11),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f663])).
% 48.64/8.23 thf(f663,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 > $i) > $i) @ (^[Y1 : ($i > $i) > $i]: ((X3 @ (^[Y2 : (($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 @ (sK18 @ X3) @ 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 @ (Y1 @ (^[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 @ (sK17 @ X3) @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f662])).
% 48.64/8.23 thf(f662,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 @ (^[Y1 : $i]: (!! @ (($i > $i) > $i) @ (^[Y2 : ($i > $i) > $i]: ((X3 @ (^[Y3 : (($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 @ (Y2 @ (^[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 @ (sK17 @ X3) @ (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))))))))) @ (sK18 @ X3)) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f661])).
% 48.64/8.23 thf(f661,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 > $i) > $i) @ (^[Y2 : ($i > $i) > $i]: ((X3 @ (^[Y3 : (($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 @ (Y2 @ (^[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 @ (sK17 @ X3) @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f660])).
% 48.64/8.23 thf(f660,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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))))))))))) @ (sK17 @ X3)) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f647])).
% 48.64/8.23 thf(f647,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false)) ) | ~spl0_11),
% 48.64/8.23 inference(avatar_component_clause,[status(thm)],[f646])).
% 48.64/8.23 thf(f652,plain,(
% 48.64/8.23 spl0_11 | spl0_12 | ~spl0_9),
% 48.64/8.23 inference(avatar_split_clause,[status(thm)],[f634,f604,f649,f646])).
% 48.64/8.23 thf(f604,definition,(
% 48.64/8.23 spl0_9 <=> ! [X1 : ((((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i) > $i > ($i > $i) > $i > $o,X3 : (((($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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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))))))))))) = $false))),
% 48.64/8.23 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 48.64/8.23 thf(f634,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => (~ (X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ($true)))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(boolean_simplification,[status(thm)],[f633])).
% 48.64/8.23 thf(f633,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ($true)))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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) => $false)))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(boolean_simplification,[status(thm)],[f632])).
% 48.64/8.23 thf(f632,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => $true)))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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) => $false)))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(boolean_simplification,[status(thm)],[f631])).
% 48.64/8.23 thf(f631,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ($false => (X3 @ (^[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) @ Y0))))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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) => $false)))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(trivial_inequality_removal,[status(thm)],[f630])).
% 48.64/8.23 thf(f630,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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) => $false)))))))) = $false) | ($true = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ($false => (X3 @ (^[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) @ Y0))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f628])).
% 48.64/8.23 thf(f628,plain,(
% 48.64/8.23 ( ! [X3 : (((($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]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: ($false)))))))) @ (^[Y0 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (sK13 @ X3 @ (^[Y1 : (((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ($false))))))))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ (^[Y1 : (((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ($false))))))))) @ c_Inj1))) @ c_Empty @ (^[Y0 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ (^[Y1 : (((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ($false))))))))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) @ c_Empty) => ((^[Y3 : (((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: ((^[Y6 : $i]: ($false)))))))) @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => (((^[Y3 : (((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: ((^[Y6 : $i]: ($false)))))))) @ (^[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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(primitive_instantiation,[status(thm)],[f619])).
% 48.64/8.23 thf(f619,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($true = (X1 @ (^[Y0 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (sK13 @ X3 @ X1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (^[Y0 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ X1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0))))))))))) ) | ~spl0_9),
% 48.64/8.23 inference(binary_proxy_clausification,[status(thm)],[f616])).
% 48.64/8.23 thf(f616,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0)))))))))) | (((X1 @ (^[Y0 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (sK13 @ X3 @ X1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (^[Y0 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ X1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y0 : (($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_binunion @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1)) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ c_Inj1))))) @ (^[Y0 : $i]: ((^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : ($i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (c_Inj1 @ (Y0 @ (^[Y1 : $i]: (sK11 @ X3 @ X1)) @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1) @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (sK14 @ X3 @ X1) @ c_Inj1)) @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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_Inj1)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(binary_proxy_clausification,[status(thm)],[f615])).
% 48.64/8.23 thf(f615,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 > $o] : (($false = ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y0 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (sK13 @ X3 @ X1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (^[Y0 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ X1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y0 : (($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_binunion @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1)) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ c_Inj1))))) @ (^[Y0 : $i]: ((^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : ($i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (c_Inj1 @ (Y0 @ (^[Y1 : $i]: (sK11 @ X3 @ X1)) @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1) @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (sK14 @ X3 @ X1) @ c_Inj1)) @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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_Inj1)))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f614])).
% 48.64/8.23 thf(f614,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = ((^[Y0 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y1 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (sK13 @ X3 @ X1) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (^[Y1 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ X1) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y1 : (($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_binunion @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1)) @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ c_Inj1))))) @ (^[Y1 : $i]: ((^[Y2 : ($i > $i) > $i]: ((^[Y3 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty))))))) @ (^[Y1 : ($i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (c_Inj1 @ (Y1 @ (^[Y2 : $i]: (sK11 @ X3 @ X1)) @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1)))))) @ (sK14 @ X3 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0))))))))))) ) | ~spl0_9),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f613])).
% 48.64/8.23 thf(f613,plain,(
% 48.64/8.23 ( ! [X3 : (((($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]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y1 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (sK13 @ X3 @ X1) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (^[Y1 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ X1) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y1 : (($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_binunion @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1)) @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ c_Inj1))))) @ (^[Y1 : $i]: ((^[Y2 : ($i > $i) > $i]: ((^[Y3 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty))))))) @ (^[Y1 : ($i > $i) > $i > $i]: (c_binunion @ (c_Repl @ (c_Inj1 @ (Y1 @ (^[Y2 : $i]: (sK11 @ X3 @ X1)) @ (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 @ (sK13 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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_Inj1))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f612])).
% 48.64/8.23 thf(f612,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y2 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (^[Y2 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ X1) @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y2 : (($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 @ Y0 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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 @ Y0 @ 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 @ Y1 @ 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 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1)))))))) @ (sK13 @ X3 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f611])).
% 48.64/8.23 thf(f611,plain,(
% 48.64/8.23 ( ! [X3 : (((($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]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y2 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK12 @ X3 @ X1) @ c_Inj1))) @ c_Empty @ (^[Y2 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ (sK12 @ X3 @ X1) @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y2 : (($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 @ Y0 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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 @ Y0 @ 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 @ Y1 @ 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]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0))))))))))) ) | ~spl0_9),
% 48.64/8.23 inference(beta_eta_normalization,[status(thm)],[f610])).
% 48.64/8.23 thf(f610,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1)))))))))) @ (sK12 @ X3 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(sigma_clausification,[status(thm)],[f605])).
% 48.64/8.23 thf(f605,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false)) ) | ~spl0_9),
% 48.64/8.23 inference(avatar_component_clause,[status(thm)],[f604])).
% 48.64/8.23 thf(f609,plain,(
% 48.64/8.23 spl0_9 | spl0_10 | ~spl0_1),
% 48.64/8.23 inference(avatar_split_clause,[status(thm)],[f601,f346,f607,f604])).
% 48.64/8.23 thf(f346,definition,(
% 48.64/8.23 spl0_1 <=> ! [X4 : (($i > $i) > $i) > $i > $o,X1 : ((((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i) > $i > ($i > $i) > $i > $o,X3 : (((($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 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false))),
% 48.64/8.23 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 48.64/8.23 thf(f601,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (($false = (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false)) ) | ~spl0_1),
% 48.64/8.23 inference(binary_proxy_clausification,[status(thm)],[f599])).
% 48.64/8.23 thf(f599,plain,(
% 48.64/8.23 ( ! [X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : ((((X3 @ (^[Y0 : (($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 : $i]: (c_binunion @ (c_Repl @ (sK10 @ X3 @ X4 @ (^[Y2 : ($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 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ (sK10 @ X3 @ X4 @ (^[Y0 : ($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) => (X4 @ (^[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 > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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))))))))))) = $false)) ) | ~spl0_1),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f598])).
% 48.64/8.24 thf(f598,plain,(
% 48.64/8.24 ( ! [X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($false = ((c_In @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Repl @ (sK10 @ X3 @ X4 @ (^[Y0 : ($i > $i) > $i > $i]: ((^[Y1 : $i > $i]: (c_Empty)))) @ c_Empty @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ c_Inj1) @ (^[Y0 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y0 : (($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 : $i]: (c_binunion @ (c_Repl @ (sK10 @ X3 @ X4 @ (^[Y2 : ($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 : $i]: (c_Repl @ Y0 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ (sK10 @ X3 @ X4 @ (^[Y0 : ($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) => (X4 @ (^[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))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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))))))))))) = $false)) ) | ~spl0_1),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f597])).
% 48.64/8.24 thf(f597,plain,(
% 48.64/8.24 ( ! [X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0)))))))))) | ($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1))) @ (c_Inj1 @ c_Empty))))) @ (sK10 @ X3 @ X4))) | ((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false)) ) | ~spl0_1),
% 48.64/8.24 inference(sigma_clausification,[status(thm)],[f592])).
% 48.64/8.24 thf(f592,plain,(
% 48.64/8.24 ( ! [X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ (((($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y3 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y1 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1))) @ c_Empty @ (^[Y3 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y0 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y3 : (($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 @ Y1 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ (sK11 @ X3 @ X1) @ 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]: (sK11 @ X3 @ X1)) @ (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))) @ 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 @ Y2 @ 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))))))))))) = $false) | ((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false)) ) | ~spl0_1),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f591])).
% 48.64/8.24 thf(f591,plain,(
% 48.64/8.24 ( ! [X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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)))))))))))) @ (sK11 @ X3 @ X1)) = $false) | ((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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) > $i > ($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false)) ) | ~spl0_1),
% 48.64/8.24 inference(sigma_clausification,[status(thm)],[f347])).
% 48.64/8.24 thf(f347,plain,(
% 48.64/8.24 ( ! [X3 : (((($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 > $o,X4 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)) ) | ~spl0_1),
% 48.64/8.24 inference(avatar_component_clause,[status(thm)],[f346])).
% 48.64/8.24 thf(f550,plain,(
% 48.64/8.24 ~spl0_3),
% 48.64/8.24 inference(avatar_contradiction_clause,[status(thm)],[f549])).
% 48.64/8.24 thf(f549,plain,(
% 48.64/8.24 $false | ~spl0_3),
% 48.64/8.24 inference(trivial_inequality_removal,[status(thm)],[f548])).
% 48.64/8.24 thf(f548,plain,(
% 48.64/8.24 ($true = $false) | ~spl0_3),
% 48.64/8.24 inference(boolean_simplification,[status(thm)],[f547])).
% 48.64/8.24 thf(f547,plain,(
% 48.64/8.24 ((~ $true) = $true) | ~spl0_3),
% 48.64/8.24 inference(forward_demodulation,[status(thm)],[f539,f433])).
% 48.64/8.24 thf(f433,plain,(
% 48.64/8.24 ( ! [X0 : ($i > $i) > ($i > $i) > $o] : (($true = (X0 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_3),
% 48.64/8.24 inference(avatar_component_clause,[status(thm)],[f432])).
% 48.64/8.24 thf(f432,definition,(
% 48.64/8.24 spl0_3 <=> ! [X0 : ($i > $i) > ($i > $i) > $o] : ($true = (X0 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))),
% 48.64/8.24 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 48.64/8.24 thf(f539,plain,(
% 48.64/8.24 ( ! [X3 : ($i > $i) > ($i > $i) > $o] : (($true = (~ (X3 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))) ) | ~spl0_3),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f533])).
% 48.64/8.24 thf(f533,plain,(
% 48.64/8.24 ( ! [X3 : ($i > $i) > ($i > $i) > $o] : ((((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (~ (X3 @ Y0 @ Y1))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))) = $true)) ) | ~spl0_3),
% 48.64/8.24 inference(primitive_instantiation,[status(thm)],[f433])).
% 48.64/8.24 thf(f526,plain,(
% 48.64/8.24 spl0_3 | ~spl0_2),
% 48.64/8.24 inference(avatar_split_clause,[status(thm)],[f523,f349,f432])).
% 48.64/8.24 thf(f349,definition,(
% 48.64/8.24 spl0_2 <=> ! [X2 : ($i > $i) > ($i > $i) > $o] : (($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty)))) | ($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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1))))))))))))),
% 48.64/8.24 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 48.64/8.24 thf(f523,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(trivial_inequality_removal,[status(thm)],[f521])).
% 48.64/8.24 thf(f521,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (($true = $false) | ($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(backward_demodulation,[status(thm)],[f425,f441])).
% 48.64/8.24 thf(f441,plain,(
% 48.64/8.24 ( ! [X0 : $i,X1 : $i] : (((c_In @ X1 @ X0) = $false)) ) | ~spl0_2),
% 48.64/8.24 inference(superposition,[status(thm)],[f316,f428])).
% 48.64/8.24 thf(f428,plain,(
% 48.64/8.24 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | ~spl0_2),
% 48.64/8.24 inference(superposition,[status(thm)],[f379,f379])).
% 48.64/8.24 thf(f379,plain,(
% 48.64/8.24 ( ! [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)) ) | ~spl0_2),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f378])).
% 48.64/8.24 thf(f378,plain,(
% 48.64/8.24 ( ! [X1 : $i] : ((((^[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) = ((^[Y0 : $i]: (Y0)) @ X1))) ) | ~spl0_2),
% 48.64/8.24 inference(argument_congruence,[status(thm)],[f375])).
% 48.64/8.24 thf(f375,plain,(
% 48.64/8.24 ((^[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))))) | ~spl0_2),
% 48.64/8.24 inference(equality_proxy_clausification,[status(thm)],[f374])).
% 48.64/8.24 thf(f374,plain,(
% 48.64/8.24 (((^[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)))) = (^[Y0 : $i]: (Y0))) = $true) | ~spl0_2),
% 48.64/8.24 inference(not_proxy_clausification,[status(thm)],[f366])).
% 48.64/8.24 thf(f366,plain,(
% 48.64/8.24 ($false = (~ ((^[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)))) = (^[Y0 : $i]: (Y0))))) | ~spl0_2),
% 48.64/8.24 inference(trivial_inequality_removal,[status(thm)],[f365])).
% 48.64/8.24 thf(f365,plain,(
% 48.64/8.24 ($true = $false) | ($false = (~ ((^[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)))) = (^[Y0 : $i]: (Y0))))) | ~spl0_2),
% 48.64/8.24 inference(boolean_simplification,[status(thm)],[f364])).
% 48.64/8.24 thf(f364,plain,(
% 48.64/8.24 ($false = (~ ((^[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)))) = (^[Y0 : $i]: (Y0))))) | ((~ $true) = $true) | ~spl0_2),
% 48.64/8.24 inference(boolean_simplification,[status(thm)],[f363])).
% 48.64/8.24 thf(f363,plain,(
% 48.64/8.24 ($false = (~ ((^[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)))) = (^[Y0 : $i]: (Y0))))) | ((~ ((^[Y0 : $i]: (c_Empty)) = (^[Y0 : $i]: (c_Empty)))) = $true) | ~spl0_2),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f359])).
% 48.64/8.24 thf(f359,plain,(
% 48.64/8.24 (((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (~ (Y1 = Y0))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))) = $true) | (((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (~ (Y1 = Y0))))) @ (^[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))))) = $false) | ~spl0_2),
% 48.64/8.24 inference(primitive_instantiation,[status(thm)],[f356])).
% 48.64/8.24 thf(f356,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (($false = (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 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f355])).
% 48.64/8.24 thf(f355,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (($false = ((c_In @ (sK7 @ X2) @ (sK6 @ X2 @ (^[Y0 : ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (sK7 @ 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 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f354])).
% 48.64/8.24 thf(f354,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty)))) | ($false = ((^[Y0 : $i]: ((c_In @ Y0 @ (sK6 @ X2 @ (^[Y1 : ($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 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1))))))) @ (sK7 @ X2)))) ) | ~spl0_2),
% 48.64/8.24 inference(sigma_clausification,[status(thm)],[f353])).
% 48.64/8.24 thf(f353,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (sK6 @ X2 @ (^[Y1 : ($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 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1))))))))) | ($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f352])).
% 48.64/8.24 thf(f352,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (($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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1))))))))) @ (sK6 @ X2))) | ($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(sigma_clausification,[status(thm)],[f350])).
% 48.64/8.24 thf(f350,plain,(
% 48.64/8.24 ( ! [X2 : ($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 = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(avatar_component_clause,[status(thm)],[f349])).
% 48.64/8.24 thf(f316,plain,(
% 48.64/8.24 ( ! [X1 : $i] : (((c_In @ X1 @ c_Empty) = $false)) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f315])).
% 48.64/8.24 thf(f315,plain,(
% 48.64/8.24 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X1))) )),
% 48.64/8.24 inference(pi_clausification,[status(thm)],[f314])).
% 48.64/8.24 thf(f314,plain,(
% 48.64/8.24 ($false = (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))),
% 48.64/8.24 inference(not_proxy_clausification,[status(thm)],[f313])).
% 48.64/8.24 thf(f313,plain,(
% 48.64/8.24 ($true = (~ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 48.64/8.24 inference(boolean_simplification,[status(thm)],[f310])).
% 48.64/8.24 thf(f310,plain,(
% 48.64/8.24 (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => $false) = $true)),
% 48.64/8.24 inference(backward_demodulation,[status(thm)],[f305,f308])).
% 48.64/8.24 thf(f308,plain,(
% 48.64/8.24 ((!! @ $o @ (^[Y0 : $o]: (Y0))) = $false)),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f307])).
% 48.64/8.24 thf(f307,plain,(
% 48.64/8.24 (((!! @ (((((($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) > $i) > ($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 > $o) @ (^[Y3 : (($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 : $i]: (c_Empty))) => (Y2 @ (^[Y5 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y5) @ Y6) => ((Y2 @ (^[Y7 : (($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 @ Y6 @ (^[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 @ Y6 @ (^[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]: (Y6)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y4 @ 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 @ Y6 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1)) @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y6 @ 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 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((Y0 @ (^[Y8 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y6 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1))) @ c_Empty @ (^[Y8 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y2 @ (^[Y8 : (($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 @ Y6 @ c_Inj1)) @ (^[Y10 : $i]: (c_Repl @ Y10 @ c_Inj1))) @ (c_Repl @ Y4 @ 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]: (Y4)) @ (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))) @ 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 @ Y7 @ 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 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y2 @ (^[Y5 : (($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) => (Y3 @ (^[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)) => ((Y3 @ (^[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))) => (Y3 @ (^[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 : $i]: ((c_In @ Y6 @ (c_Repl @ c_Empty @ c_Inj1)) => ((Y0 @ (^[Y7 : ((($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 @ Y4 @ c_Inj1) @ (^[Y7 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y7 @ c_Inj1))) @ c_Empty) => (Y2 @ (^[Y7 : (($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) @ Y4))))))))) => ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ (($i > $i) > $i) @ (^[Y7 : ($i > $i) > $i]: ((Y2 @ (^[Y8 : (($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 @ (Y7 @ (^[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 @ Y4 @ (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)))))))))))) => (!! @ $o @ (^[Y4 : $o]: (Y4))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $false)),
% 48.64/8.24 inference(not_proxy_clausification,[status(thm)],[f306])).
% 48.64/8.24 thf(f306,plain,(
% 48.64/8.24 ((~ ((!! @ (((((($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) > $i) > ($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 > $o) @ (^[Y3 : (($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 : $i]: (c_Empty))) => (Y2 @ (^[Y5 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y5) @ Y6) => ((Y2 @ (^[Y7 : (($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 @ Y6 @ (^[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 @ Y6 @ (^[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]: (Y6)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y4 @ 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 @ Y6 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1)) @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y6 @ 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 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((Y0 @ (^[Y8 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y6 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1))) @ c_Empty @ (^[Y8 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y2 @ (^[Y8 : (($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 @ Y6 @ c_Inj1)) @ (^[Y10 : $i]: (c_Repl @ Y10 @ c_Inj1))) @ (c_Repl @ Y4 @ 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]: (Y4)) @ (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))) @ 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 @ Y7 @ 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 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y2 @ (^[Y5 : (($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) => (Y3 @ (^[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)) => ((Y3 @ (^[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))) => (Y3 @ (^[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 : $i]: ((c_In @ Y6 @ (c_Repl @ c_Empty @ c_Inj1)) => ((Y0 @ (^[Y7 : ((($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 @ Y4 @ c_Inj1) @ (^[Y7 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y7 @ c_Inj1))) @ c_Empty) => (Y2 @ (^[Y7 : (($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) @ Y4))))))))) => ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ (($i > $i) > $i) @ (^[Y7 : ($i > $i) > $i]: ((Y2 @ (^[Y8 : (($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 @ (Y7 @ (^[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 @ Y4 @ (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)))))))))))) => (!! @ $o @ (^[Y4 : $o]: (Y4))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0))))) = $true)),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f301])).
% 48.64/8.24 thf(f301,plain,(
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@ $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 : $i]: (c_Empty))) => (Y2 @ (^[Y5 : (($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)))))) => ((!! 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@ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ (($i > $i) > $i) @ (^[Y7 : ($i > $i) > $i]: ((Y2 @ (^[Y8 : (($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))))))) @ (Y7 @ (^[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 @ 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_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))))))))))))) => (!! @ $o @ (^[Y4 : $o]: (Y4))))))))))))))))))))) = $true)),
% 48.64/8.24 inference(definition_unfolding,[status(thm)],[f294,f299,f298,f298,f298,f298,f298,f298,f290,f290,f298,f298,f298,f298,f290,f298,f298,f290,f298,f298,f298,f290,f298,f290,f298,f298,f298,f298,f298,f290,f290,f298,f290,f298,f298,f298,f298,f298,f298,f298,f298,f298,f290,f290,f290,f298,f298,f290,f298,f290,f298,f290,f290,f298,f298,f298,f290,f298,f298,f298,f298,f298,f298,f298,f298,f290,f298,f298,f298,f298,f298,f290,f298,f298,f298,f290,f290,f290,f298,f298,f290,f290,f298,f298,f298,f290,f298,f290,f298,f298,f290,f298,f290,f298,f290,f290,f298,f290,f298,f298,f298,f298,f298,f298,f298,f290,f298,f290,f289])).
% 48.64/8.24 thf(f289,plain,(
% 48.64/8.24 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 48.64/8.24 inference(cnf_transformation,[status(thm)],[f158])).
% 48.64/8.24 thf(f158,plain,(
% 48.64/8.24 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 48.64/8.24 inference(fool_elimination,[status(thm)],[f157])).
% 48.64/8.24 thf(f157,plain,(
% 48.64/8.24 (c_False = ! [X0 : $o] : X0)),
% 48.64/8.24 inference(rectify,[status(thm)],[f11])).
% 48.64/8.24 thf(f11,axiom,(
% 48.64/8.24 (c_False = ! [X0 : $o] : X0)),
% 48.64/8.24 file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax11)).
% 48.64/8.24 thf(f290,plain,(
% 48.64/8.24 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 48.64/8.24 inference(cnf_transformation,[status(thm)],[f125])).
% 48.64/8.24 thf(f125,plain,(
% 48.64/8.24 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 48.64/8.24 inference(fool_elimination,[status(thm)],[f70])).
% 48.64/8.24 thf(f70,axiom,(
% 48.64/8.24 ((^[X0 : $i] : (c_Repl @ X0 @ (^[X1 : $i] : (c_Inj1 @ X1)))) = c_Inj0)),
% 48.64/8.24 file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax70)).
% 48.64/8.24 thf(f298,plain,(
% 48.64/8.24 (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))))))))),
% 48.64/8.24 inference(definition_unfolding,[status(thm)],[f297,f290])).
% 48.64/8.24 thf(f297,plain,(
% 48.64/8.24 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 48.64/8.24 inference(cnf_transformation,[status(thm)],[f179])).
% 48.64/8.24 thf(f179,plain,(
% 48.64/8.24 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 48.64/8.24 inference(fool_elimination,[status(thm)],[f178])).
% 48.64/8.24 thf(f178,plain,(
% 48.64/8.24 ((^[X0 : $i, X1 : $i] : (c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : (c_Inj0 @ X2))) @ (c_Repl @ X1 @ (^[X3 : $i] : (c_Inj1 @ X3))))) = c_setsum)),
% 48.64/8.24 inference(rectify,[status(thm)],[f73])).
% 48.64/8.24 thf(f73,axiom,(
% 48.64/8.24 ((^[X0 : $i, X1 : $i] : (c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : (c_Inj0 @ X2))) @ (c_Repl @ X1 @ (^[X2 : $i] : (c_Inj1 @ X2))))) = c_setsum)),
% 48.64/8.24 file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax73)).
% 48.64/8.24 thf(f299,plain,(
% 48.64/8.24 (c_not = (^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))))),
% 48.64/8.24 inference(definition_unfolding,[status(thm)],[f291,f289])).
% 48.64/8.24 thf(f291,plain,(
% 48.64/8.24 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 48.64/8.24 inference(cnf_transformation,[status(thm)],[f155])).
% 48.64/8.24 thf(f155,plain,(
% 48.64/8.24 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 48.64/8.24 inference(fool_elimination,[status(thm)],[f154])).
% 48.64/8.24 thf(f154,plain,(
% 48.64/8.24 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 48.64/8.24 inference(rectify,[status(thm)],[f13])).
% 48.64/8.24 thf(f13,axiom,(
% 48.64/8.24 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 48.64/8.24 file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax13)).
% 48.64/8.24 thf(f294,plain,(
% 48.64/8.24 ($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) > $i) > ($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 > $o) @ (^[Y3 : (($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 : $i]: (c_Empty))) => (Y2 @ (^[Y5 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y5) @ Y6) => ((Y2 @ (^[Y7 : (($i > $i > $i) > $i) > $i]: ((^[Y8 : $i > ($i > $i) > $i]: (c_Empty)))) @ (^[Y7 : $i]: ((^[Y8 : ($i > $i) > $i]: ((^[Y9 : $i]: (c_Inj1 @ (c_setsum @ (c_setsum @ Y6 @ (c_Inj0 @ c_Empty)) @ c_Empty))))))) @ (^[Y7 : ($i > $i) > $i > $i]: (c_Empty)) @ (c_setsum @ c_Empty @ (c_setsum @ Y6 @ (c_setsum @ (c_Inj0 @ c_Empty) @ Y5))) @ c_Empty) => (Y0 @ (^[Y7 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (Y6)) @ (c_Inj1 @ (c_setsum @ (c_Inj0 @ Y4) @ c_Empty)) @ (^[Y7 : $i]: (c_setsum @ (c_setsum @ (c_setsum @ Y6 @ Y5) @ Y6) @ (c_setsum @ c_Empty @ c_Empty))) @ c_Empty))))))))) => ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ (c_setsum @ c_Empty @ Y4) @ (c_Inj0 @ (c_Inj0 @ c_Empty))) => ((Y0 @ (^[Y8 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_setsum @ Y6 @ Y5)) @ c_Empty @ (^[Y8 : $i]: (c_Inj0 @ (c_setsum @ Y5 @ c_Empty))) @ c_Empty) => (Y2 @ (^[Y8 : (($i > $i > $i) > $i) > $i]: ((^[Y9 : $i > ($i > $i) > $i]: (c_setsum @ c_Empty @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ Y6) @ Y4))))) @ (^[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 : $i]: (Y4)) @ (c_setsum @ c_Empty @ c_Empty))) @ Y6)) @ c_Empty @ (c_setsum @ (c_setsum @ (c_Inj0 @ (c_Inj0 @ c_Empty)) @ Y7) @ (c_Inj0 @ (c_setsum @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))))))))))))))) => ((!! @ (((($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 : $i]: (c_Empty)) @ c_Empty)) @ c_Empty))) => ((Y2 @ (^[Y5 : (($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) => (Y3 @ (^[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))))) => ((Y3 @ (^[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))))) => (Y3 @ (^[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 : $i]: ((c_In @ Y6 @ (c_Inj0 @ c_Empty)) => ((Y0 @ (^[Y7 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_setsum @ c_Empty @ Y5)) @ (c_Inj0 @ Y4) @ (^[Y7 : $i]: (c_setsum @ c_Empty @ Y7)) @ c_Empty) => (Y2 @ (^[Y7 : (($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) @ Y4))))))))) => ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ (($i > $i) > $i) @ (^[Y7 : ($i > $i) > $i]: ((Y2 @ (^[Y8 : (($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 @ (Y7 @ (^[Y8 : $i]: (c_Empty))) @ c_Empty) @ (c_setsum @ c_Empty @ Y6)))) => (c_In @ Y4 @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ (c_setsum @ (c_setsum @ (c_Inj0 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ c_Empty))))))))))))) => c_False)))))))))))))))))))),
% 48.64/8.24 inference(cnf_transformation,[status(thm)],[f278])).
% 48.64/8.24 thf(f278,plain,(
% 48.64/8.24 ($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) > $i) > ($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 > $o) @ (^[Y3 : (($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 : $i]: (c_Empty))) => (Y2 @ (^[Y5 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y5) @ Y6) => ((Y2 @ (^[Y7 : (($i > $i > $i) > $i) > $i]: ((^[Y8 : $i > ($i > $i) > $i]: (c_Empty)))) @ (^[Y7 : $i]: ((^[Y8 : ($i > $i) > $i]: ((^[Y9 : $i]: (c_Inj1 @ (c_setsum @ (c_setsum @ Y6 @ (c_Inj0 @ c_Empty)) @ c_Empty))))))) @ (^[Y7 : ($i > $i) > $i > $i]: (c_Empty)) @ (c_setsum @ c_Empty @ (c_setsum @ Y6 @ (c_setsum @ (c_Inj0 @ c_Empty) @ Y5))) @ c_Empty) => (Y0 @ (^[Y7 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (Y6)) @ (c_Inj1 @ (c_setsum @ (c_Inj0 @ Y4) @ c_Empty)) @ (^[Y7 : $i]: (c_setsum @ (c_setsum @ (c_setsum @ Y6 @ Y5) @ Y6) @ (c_setsum @ c_Empty @ c_Empty))) @ c_Empty))))))))) => ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ (c_setsum @ c_Empty @ Y4) @ (c_Inj0 @ (c_Inj0 @ c_Empty))) => ((Y0 @ (^[Y8 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_setsum @ Y6 @ Y5)) @ c_Empty @ (^[Y8 : $i]: (c_Inj0 @ (c_setsum @ Y5 @ c_Empty))) @ c_Empty) => (Y2 @ (^[Y8 : (($i > $i > $i) > $i) > $i]: ((^[Y9 : $i > ($i > $i) > $i]: (c_setsum @ c_Empty @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ Y6) @ Y4))))) @ (^[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 : $i]: (Y4)) @ (c_setsum @ c_Empty @ c_Empty))) @ Y6)) @ c_Empty @ (c_setsum @ (c_setsum @ (c_Inj0 @ (c_Inj0 @ c_Empty)) @ Y7) @ (c_Inj0 @ (c_setsum @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))))))))))))))) => ((!! @ (((($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 : $i]: (c_Empty)) @ c_Empty)) @ c_Empty))) => ((Y2 @ (^[Y5 : (($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) => (Y3 @ (^[Y5 : $i > $i]: (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ (Y5 @ c_Empty))) @ (c_setsum @ (c_setsum @ (Y5 @ c_Empty) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) => ((!! 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% 48.64/8.24 inference(fool_elimination,[status(thm)],[f277])).
% 48.64/8.24 thf(f277,plain,(
% 48.64/8.24 ~(c_not @ ! [X0 : (($i > $i) > $i) > $i > $o,X1 : (((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $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] : (! [X4 : $i,X6 : ((($i > $i) > $i) > $i > $i > $i) > $i] : ((c_In @ X4 @ (X6 @ (^[X8 : ($i > $i) > $i, X9 : $i, X10 : $i] : (c_Inj1 @ (c_setsum @ X4 @ (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))))))) => (! [X14 : $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))) @ X14) => ((X2 @ (^[X17 : $i] : (c_Empty)) @ (^[X18 : $i] : (c_Empty))) => (X1 @ (^[X19 : (($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] : (X14)) @ c_Empty @ (c_Inj0 @ c_Empty)))) => (! [X26 : $i,X27 : $i,X29 : $i] : ((c_In @ (c_Inj1 @ X27) @ X26) => ((X1 @ (^[X30 : (($i > $i > $i) > $i) > $i, X31 : $i > ($i > $i) > $i] : (c_Empty)) @ (^[X32 : $i, X33 : ($i > $i) > $i, X34 : $i] : (c_Inj1 @ (c_setsum @ (c_setsum @ X26 @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (^[X35 : ($i > $i) > $i > $i] : (c_Empty)) @ (c_setsum @ c_Empty @ (c_setsum @ X26 @ (c_setsum @ (c_Inj0 @ c_Empty) @ X27))) @ c_Empty) => (X3 @ (^[X36 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i] : (X26)) @ (c_Inj1 @ (c_setsum @ (c_Inj0 @ X29) @ c_Empty)) @ (^[X37 : $i] : (c_setsum @ (c_setsum @ (c_setsum @ X26 @ X27) @ X26) @ (c_setsum @ c_Empty @ c_Empty))) @ c_Empty))) => (! [X38 : $i,X39 : $i,X40 : $i,X41 : $i] : ((c_In @ (c_setsum @ c_Empty @ X41) @ (c_Inj0 @ (c_Inj0 @ c_Empty))) => ((X3 @ (^[X42 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i] : (c_setsum @ X39 @ X40)) @ c_Empty @ (^[X43 : $i] : (c_Inj0 @ (c_setsum @ X40 @ c_Empty))) @ c_Empty) => (X1 @ (^[X44 : (($i > $i > $i) > $i) > $i, X45 : $i > ($i > $i) > $i] : (c_setsum @ c_Empty @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ X39) @ X41))) @ (^[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 : $i] : (X41)) @ (c_setsum @ c_Empty @ c_Empty))) @ X39)) @ c_Empty @ (c_setsum @ (c_setsum @ (c_Inj0 @ (c_Inj0 @ c_Empty)) @ X38) @ (c_Inj0 @ (c_setsum @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))))))) => (! [X52 : ((($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 : $i] : (c_Empty)) @ c_Empty)) @ c_Empty))) => ((X1 @ (^[X58 : (($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) => (X0 @ (^[X71 : $i > $i] : (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ (X71 @ c_Empty))) @ (c_setsum @ (c_setsum @ (X71 @ c_Empty) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))) => (! [X73 : ($i > ($i > $i) > $i) > $i > $i > $i > $i,X74 : $i > $i,X75 : ($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 @ (X73 @ (^[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))))) => ((X0 @ (^[X78 : $i > $i] : (X74 @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))))) @ (c_setsum @ (X75 @ (^[X79 : $i] : (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (c_Inj0 @ (c_Inj1 @ (c_Inj0 @ c_Empty))))) => (X0 @ (^[X80 : $i > $i] : (c_Inj1 @ (c_setsum @ (X80 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_setsum @ (c_Inj1 @ c_Empty) @ (X75 @ (^[X81 : $i] : (c_Empty))))))) @ c_Empty))) => (! [X82 : $i,X83 : $i,X84 : $i] : ((c_In @ X82 @ (c_Inj0 @ c_Empty)) => ((X3 @ (^[X86 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i] : (c_setsum @ c_Empty @ X83)) @ (c_Inj0 @ X84) @ (^[X87 : $i] : (c_setsum @ c_Empty @ X87)) @ c_Empty) => (X1 @ (^[X88 : (($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 > $i] : (c_setsum @ (c_Inj1 @ c_Empty) @ X83)) @ (c_Inj0 @ c_Empty) @ X84))) => (! [X94 : ($i > $i) > $i,X95 : $i,X96 : $i,X97 : $i] : ((X1 @ (^[X98 : (($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 @ (X94 @ (^[X110 : $i] : (c_Empty))) @ c_Empty) @ (c_setsum @ c_Empty @ X95)))) => (c_In @ X97 @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ (c_setsum @ (c_setsum @ (c_Inj0 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ c_Empty))))) => c_False)))))))))),
% 48.64/8.24 inference(rectify,[status(thm)],[f110])).
% 48.64/8.24 thf(f110,negated_conjecture,(
% 48.64/8.24 ~(c_not @ ! [X1 : (($i > $i) > $i) > $i > $o,X0 : (((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o,X3 : ($i > $i) > ($i > $i) > $o,X2 : ((((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i) > $i > ($i > $i) > $i > $o] : (! [X7 : $i,X5 : $i,X6 : ((($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))))))) => (! [X6 : $i,X5 : $i,X7 : $i,X4 : $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)))) => (! [X7 : $i,X6 : $i,X5 : $i,X4 : $i] : ((c_In @ (c_Inj1 @ X6) @ X7) => ((X0 @ (^[X8 : (($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))) => (! [X4 : $i,X7 : $i,X5 : $i,X6 : $i] : ((c_In @ (c_setsum @ c_Empty @ X6) @ (c_Inj0 @ (c_Inj0 @ c_Empty))) => ((X2 @ (^[X8 : ((($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))))))) => (! [X4 : $i,X7 : ((($i > $i) > $i > $i) > ($i > $i) > $i) > $i > ($i > $i) > $i > $i,X6 : $i,X5 : $i] : ((c_In @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ (X7 @ (^[X8 : ($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)))) => (! [X5 : $i,X4 : ($i > ($i > $i) > $i) > $i > $i > $i > $i,X6 : $i > $i,X7 : ($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 @ (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))) => (! [X4 : $i,X5 : $i,X7 : $i,X6 : $i > $i] : ((c_In @ X4 @ (c_Inj0 @ c_Empty)) => ((X2 @ (^[X8 : ((($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 > $i] : (c_setsum @ (c_Inj1 @ c_Empty) @ X5)) @ (c_Inj0 @ c_Empty) @ X7))) => (! [X6 : ($i > $i) > $i,X5 : $i,X7 : $i,X4 : $i] : ((X0 @ (^[X8 : (($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 : $i] : (c_Empty))) @ c_Empty) @ (c_setsum @ c_Empty @ X5)))) => (c_In @ X4 @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ (c_setsum @ (c_setsum @ (c_Inj0 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ c_Empty))))) => c_False)))))))))),
% 48.64/8.24 inference(negated_conjecture,[status(cth)],[f109])).
% 48.64/8.24 thf(f109,conjecture,(
% 48.64/8.24 (c_not @ ! [X1 : (($i > $i) > $i) > $i > $o,X0 : (((($i > $i > $i) > $i) > $i) > ($i > ($i > $i) > $i) > $i) > ($i > (($i > $i) > $i) > $i > $i) > ((($i > $i) > $i > $i) > $i) > $i > $i > $o,X3 : ($i > $i) > ($i > $i) > $o,X2 : ((((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i) > $i > ($i > $i) > $i > $o] : (! [X7 : $i,X5 : $i,X6 : ((($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))))))) => (! [X6 : $i,X5 : $i,X7 : $i,X4 : $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)))) => (! [X7 : $i,X6 : $i,X5 : $i,X4 : $i] : ((c_In @ (c_Inj1 @ X6) @ X7) => ((X0 @ (^[X8 : (($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))) => (! [X4 : $i,X7 : $i,X5 : $i,X6 : $i] : ((c_In @ (c_setsum @ c_Empty @ X6) @ (c_Inj0 @ (c_Inj0 @ c_Empty))) => ((X2 @ (^[X8 : ((($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))))))) => (! [X4 : $i,X7 : ((($i > $i) > $i > $i) > ($i > $i) > $i) > $i > ($i > $i) > $i > $i,X6 : $i,X5 : $i] : ((c_In @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ (X7 @ (^[X8 : ($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)))) => (! [X5 : $i,X4 : ($i > ($i > $i) > $i) > $i > $i > $i > $i,X6 : $i > $i,X7 : ($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 @ (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))) => (! [X4 : $i,X5 : $i,X7 : $i,X6 : $i > $i] : ((c_In @ X4 @ (c_Inj0 @ c_Empty)) => ((X2 @ (^[X8 : ((($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 > $i] : (c_setsum @ (c_Inj1 @ c_Empty) @ X5)) @ (c_Inj0 @ c_Empty) @ X7))) => (! [X6 : ($i > $i) > $i,X5 : $i,X7 : $i,X4 : $i] : ((X0 @ (^[X8 : (($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)))))))))),
% 48.64/8.24 file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',conj)).
% 48.64/8.24 thf(f305,plain,(
% 48.64/8.24 (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f302])).
% 48.64/8.24 thf(f302,plain,(
% 48.64/8.24 (((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $true)),
% 48.64/8.24 inference(definition_unfolding,[status(thm)],[f296,f299])).
% 48.64/8.24 thf(f296,plain,(
% 48.64/8.24 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 48.64/8.24 inference(cnf_transformation,[status(thm)],[f214])).
% 48.64/8.24 thf(f214,plain,(
% 48.64/8.24 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 48.64/8.24 inference(fool_elimination,[status(thm)],[f213])).
% 48.64/8.24 thf(f213,plain,(
% 48.64/8.24 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 48.64/8.24 inference(rectify,[status(thm)],[f5])).
% 48.64/8.24 thf(f5,axiom,(
% 48.64/8.24 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 48.64/8.24 file('/export/starexec/sandbox/tmp/tmp.XMFwlaS2IK/DTF2THF_32257.p',ax5)).
% 48.64/8.24 thf(f425,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (((c_In @ (sK7 @ X2) @ (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)))) = $true) | ($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(backward_demodulation,[status(thm)],[f357,f379])).
% 48.64/8.24 thf(f357,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o] : (((c_In @ (sK7 @ X2) @ (sK6 @ X2 @ (^[Y0 : ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (sK7 @ 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)))))))))) = $true) | ($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) ) | ~spl0_2),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f355])).
% 48.64/8.24 thf(f351,plain,(
% 48.64/8.24 spl0_1 | spl0_2),
% 48.64/8.24 inference(avatar_split_clause,[status(thm)],[f344,f349,f346])).
% 48.64/8.24 thf(f344,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (($true = (X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty)))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0)))))))))) | ((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1))))))))))))))) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f341])).
% 48.64/8.24 thf(f341,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | (((X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))) => (X3 @ (^[Y0 : (($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]: (sK5 @ X3 @ X2)) @ c_Empty @ (c_Repl @ c_Empty @ c_Inj1))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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))))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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) > $i > ($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false)) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f340])).
% 48.64/8.24 thf(f340,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ($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))))))))))) | (((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)) @ (sK5 @ X3 @ X2)) => ((X2 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i]: (c_Empty))) => (X3 @ (^[Y0 : (($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]: (sK5 @ X3 @ X2)) @ c_Empty @ (c_Repl @ c_Empty @ c_Inj1)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0)))))))))) | ((!! @ (((($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false)) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f339])).
% 48.64/8.24 thf(f339,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($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 = ((^[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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 > $i]: (Y0)) @ c_Empty @ (c_Repl @ c_Empty @ c_Inj1))))) @ (sK5 @ X3 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0)))))))))) | ((!! @ (((($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1))))))))))))))) )),
% 48.64/8.24 inference(sigma_clausification,[status(thm)],[f338])).
% 48.64/8.24 thf(f338,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ $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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 > $i) @ (^[Y0 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_binunion @ (c_Repl @ (c_Inj1 @ 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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y1 : $i > $i]: (sK4 @ X4 @ (c_Repl @ (c_Inj1 @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))) @ c_Inj1))) @ (c_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y1 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y1 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y1 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y1 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty))))) = $false) | ($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))))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0))))))))))) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f337])).
% 48.64/8.24 thf(f337,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ (((($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | (((^[Y0 : $i > $i]: (!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y1 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (Y1 @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y2 : $i > $i]: (Y0 @ (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_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y2 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y2 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y3 : $i]: (c_Empty))) @ c_Inj1)) @ c_Inj1)))) @ c_Empty)))))) @ (sK4 @ X4)) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($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))))))))))) | ((!! @ $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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1))))))))))))))) )),
% 48.64/8.24 inference(sigma_clausification,[status(thm)],[f336])).
% 48.64/8.24 thf(f336,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ (($i > ($i > $i) > $i) > $i > $i > $i > $i) @ (^[Y1 : ($i > ($i > $i) > $i) > $i > $i > $i > $i]: ((c_In @ (c_Inj1 @ (c_binunion @ (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)) @ (^[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))) @ (c_Repl @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (Y1 @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1))))) @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ (c_Repl @ c_Empty @ c_Inj1) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1)) => ((X4 @ (^[Y2 : $i > $i]: (Y0 @ (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_binunion @ (c_Repl @ (sK3 @ X4 @ (^[Y2 : $i]: (c_Inj1 @ (c_Inj1 @ c_Empty)))) @ (^[Y2 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ (c_Repl @ (c_Inj1 @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1) @ c_Inj1))) => (X4 @ (^[Y2 : $i > $i]: (c_Inj1 @ (c_binunion @ (c_Repl @ (Y2 @ (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_binunion @ (c_Repl @ (c_Inj1 @ c_Empty) @ (^[Y3 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (sK3 @ X4 @ (^[Y3 : $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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 @ (^[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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1)))))))))))) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f335])).
% 48.64/8.24 thf(f335,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | (((^[Y0 : ($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)) => ((X4 @ (^[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))) => (X4 @ (^[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)))))))) @ (sK3 @ X4)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1)))))))))))) )),
% 48.64/8.24 inference(sigma_clausification,[status(thm)],[f334])).
% 48.64/8.24 thf(f334,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($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)) => ((X4 @ (^[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))) => (X4 @ (^[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 > $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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 @ (^[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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) = $false) | ($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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1)))))))))))) )),
% 48.64/8.24 inference(not_proxy_clausification,[status(thm)],[f333])).
% 48.64/8.24 thf(f333,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 > $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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1) @ Y0)))))))))) | ((!! @ (((($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false)) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f332])).
% 48.64/8.24 thf(f332,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 > $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)) => ((X4 @ (^[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))) => (X4 @ (^[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 > $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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1))))))))))))))) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f331])).
% 48.64/8.24 thf(f331,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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))))))))))))))) = $true) | ((!! @ (((($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ (c_Inj1 @ c_Empty) @ c_Inj1)) @ c_Inj1)))))))))))) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f330])).
% 48.64/8.24 thf(f330,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (($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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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))))))))))) | ((!! @ $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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Inj1) @ c_Inj1))))))))))))))) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f329])).
% 48.64/8.24 thf(f329,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($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))))))))))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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) | ((!! @ $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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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))))))))) = $false)) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f328])).
% 48.64/8.24 thf(f328,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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 > $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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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)))))) = $false)) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f327])).
% 48.64/8.24 thf(f327,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($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))))))))))) | (((!! @ $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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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))))))))))))))))))) = $true)) )),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f326])).
% 48.64/8.24 thf(f326,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : ((((!! @ (((($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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))))))))))) = $true)) )),
% 48.64/8.24 inference(boolean_simplification,[status(thm)],[f325])).
% 48.64/8.24 thf(f325,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : ((((!! @ (((($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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))) = $true)) )),
% 48.64/8.24 inference(forward_demodulation,[status(thm)],[f324,f308])).
% 48.64/8.24 thf(f324,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($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 : $i]: (c_Empty))) => (X3 @ (^[Y1 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y1) @ Y2) => ((X3 @ (^[Y3 : (($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 @ Y2 @ (^[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 @ Y2 @ (^[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]: (Y2)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y0 @ 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 @ Y2 @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y2 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y0 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y4 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y2 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1))) @ c_Empty @ (^[Y4 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y1 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y4 : (($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 @ Y2 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y0 @ 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]: (Y0)) @ (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))) @ 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 @ Y3 @ 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 : $i]: (c_Repl @ Y1 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y1 : (($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) => (X4 @ (^[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)) => ((X4 @ (^[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))) => (X4 @ (^[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 : $i]: ((c_In @ Y2 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y3 : ((($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 @ Y0 @ c_Inj1) @ (^[Y3 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y4 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y3 : (($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) @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ (($i > $i) > $i) @ (^[Y3 : ($i > $i) > $i]: ((X3 @ (^[Y4 : (($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 @ (Y3 @ (^[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 @ Y0 @ (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)))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0))))))))))))) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f323])).
% 48.64/8.24 thf(f323,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o,X4 : (($i > $i) > $i) > $i > $o] : (($true = ((^[Y0 : (($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 : $i]: (c_Empty))) => (X3 @ (^[Y2 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y2) @ Y3) => ((X3 @ (^[Y4 : (($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 @ Y3 @ (^[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 @ Y3 @ (^[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]: (Y3)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y1 @ 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 @ Y3 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y2 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y3 @ 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 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y5 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y3 @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y2 @ c_Inj1))) @ c_Empty @ (^[Y5 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y5 : (($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 @ Y3 @ c_Inj1)) @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y1 @ 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]: (Y1)) @ (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))) @ 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 @ Y4 @ 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 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y2 : (($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) => (Y0 @ (^[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)) => ((Y0 @ (^[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))) => (Y0 @ (^[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 : $i]: ((c_In @ Y3 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y4 : ((($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 @ Y1 @ c_Inj1) @ (^[Y4 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y4 : (($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) @ Y1))))))))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ (($i > $i) > $i) @ (^[Y4 : ($i > $i) > $i]: ((X3 @ (^[Y5 : (($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 @ (Y4 @ (^[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 @ Y1 @ (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)))))))))))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))))))) @ X4))) )),
% 48.64/8.24 inference(pi_clausification,[status(thm)],[f322])).
% 48.64/8.24 thf(f322,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $i) > $i) > $i > $o) @ (^[Y0 : (($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 : $i]: (c_Empty))) => (X3 @ (^[Y2 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y2) @ Y3) => ((X3 @ (^[Y4 : (($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 @ Y3 @ (^[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 @ Y3 @ (^[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]: (Y3)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y1 @ 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 @ Y3 @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y2 @ c_Inj1)) @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y3 @ 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 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y1 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y5 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y3 @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y2 @ c_Inj1))) @ c_Empty @ (^[Y5 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (X3 @ (^[Y5 : (($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 @ Y3 @ c_Inj1)) @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y1 @ 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]: (Y1)) @ (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))) @ 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 @ Y4 @ 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 : $i]: (c_Repl @ Y2 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((X3 @ (^[Y2 : (($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) => (Y0 @ (^[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)) => ((Y0 @ (^[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))) => (Y0 @ (^[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 : $i]: ((c_In @ Y3 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y4 : ((($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 @ Y1 @ c_Inj1) @ (^[Y4 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y5 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1))) @ c_Empty) => (X3 @ (^[Y4 : (($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) @ Y1))))))))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ (($i > $i) > $i) @ (^[Y4 : ($i > $i) > $i]: ((X3 @ (^[Y5 : (($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 @ (Y4 @ (^[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 @ Y1 @ (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)))))))))))) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))))))) = $true)) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f321])).
% 48.64/8.24 thf(f321,plain,(
% 48.64/8.24 ( ! [X2 : ($i > $i) > ($i > $i) > $o,X3 : (((($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 > $o] : (($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 > $o) @ (^[Y1 : (($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 : $i]: (c_Empty))) => (Y0 @ (^[Y3 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y3) @ Y4) => ((Y0 @ (^[Y5 : (($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 @ Y4 @ (^[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 @ Y4 @ (^[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]: (Y4)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y2 @ 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 @ Y4 @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y4 @ 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 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y2 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y6 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y4 @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty @ (^[Y6 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y3 @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y0 @ (^[Y6 : (($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 @ Y4 @ c_Inj1)) @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y2 @ 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]: (Y2)) @ (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))) @ 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 @ Y5 @ 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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y0 @ (^[Y3 : (($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) => (Y1 @ (^[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)) => ((Y1 @ (^[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))) => (Y1 @ (^[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 : $i]: ((c_In @ Y4 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y5 : ((($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 @ Y2 @ c_Inj1) @ (^[Y5 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1))) @ c_Empty) => (Y0 @ (^[Y5 : (($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) @ Y2))))))))) => ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ (($i > $i) > $i) @ (^[Y5 : ($i > $i) > $i]: ((Y0 @ (^[Y6 : (($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 @ (Y5 @ (^[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 @ Y2 @ (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)))))))))))) => (!! @ $o @ (^[Y2 : $o]: (Y2)))))))))))))) @ X3))) )),
% 48.64/8.24 inference(pi_clausification,[status(thm)],[f320])).
% 48.64/8.24 thf(f320,plain,(
% 48.64/8.24 ( ! [X2 : ($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) > $i) > ($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 > $o) @ (^[Y1 : (($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 : $i]: (c_Empty))) => (Y0 @ (^[Y3 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y3) @ Y4) => ((Y0 @ (^[Y5 : (($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 @ Y4 @ (^[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 @ Y4 @ (^[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]: (Y4)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y2 @ 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 @ Y4 @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1)) @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y4 @ 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 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y2 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y6 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y4 @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1))) @ c_Empty @ (^[Y6 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y3 @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y0 @ (^[Y6 : (($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 @ Y4 @ c_Inj1)) @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y2 @ 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]: (Y2)) @ (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))) @ 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 @ Y5 @ 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 : $i]: (c_Repl @ Y3 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y0 @ (^[Y3 : (($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) => (Y1 @ (^[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)) => ((Y1 @ (^[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))) => (Y1 @ (^[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 : $i]: ((c_In @ Y4 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y5 : ((($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 @ Y2 @ c_Inj1) @ (^[Y5 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y6 : $i]: (c_Repl @ Y6 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1))) @ c_Empty) => (Y0 @ (^[Y5 : (($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) @ Y2))))))))) => ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ (($i > $i) > $i) @ (^[Y5 : ($i > $i) > $i]: ((Y0 @ (^[Y6 : (($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 @ (Y5 @ (^[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 @ Y2 @ (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)))))))))))) => (!! @ $o @ (^[Y2 : $o]: (Y2))))))))))))))))) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f319])).
% 48.64/8.24 thf(f319,plain,(
% 48.64/8.24 ( ! [X2 : ($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 > $o) @ (^[Y2 : (($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 : $i]: (c_Empty))) => (Y1 @ (^[Y4 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y4) @ Y5) => ((Y1 @ (^[Y6 : (($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 @ Y5 @ (^[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 @ Y5 @ (^[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]: (Y5)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y3 @ 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 @ Y5 @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1)) @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y5 @ 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 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y7 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y5 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1))) @ c_Empty @ (^[Y7 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y4 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y1 @ (^[Y7 : (($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 @ Y5 @ c_Inj1)) @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ Y3 @ 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]: (Y3)) @ (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))) @ 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 @ Y6 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y1 @ (^[Y4 : (($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) => (Y2 @ (^[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)) => ((Y2 @ (^[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))) => (Y2 @ (^[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 : $i]: ((c_In @ Y5 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y6 : ((($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 @ Y3 @ c_Inj1) @ (^[Y6 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y6 @ c_Inj1))) @ c_Empty) => (Y1 @ (^[Y6 : (($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) @ Y3))))))))) => ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ (($i > $i) > $i) @ (^[Y6 : ($i > $i) > $i]: ((Y1 @ (^[Y7 : (($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 @ (Y6 @ (^[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 @ Y3 @ (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)))))))))))) => (!! @ $o @ (^[Y3 : $o]: (Y3)))))))))))))))) @ X2) = $true)) )),
% 48.64/8.24 inference(pi_clausification,[status(thm)],[f318])).
% 48.64/8.24 thf(f318,plain,(
% 48.64/8.24 ( ! [X1 : ((((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i) > $i) > $i > ($i > $i) > $i > $o] : (((!! @ (($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 > $o) @ (^[Y2 : (($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 : $i]: (c_Empty))) => (Y1 @ (^[Y4 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y4) @ Y5) => ((Y1 @ (^[Y6 : (($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 @ Y5 @ (^[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 @ Y5 @ (^[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]: (Y5)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y3 @ 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 @ Y5 @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1)) @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y5 @ 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 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y3 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((X1 @ (^[Y7 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y5 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1))) @ c_Empty @ (^[Y7 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y4 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y1 @ (^[Y7 : (($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 @ Y5 @ c_Inj1)) @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ Y3 @ 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]: (Y3)) @ (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))) @ 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 @ Y6 @ 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 : $i]: (c_Repl @ Y4 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y1 @ (^[Y4 : (($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) => (Y2 @ (^[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)) => ((Y2 @ (^[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))) => (Y2 @ (^[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 : $i]: ((c_In @ Y5 @ (c_Repl @ c_Empty @ c_Inj1)) => ((X1 @ (^[Y6 : ((($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 @ Y3 @ c_Inj1) @ (^[Y6 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y7 : $i]: (c_Repl @ Y7 @ c_Inj1))) @ (c_Repl @ Y6 @ c_Inj1))) @ c_Empty) => (Y1 @ (^[Y6 : (($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) @ Y3))))))))) => ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ (($i > $i) > $i) @ (^[Y6 : ($i > $i) > $i]: ((Y1 @ (^[Y7 : (($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 @ (Y6 @ (^[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 @ Y3 @ (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)))))))))))) => (!! @ $o @ (^[Y3 : $o]: (Y3))))))))))))))))) = $true)) )),
% 48.64/8.24 inference(beta_eta_normalization,[status(thm)],[f317])).
% 48.64/8.24 thf(f317,plain,(
% 48.64/8.24 ( ! [X1 : ((((($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) > $i) > ($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 > $o) @ (^[Y3 : (($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 : $i]: (c_Empty))) => (Y2 @ (^[Y5 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y5) @ Y6) => ((Y2 @ (^[Y7 : (($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 @ Y6 @ (^[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 @ Y6 @ (^[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]: (Y6)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y4 @ 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 @ Y6 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1)) @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y6 @ 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 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((Y0 @ (^[Y8 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y6 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1))) @ c_Empty @ (^[Y8 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y2 @ (^[Y8 : (($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 @ Y6 @ c_Inj1)) @ (^[Y10 : $i]: (c_Repl @ Y10 @ c_Inj1))) @ (c_Repl @ Y4 @ 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]: (Y4)) @ (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))) @ 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 @ Y7 @ 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 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y2 @ (^[Y5 : (($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) => (Y3 @ (^[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)) => ((Y3 @ (^[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))) => (Y3 @ (^[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 : $i]: ((c_In @ Y6 @ (c_Repl @ c_Empty @ c_Inj1)) => ((Y0 @ (^[Y7 : ((($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 @ Y4 @ c_Inj1) @ (^[Y7 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y7 @ c_Inj1))) @ c_Empty) => (Y2 @ (^[Y7 : (($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) @ Y4))))))))) => ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ (($i > $i) > $i) @ (^[Y7 : ($i > $i) > $i]: ((Y2 @ (^[Y8 : (($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 @ (Y7 @ (^[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 @ Y4 @ (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)))))))))))) => (!! @ $o @ (^[Y4 : $o]: (Y4)))))))))))))))))) @ X1) = $true)) )),
% 48.64/8.24 inference(pi_clausification,[status(thm)],[f309])).
% 48.64/8.24 thf(f309,plain,(
% 48.64/8.24 ((!! @ (((((($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) > $i) > ($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 > $o) @ (^[Y3 : (($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 : $i]: (c_Empty))) => (Y2 @ (^[Y5 : (($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 : $i]: ((c_In @ (c_Inj1 @ Y5) @ Y6) => ((Y2 @ (^[Y7 : (($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 @ Y6 @ (^[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 @ Y6 @ (^[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]: (Y6)) @ (c_Inj1 @ (c_binunion @ (c_Repl @ (c_Repl @ Y4 @ 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 @ Y6 @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1)) @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y6 @ 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 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y4 @ c_Inj1)) @ (c_Repl @ (c_Repl @ c_Empty @ c_Inj1) @ c_Inj1)) => ((Y0 @ (^[Y8 : ((($i > $i) > $i > $i) > $i) > ($i > $i > $i) > $i > $i]: (c_binunion @ (c_Repl @ Y6 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ Y5 @ c_Inj1))) @ c_Empty @ (^[Y8 : $i]: (c_Repl @ (c_binunion @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ Y9 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) @ c_Empty) => (Y2 @ (^[Y8 : (($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 @ Y6 @ c_Inj1)) @ (^[Y10 : $i]: (c_Repl @ Y10 @ c_Inj1))) @ (c_Repl @ Y4 @ 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]: (Y4)) @ (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))) @ 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 @ Y7 @ 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 : $i]: (c_Repl @ Y5 @ c_Inj1))) @ (c_Repl @ c_Empty @ c_Inj1)) @ c_Inj1)) => ((Y2 @ (^[Y5 : (($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) => (Y3 @ (^[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)) => ((Y3 @ (^[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))) => (Y3 @ (^[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 : $i]: ((c_In @ Y6 @ (c_Repl @ c_Empty @ c_Inj1)) => ((Y0 @ (^[Y7 : ((($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 @ Y4 @ c_Inj1) @ (^[Y7 : $i]: (c_binunion @ (c_Repl @ c_Empty @ (^[Y8 : $i]: (c_Repl @ Y8 @ c_Inj1))) @ (c_Repl @ Y7 @ c_Inj1))) @ c_Empty) => (Y2 @ (^[Y7 : (($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) @ Y4))))))))) => ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ (($i > $i) > $i) @ (^[Y7 : ($i > $i) > $i]: ((Y2 @ (^[Y8 : (($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 @ (Y7 @ (^[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 @ Y4 @ (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)))))))))))) => (!! @ $o @ (^[Y4 : $o]: (Y4))))))))))))))))))) = $true)),
% 48.64/8.24 inference(binary_proxy_clausification,[status(thm)],[f307])).
% 48.64/8.24 % SZS output end Proof for DTF2THF_32257
% 48.64/8.24 % (310)------------------------------
% 48.64/8.24 % (310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.64/8.24 % (310)Termination reason: Refutation
% 48.64/8.24
% 48.64/8.24 % (310)Memory used [KB]: 15223
% 48.64/8.24 % (310)Time elapsed: 0.425 s
% 48.64/8.24 % (310)Instructions burned: 1342 (million)
% 48.64/8.24 % (310)------------------------------
% 48.64/8.24 % (310)------------------------------
% 48.64/8.24 % (32355)Success in time 6.659 s
%------------------------------------------------------------------------------