%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV529^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:38 AM UTC 2026
% Result : Theorem 7.76s 1.44s
% Output : Refutation 7.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 106 ( 85 unt; 0 typ; 9 def)
% Number of atoms : 2391 ( 404 equ; 0 cnn)
% Maximal formula atoms : 68 ( 22 avg)
% Number of connectives : 7860 ( 42 ~; 38 |; 32 &;5881 @)
% ( 0 <=>;1352 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1644 (1644 >; 0 *; 0 +; 0 <<)
% Number of symbols : 175 ( 170 usr; 22 con; 0-14 aty)
% ( 510 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 3330 (3126 ^; 190 !; 14 ?;3330 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c_Eps_i: ( $i > $o ) > $i ).
thf(func_def_1,type,
c_False: $o ).
thf(func_def_2,type,
c_True: $o ).
thf(func_def_3,type,
c_not: $o > $o ).
thf(func_def_4,type,
c_and: $o > $o > $o ).
thf(func_def_5,type,
c_or: $o > $o > $o ).
thf(func_def_6,type,
c_iff: $o > $o > $o ).
thf(func_def_7,type,
c_In: $i > $i > $o ).
thf(func_def_8,type,
c_Subq: $i > $i > $o ).
thf(func_def_10,type,
c_Union: $i > $i ).
thf(func_def_11,type,
c_Power: $i > $i ).
thf(func_def_12,type,
c_Repl: $i > ( $i > $i ) > $i ).
thf(func_def_13,type,
c_TransSet: $i > $o ).
thf(func_def_14,type,
c_atleast2: $i > $o ).
thf(func_def_15,type,
c_atleast3: $i > $o ).
thf(func_def_16,type,
c_atleast4: $i > $o ).
thf(func_def_17,type,
c_atleast5: $i > $o ).
thf(func_def_18,type,
c_atleast6: $i > $o ).
thf(func_def_19,type,
c_exactly2: $i > $o ).
thf(func_def_20,type,
c_exactly3: $i > $o ).
thf(func_def_21,type,
c_exactly4: $i > $o ).
thf(func_def_22,type,
c_exactly5: $i > $o ).
thf(func_def_23,type,
c_exu_i: ( $i > $o ) > $o ).
thf(func_def_24,type,
c_reflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
c_irreflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
c_symmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
c_antisymmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
c_transitive_i: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
c_eqreln_i: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
c_per_i: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
c_linear_i: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
c_partialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_34,type,
c_totalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_37,type,
c_If_i: $o > $i > $i > $i ).
thf(func_def_38,type,
c_exactly1of2: $o > $o > $o ).
thf(func_def_39,type,
c_exactly1of3: $o > $o > $o > $o ).
thf(func_def_40,type,
c_nIn: $i > $i > $o ).
thf(func_def_41,type,
c_nSubq: $i > $i > $o ).
thf(func_def_42,type,
c_UPair: $i > $i > $i ).
thf(func_def_43,type,
c_Sing: $i > $i ).
thf(func_def_44,type,
c_binunion: $i > $i > $i ).
thf(func_def_45,type,
c_SetAdjoin: $i > $i > $i ).
thf(func_def_46,type,
c_famunion: $i > ( $i > $i ) > $i ).
thf(func_def_47,type,
c_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_49,type,
c_binintersect: $i > $i > $i ).
thf(func_def_50,type,
c_setminus: $i > $i > $i ).
thf(func_def_51,type,
c_inj: $i > $i > ( $i > $i ) > $o ).
thf(func_def_52,type,
c_bij: $i > $i > ( $i > $i ) > $o ).
thf(func_def_53,type,
c_atleastp: $i > $i > $o ).
thf(func_def_54,type,
c_equip: $i > $i > $o ).
thf(func_def_55,type,
c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_56,type,
c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_57,type,
c_ordsucc: $i > $i ).
thf(func_def_58,type,
c_nat_p: $i > $o ).
thf(func_def_59,type,
c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
thf(func_def_60,type,
c_add_nat: $i > $i > $i ).
thf(func_def_61,type,
c_mul_nat: $i > $i > $i ).
thf(func_def_62,type,
c_ordinal: $i > $o ).
thf(func_def_63,type,
c_V_: $i > $i ).
thf(func_def_64,type,
c_Inj1: $i > $i ).
thf(func_def_65,type,
c_Inj0: $i > $i ).
thf(func_def_66,type,
c_Unj: $i > $i ).
thf(func_def_67,type,
c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_68,type,
c_setsum: $i > $i > $i ).
thf(func_def_69,type,
c_proj0: $i > $i ).
thf(func_def_70,type,
c_proj1: $i > $i ).
thf(func_def_71,type,
c_binrep: $i > $i > $i ).
thf(func_def_72,type,
c_lam: $i > ( $i > $i ) > $i ).
thf(func_def_73,type,
c_setprod: $i > $i > $i ).
thf(func_def_74,type,
c_ap: $i > $i > $i ).
thf(func_def_75,type,
c_setsum_p: $i > $o ).
thf(func_def_76,type,
c_tuple_p: $i > $i > $o ).
thf(func_def_77,type,
c_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_78,type,
c_setexp: $i > $i > $i ).
thf(func_def_79,type,
c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
c_set_of_pairs: $i > $o ).
thf(func_def_81,type,
c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_82,type,
c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_83,type,
c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_84,type,
c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_85,type,
c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_86,type,
c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_87,type,
c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_88,type,
c_SNoElts_: $i > $i ).
thf(func_def_89,type,
c_SNo_: $i > $i > $o ).
thf(func_def_90,type,
c_PSNo: $i > ( $i > $o ) > $i ).
thf(func_def_91,type,
c_SNo: $i > $o ).
thf(func_def_92,type,
c_SNoLev: $i > $i ).
thf(func_def_93,type,
c_SNoEq_: $i > $i > $i > $o ).
thf(func_def_94,type,
c_SNoLt: $i > $i > $o ).
thf(func_def_95,type,
c_SNoLe: $i > $i > $o ).
thf(func_def_96,type,
c_binop_on: $i > ( $i > $i > $i ) > $o ).
thf(func_def_97,type,
c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
thf(func_def_98,type,
c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_99,type,
c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_100,type,
c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_101,type,
c_combinator: $i > $o ).
thf(func_def_102,type,
c_combinator_equiv: $i > $i > $o ).
thf(func_def_103,type,
c_equip_mod: $i > $i > $i > $o ).
thf(func_def_107,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_108,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_109,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_110,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_111,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_112,type,
vIMP: $o > $o > $o ).
thf(func_def_113,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_114,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_115,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_116,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_117,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_118,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
db13:
!>[X0: $tType] : X0 ).
thf(func_def_120,type,
db12:
!>[X0: $tType] : X0 ).
thf(func_def_121,type,
db11:
!>[X0: $tType] : X0 ).
thf(func_def_122,type,
db10:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
db14:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
db15:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db16:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db17:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db18:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
sP0: ( $i > $o ) > $o ).
thf(func_def_132,type,
sP1: ( $i > $o ) > $o ).
thf(func_def_133,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_134,type,
sK3: ( $i > $o ) > $i > $i ).
thf(func_def_135,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_136,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_137,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_138,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_139,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_140,type,
sK9: ( $i > $i ) > $i > $o ).
thf(func_def_141,type,
sK10: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o ).
thf(func_def_142,type,
sK11: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o ).
thf(func_def_143,type,
sK12: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o ).
thf(func_def_152,type,
sF21: $o ).
thf(func_def_158,type,
sF27: $o ).
thf(func_def_162,type,
sF31: $o ).
thf(func_def_171,type,
sF40: $o ).
thf(func_def_177,type,
sF46: $o ).
thf(func_def_178,type,
vNOT: $o > $o ).
thf(func_def_179,type,
sK47: $o ).
thf(func_def_180,type,
sK48: $o ).
thf(func_def_181,type,
sK49: ( $i > $i ) > $i > $i > $i ).
thf(func_def_182,type,
sK50: $i > ( $i > $i ) > $i > $i > $o ).
thf(func_def_183,type,
sK51: $i > $i > $i ).
thf(func_def_184,type,
sK52: $i > $i > $i ).
thf(func_def_185,type,
sK53: $i > $i > $i > $o ).
thf(func_def_186,type,
sK54: $i > $i > $i ).
thf(func_def_187,type,
sK55: $i > $i > $i ).
thf(func_def_188,type,
sK56: $o > $o > $o ).
thf(func_def_189,type,
sK57: $o > $o > $o ).
thf(func_def_190,type,
sK58: $i > ( $i > $i > $i ) > $i ).
thf(func_def_191,type,
sK59: ( $i > $i > $i ) > $i ).
thf(func_def_192,type,
sK60: ( $i > $i > $i ) > $i ).
thf(f5,axiom,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(f13,axiom,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(f14,axiom,
( c_and
= ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> ( X1
=> X2 ) )
=> X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
thf(f15,axiom,
( c_or
= ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> X2 )
=> ( ( X1
=> X2 )
=> X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(f42,axiom,
( c_If_i
= ( ^ [X0: $o,X1: $i,X2: $i] :
( c_Eps_i
@ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(f47,axiom,
( c_UPair
= ( ^ [X0: $i,X1: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(f48,axiom,
( c_Sing
= ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(f49,axiom,
( c_binunion
= ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(f60,axiom,
( c_In_rec_poly_G_i
= ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ! [X4: $i,X5: $i > $i] :
( ! [X6: $i] :
( ( c_In @ X6 @ X4 )
=> ( X3 @ X6 @ ( X5 @ X6 ) ) )
=> ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(f61,axiom,
( c_In_rec_poly_i
= ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
( c_Eps_i
@ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(f69,axiom,
( c_Inj1
= ( c_In_rec_poly_i
@ ^ [X0: $i,X1: $i > $i] :
( c_binunion @ ( c_Sing @ c_Empty )
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(f70,axiom,
( c_Inj0
= ( ^ [X0: $i] :
( c_Repl @ X0
@ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
thf(f73,axiom,
( c_setsum
= ( ^ [X0: $i,X1: $i] :
( c_binunion
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
@ ( c_Repl @ X1
@ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(f109,conjecture,
! [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i] :
( X3
@ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
@ ^ [X8: $i] : X5
@ ^ [X8: $i] :
( X6 @ c_Empty
@ ^ [X9: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [X4: $i > ( $i > $i ) > $i > $i > $i,X5: $i,X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,X7: $i] :
( ( X3
@ ^ [X8: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [X9: ( $i > $i ) > $i,X10: $i > $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X8: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X8 ) )
@ ^ [X8: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [X4: $i > $i > $i,X5: ( ( $i > $i > $i ) > $i ) > $i,X6: $i > ( $i > $i > $i ) > $i,X7: ( $i > $i > $i > $i ) > $i] :
( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X12 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [X8: $i > $i,X9: $i] :
( c_setsum @ X9
@ ( X7
@ ^ [X10: $i,X11: $i,X12: $i] : c_Empty ) ) )
=> ( ! [X4: ( $i > ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X7 ) )
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty ) )
=> ( ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty )
@ c_Empty )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj1 @ c_Empty ) )
=> ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X4: $i,X5: ( $i > $i > $i ) > $i > $i,X6: ( $i > $i > $i > $i ) > $i,X7: $i > $i] :
( ( c_In
@ ( X6
@ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ X9 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X0
@ ^ [X8: $i] : X8
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( X1
@ ^ [X8: $i,X9: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X9 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X7 @ ( X7 @ c_Empty ) ) ) )
@ ^ [X8: $i > $i] : c_Empty ) ) )
=> ( ! [X4: $i,X5: $i,X6: $i > $i,X7: $i] :
( ( X1
@ ^ [X8: $i,X9: $i] : X8
@ ^ [X8: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ! [X4: $i,X5: $i,X6: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,X7: $i > $i] :
( X0
@ ^ [X8: $i] : X8
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i] :
( ( X0
@ ^ [X8: $i] : X8
@ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X4
@ ^ [X8: $i] : c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_setsum @ X9 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X4
@ ^ [X8: $i] : X8
@ ^ [X8: $i > $i,X9: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f110,negated_conjecture,
~ ! [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i] :
( X3
@ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
@ ^ [X8: $i] : X5
@ ^ [X8: $i] :
( X6 @ c_Empty
@ ^ [X9: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [X4: $i > ( $i > $i ) > $i > $i > $i,X5: $i,X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,X7: $i] :
( ( X3
@ ^ [X8: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [X9: ( $i > $i ) > $i,X10: $i > $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X8: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X8 ) )
@ ^ [X8: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [X4: $i > $i > $i,X5: ( ( $i > $i > $i ) > $i ) > $i,X6: $i > ( $i > $i > $i ) > $i,X7: ( $i > $i > $i > $i ) > $i] :
( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X12 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [X8: $i > $i,X9: $i] :
( c_setsum @ X9
@ ( X7
@ ^ [X10: $i,X11: $i,X12: $i] : c_Empty ) ) )
=> ( ! [X4: ( $i > ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X7 ) )
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty ) )
=> ( ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty )
@ c_Empty )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj1 @ c_Empty ) )
=> ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X4: $i,X5: ( $i > $i > $i ) > $i > $i,X6: ( $i > $i > $i > $i ) > $i,X7: $i > $i] :
( ( c_In
@ ( X6
@ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ X9 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X0
@ ^ [X8: $i] : X8
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( X1
@ ^ [X8: $i,X9: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X9 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X7 @ ( X7 @ c_Empty ) ) ) )
@ ^ [X8: $i > $i] : c_Empty ) ) )
=> ( ! [X4: $i,X5: $i,X6: $i > $i,X7: $i] :
( ( X1
@ ^ [X8: $i,X9: $i] : X8
@ ^ [X8: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ! [X4: $i,X5: $i,X6: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,X7: $i > $i] :
( X0
@ ^ [X8: $i] : X8
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i] :
( ( X0
@ ^ [X8: $i] : X8
@ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X4
@ ^ [X8: $i] : c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_setsum @ X9 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X4
@ ^ [X8: $i] : X8
@ ^ [X8: $i > $i,X9: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
thf(f119,plain,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
inference(rectify,[],[f5]) ).
thf(f120,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(fool_elimination,[],[f119]) ).
thf(f135,plain,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
inference(rectify,[],[f13]) ).
thf(f136,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(fool_elimination,[],[f135]) ).
thf(f137,plain,
( c_and
= ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> ( X1
=> X2 ) )
=> X2 ) ) ),
inference(rectify,[],[f14]) ).
thf(f138,plain,
( c_and
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> ( Y1
=> Y2 ) )
=> Y2 ) ) ) ),
inference(fool_elimination,[],[f137]) ).
thf(f139,plain,
( c_or
= ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> X2 )
=> ( ( X1
=> X2 )
=> X2 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f140,plain,
( c_or
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> Y2 )
=> ( ( Y1
=> Y2 )
=> Y2 ) ) ) ) ),
inference(fool_elimination,[],[f139]) ).
thf(f183,plain,
( c_If_i
= ( ^ [X0: $o,X1: $i,X2: $i] :
( c_Eps_i
@ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f184,plain,
( c_If_i
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( c_Eps_i
@ ^ [Y3: $i] : ( c_or @ ( c_and @ Y0 @ ( Y1 = Y3 ) ) @ ( c_and @ ( c_not @ Y0 ) @ ( Y2 = Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f183]) ).
thf(f189,plain,
( c_UPair
= ( ^ [X0: $i,X1: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f190,plain,
( c_UPair
= ( ^ [Y0: $i,Y1: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y2: $i] : ( c_If_i @ ( c_In @ c_Empty @ Y2 ) @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f189]) ).
thf(f191,plain,
( c_Sing
= ( ^ [Y0: $i] : ( c_UPair @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f192,plain,
( c_binunion
= ( ^ [Y0: $i,Y1: $i] : ( c_Union @ ( c_UPair @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f212,plain,
( c_In_rec_poly_G_i
= ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ! [X4: $i,X5: $i > $i] :
( ! [X6: $i] :
( ( c_In @ X6 @ X4 )
=> ( X3 @ X6 @ ( X5 @ X6 ) ) )
=> ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f60]) ).
thf(f213,plain,
( c_In_rec_poly_G_i
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y6 @ Y5 )
=> ( Y3 @ Y6 @ ( Y4 @ Y6 ) ) ) )
=> ( Y3 @ Y5 @ ( Y0 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f212]) ).
thf(f214,plain,
( c_In_rec_poly_i
= ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
( c_Eps_i
@ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f61]) ).
thf(f215,plain,
( c_In_rec_poly_i
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] : ( c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f214]) ).
thf(f229,plain,
( c_Inj1
= ( c_In_rec_poly_i
@ ^ [X0: $i,X1: $i > $i] :
( c_binunion @ ( c_Sing @ c_Empty )
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f69]) ).
thf(f230,plain,
( c_Inj1
= ( c_In_rec_poly_i
@ ^ [Y0: $i,Y1: $i > $i] :
( c_binunion @ ( c_Sing @ c_Empty )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f229]) ).
thf(f231,plain,
( c_Inj0
= ( ^ [X0: $i] :
( c_Repl @ X0
@ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f232,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f231]) ).
thf(f237,plain,
( c_setsum
= ( ^ [X0: $i,X1: $i] :
( c_binunion
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
@ ( c_Repl @ X1
@ ^ [X3: $i] : ( c_Inj1 @ X3 ) ) ) ) ),
inference(rectify,[],[f73]) ).
thf(f238,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,[],[f237]) ).
thf(f306,plain,
~ ! [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ! [X5: $i,X6: $i > ( $i > $i ) > $i] :
( X3
@ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
@ ^ [X9: $i] : X5
@ ^ [X10: $i] :
( X6 @ c_Empty
@ ^ [X11: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( X3
@ ^ [X16: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [X17: ( $i > $i ) > $i,X18: $i > $i,X19: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X20: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X20 ) )
@ ^ [X21: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [X25: ( $i > $i > $i > $i ) > $i] :
( X2
@ ^ [X26: $i > ( ( $i > $i ) > $i ) > $i,X27: $i,X28: $i,X29: $i > $i,X30: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X30 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [X31: $i > $i,X32: $i] :
( c_setsum @ X32
@ ( X25
@ ^ [X33: $i,X34: $i,X35: $i] : c_Empty ) ) )
=> ( ! [X36: ( $i > ( $i > $i ) > $i > $i ) > $i,X39: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X39 ) )
@ ( X36
@ ^ [X40: $i,X41: $i > $i,X42: $i] : c_Empty ) )
=> ( ( X2
@ ^ [X43: $i > ( ( $i > $i ) > $i ) > $i,X44: $i,X45: $i,X46: $i > $i,X47: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X36
@ ^ [X48: $i,X49: $i > $i,X50: $i] : c_Empty )
@ c_Empty )
@ ^ [X51: $i > $i,X52: $i] : ( c_Inj1 @ c_Empty ) )
=> ( X2
@ ^ [X53: $i > ( ( $i > $i ) > $i ) > $i,X54: $i,X55: $i,X56: $i > $i,X57: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [X58: $i > $i,X59: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X62: ( $i > $i > $i > $i ) > $i,X63: $i > $i] :
( ( c_In
@ ( X62
@ ^ [X64: $i,X65: $i,X66: $i] : ( c_Inj1 @ X65 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X0
@ ^ [X67: $i] : X67
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( X1
@ ^ [X68: $i,X69: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X69 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X63 @ ( X63 @ c_Empty ) ) ) )
@ ^ [X70: $i > $i] : c_Empty ) ) )
=> ( ( ( X1
@ ^ [X75: $i,X76: $i] : X75
@ ^ [X77: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ( X0
@ ^ [X82: $i] : X82
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [X83: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X84: $i > $i > $i,X85: $i > $i > $i > $i] :
( ( X0
@ ^ [X87: $i] : X87
@ ( X85 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X84 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X85 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X83
@ ^ [X88: $i] : c_Empty
@ ^ [X89: $i > $i,X90: $i] : ( c_setsum @ X90 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X83
@ ^ [X91: $i] : X91
@ ^ [X92: $i > $i,X93: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f307,plain,
~ ! [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ! [X5: $i,X6: $i > ( $i > $i ) > $i] :
( $true
= ( X3
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X5
@ ^ [Y0: $i] :
( X6 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
=> ( ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( $true
= ( X3
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true ) )
=> ( ! [X25: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X25
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
=> ( ! [X36: ( $i > ( $i > $i ) > $i > $i ) > $i,X39: $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X39 ) )
@ ( X36
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
=> ( ( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X36
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
=> ( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) ) )
=> ( ! [X62: ( $i > $i > $i > $i ) > $i,X63: $i > $i] :
( ( $true
= ( c_In
@ ( X62
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( $true
= ( X1
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X63 @ ( X63 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) ) ) )
=> ( ( ( $true
= ( X1
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
=> ( c_False = $true ) )
=> ( ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
=> ( ! [X83: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X84: $i > $i > $i,X85: $i > $i > $i > $i] :
( ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( X85 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X84 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X85 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X83
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X83
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
=> ( c_False = $true ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f306]) ).
thf(f309,plain,
~ ! [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ! [X4: $i,X5: $i > ( $i > $i ) > $i] :
( $true
= ( X3
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X4
@ ^ [Y0: $i] :
( X5 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
=> ( ! [X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( $true
= ( X3
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true ) )
=> ( ! [X7: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X7
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
=> ( ! [X8: ( $i > ( $i > $i ) > $i > $i ) > $i,X9: $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X9 ) )
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
=> ( ( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
=> ( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) ) )
=> ( ! [X10: ( $i > $i > $i > $i ) > $i,X11: $i > $i] :
( ( $true
= ( c_In
@ ( X10
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( $true
= ( X1
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X11 @ ( X11 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) ) ) )
=> ( ( ( $true
= ( X1
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
=> ( c_False = $true ) )
=> ( ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
=> ( ! [X12: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X13: $i > $i > $i,X14: $i > $i > $i > $i] :
( ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( X14 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X13 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X14 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X12
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X12
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
=> ( c_False = $true ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f307]) ).
thf(f318,plain,
? [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ( c_False != $true )
& ! [X12: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X13: $i > $i > $i,X14: $i > $i > $i > $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X12
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) )
| ( $true
!= ( X0
@ ^ [Y0: $i] : Y0
@ ( X14 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X13 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X14 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X12
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ( ( c_False = $true )
| ( $true
!= ( X1
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ! [X10: ( $i > $i > $i > $i ) > $i,X11: $i > $i] :
( ( $true
= ( X1
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X11 @ ( X11 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
| ( $true
!= ( c_In
@ ( X10
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ! [X8: ( $i > ( $i > $i ) > $i > $i ) > $i,X9: $i] :
( ( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) )
| ( $true
!= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X9 ) )
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) ) )
& ! [X7: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X7
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( X3
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ! [X4: $i,X5: $i > ( $i > $i ) > $i] :
( $true
= ( X3
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X4
@ ^ [Y0: $i] :
( X5 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) ),
inference(ennf_transformation,[],[f309]) ).
thf(f319,plain,
? [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ( c_False != $true )
& ! [X12: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X13: $i > $i > $i,X14: $i > $i > $i > $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X12
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) )
| ( $true
!= ( X0
@ ^ [Y0: $i] : Y0
@ ( X14 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X13 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X14 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X12
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ( ( c_False = $true )
| ( $true
!= ( X1
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ! [X10: ( $i > $i > $i > $i ) > $i,X11: $i > $i] :
( ( $true
= ( X1
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X11 @ ( X11 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
| ( $true
!= ( c_In
@ ( X10
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ! [X8: ( $i > ( $i > $i ) > $i > $i ) > $i,X9: $i] :
( ( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) )
| ( $true
!= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X9 ) )
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) ) )
& ! [X7: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X7
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( X3
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ! [X4: $i,X5: $i > ( $i > $i ) > $i] :
( $true
= ( X3
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X4
@ ^ [Y0: $i] :
( X5 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) ),
inference(flattening,[],[f318]) ).
thf(f332,plain,
? [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $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 > $o] :
( ( c_False != $true )
& ! [X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i,X6: $i > $i > $i > $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X4
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) )
| ( $true
!= ( X0
@ ^ [Y0: $i] : Y0
@ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X4
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ( ( c_False = $true )
| ( $true
!= ( X1
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ! [X7: ( $i > $i > $i > $i ) > $i,X8: $i > $i] :
( ( $true
= ( X1
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X8 @ ( X8 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( X0
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
| ( $true
!= ( c_In
@ ( X7
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ! [X9: ( $i > ( $i > $i ) > $i > $i ) > $i,X10: $i] :
( ( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) )
| ( $true
!= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X10 ) )
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) ) )
& ! [X11: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X2
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X11
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X12: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( X3
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X12
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ! [X13: $i,X14: $i > ( $i > $i ) > $i] :
( $true
= ( X3
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X13
@ ^ [Y0: $i] :
( X14 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) ),
inference(rectify,[],[f319]) ).
thf(f333,plain,
( ( c_False != $true )
& ! [X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i,X6: $i > $i > $i > $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X4
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) )
| ( $true
!= ( sK9
@ ^ [Y0: $i] : Y0
@ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X4
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( sK9
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ( ( c_False = $true )
| ( $true
!= ( sK10
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ! [X7: ( $i > $i > $i > $i ) > $i,X8: $i > $i] :
( ( $true
= ( sK10
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X8 @ ( X8 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( sK9
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
| ( $true
!= ( c_In
@ ( X7
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ! [X9: ( $i > ( $i > $i ) > $i > $i ) > $i,X10: $i] :
( ( $true
= ( sK11
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) )
| ( $true
!= ( sK11
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X10 ) )
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) ) )
& ! [X11: ( $i > $i > $i > $i ) > $i] :
( $true
= ( sK11
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X11
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X12: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( sK12
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X12
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ! [X13: $i,X14: $i > ( $i > $i ) > $i] :
( $true
= ( sK12
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X13
@ ^ [Y0: $i] :
( X14 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f332]) ).
thf(f338,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(cnf_transformation,[],[f120]) ).
thf(f356,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(cnf_transformation,[],[f136]) ).
thf(f357,plain,
( c_and
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> ( Y1
=> Y2 ) )
=> Y2 ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f358,plain,
( c_or
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> Y2 )
=> ( ( Y1
=> Y2 )
=> Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f140]) ).
thf(f385,plain,
( c_If_i
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( c_Eps_i
@ ^ [Y3: $i] : ( c_or @ ( c_and @ Y0 @ ( Y1 = Y3 ) ) @ ( c_and @ ( c_not @ Y0 ) @ ( Y2 = Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f184]) ).
thf(f390,plain,
( c_UPair
= ( ^ [Y0: $i,Y1: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y2: $i] : ( c_If_i @ ( c_In @ c_Empty @ Y2 ) @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f190]) ).
thf(f391,plain,
( c_Sing
= ( ^ [Y0: $i] : ( c_UPair @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f191]) ).
thf(f392,plain,
( c_binunion
= ( ^ [Y0: $i,Y1: $i] : ( c_Union @ ( c_UPair @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f192]) ).
thf(f403,plain,
( c_In_rec_poly_G_i
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ Y6 @ Y5 )
=> ( Y3 @ Y6 @ ( Y4 @ Y6 ) ) ) )
=> ( Y3 @ Y5 @ ( Y0 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f213]) ).
thf(f404,plain,
( c_In_rec_poly_i
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] : ( c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f215]) ).
thf(f412,plain,
( c_Inj1
= ( c_In_rec_poly_i
@ ^ [Y0: $i,Y1: $i > $i] :
( c_binunion @ ( c_Sing @ c_Empty )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f230]) ).
thf(f413,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f232]) ).
thf(f416,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,[],[f238]) ).
thf(f458,plain,
( $true
= ( sK9
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) ),
inference(cnf_transformation,[],[f333]) ).
thf(f459,plain,
! [X6: $i > $i > $i > $i,X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X4
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) )
| ( $true
!= ( sK9
@ ^ [Y0: $i] : Y0
@ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X4
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f333]) ).
thf(f460,plain,
c_False != $true,
inference(cnf_transformation,[],[f333]) ).
thf(f484,plain,
( c_If_i
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( c_Eps_i
@ ^ [Y3: $i] :
( ^ [Y4: $o,Y5: $o] :
( !! @ $o
@ ^ [Y6: $o] :
( ( Y4
=> Y6 )
=> ( ( Y5
=> Y6 )
=> Y6 ) ) )
@ ( ^ [Y4: $o,Y5: $o] :
( !! @ $o
@ ^ [Y6: $o] :
( ( Y4
=> ( Y5
=> Y6 ) )
=> Y6 ) )
@ Y0
@ ( Y1 = Y3 ) )
@ ( ^ [Y4: $o,Y5: $o] :
( !! @ $o
@ ^ [Y6: $o] :
( ( Y4
=> ( Y5
=> Y6 ) )
=> Y6 ) )
@ ( ^ [Y4: $o] :
( Y4
=> c_False )
@ Y0 )
@ ( Y2 = Y3 ) ) ) ) ) ),
inference(definition_unfolding,[],[f385,f358,f357,f357,f356]) ).
thf(f489,plain,
( c_UPair
= ( ^ [Y0: $i,Y1: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y2: $i] :
( ^ [Y3: $o,Y4: $i,Y5: $i] :
( c_Eps_i
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $o] :
( !! @ $o
@ ^ [Y9: $o] :
( ( Y7
=> Y9 )
=> ( ( Y8
=> Y9 )
=> Y9 ) ) )
@ ( ^ [Y7: $o,Y8: $o] :
( !! @ $o
@ ^ [Y9: $o] :
( ( Y7
=> ( Y8
=> Y9 ) )
=> Y9 ) )
@ Y3
@ ( Y4 = Y6 ) )
@ ( ^ [Y7: $o,Y8: $o] :
( !! @ $o
@ ^ [Y9: $o] :
( ( Y7
=> ( Y8
=> Y9 ) )
=> Y9 ) )
@ ( ^ [Y7: $o] :
( Y7
=> c_False )
@ Y3 )
@ ( Y5 = Y6 ) ) ) )
@ ( c_In @ c_Empty @ Y2 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f390,f484]) ).
thf(f490,plain,
( c_Sing
= ( ^ [Y0: $i] :
( ^ [Y1: $i,Y2: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y3: $i] :
( ^ [Y4: $o,Y5: $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> Y10 )
=> ( ( Y9
=> Y10 )
=> Y10 ) ) )
@ ( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> ( Y9
=> Y10 ) )
=> Y10 ) )
@ Y4
@ ( Y5 = Y7 ) )
@ ( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> ( Y9
=> Y10 ) )
=> Y10 ) )
@ ( ^ [Y8: $o] :
( Y8
=> c_False )
@ Y4 )
@ ( Y6 = Y7 ) ) ) )
@ ( c_In @ c_Empty @ Y3 )
@ Y1
@ Y2 ) )
@ Y0
@ Y0 ) ) ),
inference(definition_unfolding,[],[f391,f489]) ).
thf(f491,plain,
( c_binunion
= ( ^ [Y0: $i,Y1: $i] :
( c_Union
@ ( ^ [Y2: $i,Y3: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y4: $i] :
( ^ [Y5: $o,Y6: $i,Y7: $i] :
( c_Eps_i
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $o] :
( !! @ $o
@ ^ [Y11: $o] :
( ( Y9
=> Y11 )
=> ( ( Y10
=> Y11 )
=> Y11 ) ) )
@ ( ^ [Y9: $o,Y10: $o] :
( !! @ $o
@ ^ [Y11: $o] :
( ( Y9
=> ( Y10
=> Y11 ) )
=> Y11 ) )
@ Y5
@ ( Y6 = Y8 ) )
@ ( ^ [Y9: $o,Y10: $o] :
( !! @ $o
@ ^ [Y11: $o] :
( ( Y9
=> ( Y10
=> Y11 ) )
=> Y11 ) )
@ ( ^ [Y9: $o] :
( Y9
=> c_False )
@ Y5 )
@ ( Y7 = Y8 ) ) ) )
@ ( c_In @ c_Empty @ Y4 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f392,f489]) ).
thf(f501,plain,
( c_In_rec_poly_i
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[],[f404,f403]) ).
thf(f509,plain,
( c_Inj1
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ ^ [Y0: $i,Y1: $i > $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y5: $i] :
( ^ [Y6: $o,Y7: $i,Y8: $i] :
( c_Eps_i
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> Y12 )
=> ( ( Y11
=> Y12 )
=> Y12 ) ) )
@ ( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> ( Y11
=> Y12 ) )
=> Y12 ) )
@ Y6
@ ( Y7 = Y9 ) )
@ ( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> ( Y11
=> Y12 ) )
=> Y12 ) )
@ ( ^ [Y10: $o] :
( Y10
=> c_False )
@ Y6 )
@ ( Y8 = Y9 ) ) ) )
@ ( c_In @ c_Empty @ Y5 )
@ Y3
@ Y4 ) )
@ Y2
@ Y2 )
@ c_Empty )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f412,f501,f491,f490]) ).
thf(f510,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] :
( ^ [Y2: $i > ( $i > $i ) > $i,Y3: $i] :
( c_Eps_i
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10 @ ( Y5 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
@ Y2
@ Y3
@ Y4 ) )
@ ^ [Y2: $i,Y3: $i > $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $i,Y10: $i] :
( c_Eps_i
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> Y14 )
=> ( ( Y13
=> Y14 )
=> Y14 ) ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ Y8
@ ( Y9 = Y11 ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ ( ^ [Y12: $o] :
( Y12
=> c_False )
@ Y8 )
@ ( Y10 = Y11 ) ) ) )
@ ( c_In @ c_Empty @ Y7 )
@ Y5
@ Y6 ) )
@ Y4
@ Y4 )
@ c_Empty )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f413,f509]) ).
thf(f513,plain,
( c_setsum
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y5
@ Y5 )
@ c_Empty )
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f416,f491,f510,f509]) ).
thf(f551,plain,
( $true
= ( ^ [Y0: $o] :
( Y0
=> c_False )
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(definition_unfolding,[],[f338,f356]) ).
thf(f555,plain,
! [X6: $i > $i > $i > $i,X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i] :
( ( $true
= ( c_In
@ ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] :
( ^ [Y2: $i > ( $i > $i ) > $i,Y3: $i] :
( c_Eps_i
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10 @ ( Y5 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
@ Y2
@ Y3
@ Y4 ) )
@ ^ [Y2: $i,Y3: $i > $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $i,Y10: $i] :
( c_Eps_i
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> Y14 )
=> ( ( Y13
=> Y14 )
=> Y14 ) ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ Y8
@ ( Y9 = Y11 ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ ( ^ [Y12: $o] :
( Y12
=> c_False )
@ Y8 )
@ ( Y10 = Y11 ) ) ) )
@ ( c_In @ c_Empty @ Y7 )
@ Y5
@ Y6 ) )
@ Y4
@ Y4 )
@ c_Empty )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1 ) )
@ c_Empty )
@ ( X4
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) )
| ( $true
!= ( sK9
@ ^ [Y0: $i] : Y0
@ ( X6
@ ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y5
@ Y5 )
@ c_Empty )
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ ^ [Y0: $i,Y1: $i > $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y5: $i] :
( ^ [Y6: $o,Y7: $i,Y8: $i] :
( c_Eps_i
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> Y12 )
=> ( ( Y11
=> Y12 )
=> Y12 ) ) )
@ ( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> ( Y11
=> Y12 ) )
=> Y12 ) )
@ Y6
@ ( Y7 = Y9 ) )
@ ( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> ( Y11
=> Y12 ) )
=> Y12 ) )
@ ( ^ [Y10: $o] :
( Y10
=> c_False )
@ Y6 )
@ ( Y8 = Y9 ) ) ) )
@ ( c_In @ c_Empty @ Y5 )
@ Y3
@ Y4 ) )
@ Y2
@ Y2 )
@ c_Empty )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] :
( ^ [Y2: $i > ( $i > $i ) > $i,Y3: $i] :
( c_Eps_i
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10 @ ( Y5 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
@ Y2
@ Y3
@ Y4 ) )
@ ^ [Y2: $i,Y3: $i > $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $i,Y10: $i] :
( c_Eps_i
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> Y14 )
=> ( ( Y13
=> Y14 )
=> Y14 ) ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ Y8
@ ( Y9 = Y11 ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ ( ^ [Y12: $o] :
( Y12
=> c_False )
@ Y8 )
@ ( Y10 = Y11 ) ) ) )
@ ( c_In @ c_Empty @ Y7 )
@ Y5
@ Y6 ) )
@ Y4
@ Y4 )
@ c_Empty )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1 ) )
@ c_Empty ) )
@ ( X5 @ c_Empty @ c_Empty ) )
@ ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y5
@ Y5 )
@ c_Empty )
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y5
@ Y5 )
@ c_Empty )
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ c_Empty
@ ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y5
@ Y5 )
@ c_Empty )
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ c_Empty
@ c_Empty ) )
@ ( X6
@ ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] :
( ^ [Y2: $i > ( $i > $i ) > $i,Y3: $i] :
( c_Eps_i
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10 @ ( Y5 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
@ Y2
@ Y3
@ Y4 ) )
@ ^ [Y2: $i,Y3: $i > $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $i,Y10: $i] :
( c_Eps_i
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> Y14 )
=> ( ( Y13
=> Y14 )
=> Y14 ) ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ Y8
@ ( Y9 = Y11 ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ ( ^ [Y12: $o] :
( Y12
=> c_False )
@ Y8 )
@ ( Y10 = Y11 ) ) ) )
@ ( c_In @ c_Empty @ Y7 )
@ Y5
@ Y6 ) )
@ Y4
@ Y4 )
@ c_Empty )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1 ) )
@ c_Empty )
@ ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ ^ [Y0: $i,Y1: $i > $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y5: $i] :
( ^ [Y6: $o,Y7: $i,Y8: $i] :
( c_Eps_i
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> Y12 )
=> ( ( Y11
=> Y12 )
=> Y12 ) ) )
@ ( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> ( Y11
=> Y12 ) )
=> Y12 ) )
@ Y6
@ ( Y7 = Y9 ) )
@ ( ^ [Y10: $o,Y11: $o] :
( !! @ $o
@ ^ [Y12: $o] :
( ( Y10
=> ( Y11
=> Y12 ) )
=> Y12 ) )
@ ( ^ [Y10: $o] :
( Y10
=> c_False )
@ Y6 )
@ ( Y8 = Y9 ) ) ) )
@ ( c_In @ c_Empty @ Y5 )
@ Y3
@ Y4 ) )
@ Y2
@ Y2 )
@ c_Empty )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ c_Empty )
@ ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y5
@ Y5 )
@ c_Empty )
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ ( X4
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] :
( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] :
( ^ [Y7: $i > ( $i > $i ) > $i,Y8: $i] :
( c_Eps_i
@ ^ [Y9: $i] :
( ^ [Y10: $i > ( $i > $i ) > $i,Y11: $i,Y12: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y13: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y14: $i > $i] :
( !! @ $i
@ ^ [Y15: $i] :
( ( !! @ $i
@ ^ [Y16: $i] :
( ( c_In @ Y16 @ Y15 )
=> ( Y13 @ Y16 @ ( Y14 @ Y16 ) ) ) )
=> ( Y13 @ Y15 @ ( Y10 @ Y15 @ Y14 ) ) ) ) )
=> ( Y13 @ Y11 @ Y12 ) ) )
@ Y7
@ Y8
@ Y9 ) )
@ ^ [Y7: $i,Y8: $i > $i] :
( ^ [Y9: $i,Y10: $i] :
( c_Union
@ ( ^ [Y11: $i,Y12: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $i,Y16: $i] :
( c_Eps_i
@ ^ [Y17: $i] :
( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> Y20 )
=> ( ( Y19
=> Y20 )
=> Y20 ) ) )
@ ( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> ( Y19
=> Y20 ) )
=> Y20 ) )
@ Y14
@ ( Y15 = Y17 ) )
@ ( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> ( Y19
=> Y20 ) )
=> Y20 ) )
@ ( ^ [Y18: $o] :
( Y18
=> c_False )
@ Y14 )
@ ( Y16 = Y17 ) ) ) )
@ ( c_In @ c_Empty @ Y13 )
@ Y11
@ Y12 ) )
@ Y9
@ Y10 ) )
@ ( ^ [Y9: $i] :
( ^ [Y10: $i,Y11: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $i,Y15: $i] :
( c_Eps_i
@ ^ [Y16: $i] :
( ^ [Y17: $o,Y18: $o] :
( !! @ $o
@ ^ [Y19: $o] :
( ( Y17
=> Y19 )
=> ( ( Y18
=> Y19 )
=> Y19 ) ) )
@ ( ^ [Y17: $o,Y18: $o] :
( !! @ $o
@ ^ [Y19: $o] :
( ( Y17
=> ( Y18
=> Y19 ) )
=> Y19 ) )
@ Y13
@ ( Y14 = Y16 ) )
@ ( ^ [Y17: $o,Y18: $o] :
( !! @ $o
@ ^ [Y19: $o] :
( ( Y17
=> ( Y18
=> Y19 ) )
=> Y19 ) )
@ ( ^ [Y17: $o] :
( Y17
=> c_False )
@ Y13 )
@ ( Y15 = Y16 ) ) ) )
@ ( c_In @ c_Empty @ Y12 )
@ Y10
@ Y11 ) )
@ Y9
@ Y9 )
@ c_Empty )
@ ( c_Repl @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y6 ) )
@ Y4 ) )
@ ( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) ) )
@ Y1
@ ( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] :
( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] :
( ^ [Y7: $i > ( $i > $i ) > $i,Y8: $i] :
( c_Eps_i
@ ^ [Y9: $i] :
( ^ [Y10: $i > ( $i > $i ) > $i,Y11: $i,Y12: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y13: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y14: $i > $i] :
( !! @ $i
@ ^ [Y15: $i] :
( ( !! @ $i
@ ^ [Y16: $i] :
( ( c_In @ Y16 @ Y15 )
=> ( Y13 @ Y16 @ ( Y14 @ Y16 ) ) ) )
=> ( Y13 @ Y15 @ ( Y10 @ Y15 @ Y14 ) ) ) ) )
=> ( Y13 @ Y11 @ Y12 ) ) )
@ Y7
@ Y8
@ Y9 ) )
@ ^ [Y7: $i,Y8: $i > $i] :
( ^ [Y9: $i,Y10: $i] :
( c_Union
@ ( ^ [Y11: $i,Y12: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $i,Y16: $i] :
( c_Eps_i
@ ^ [Y17: $i] :
( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> Y20 )
=> ( ( Y19
=> Y20 )
=> Y20 ) ) )
@ ( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> ( Y19
=> Y20 ) )
=> Y20 ) )
@ Y14
@ ( Y15 = Y17 ) )
@ ( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> ( Y19
=> Y20 ) )
=> Y20 ) )
@ ( ^ [Y18: $o] :
( Y18
=> c_False )
@ Y14 )
@ ( Y16 = Y17 ) ) ) )
@ ( c_In @ c_Empty @ Y13 )
@ Y11
@ Y12 ) )
@ Y9
@ Y10 ) )
@ ( ^ [Y9: $i] :
( ^ [Y10: $i,Y11: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $i,Y15: $i] :
( c_Eps_i
@ ^ [Y16: $i] :
( ^ [Y17: $o,Y18: $o] :
( !! @ $o
@ ^ [Y19: $o] :
( ( Y17
=> Y19 )
=> ( ( Y18
=> Y19 )
=> Y19 ) ) )
@ ( ^ [Y17: $o,Y18: $o] :
( !! @ $o
@ ^ [Y19: $o] :
( ( Y17
=> ( Y18
=> Y19 ) )
=> Y19 ) )
@ Y13
@ ( Y14 = Y16 ) )
@ ( ^ [Y17: $o,Y18: $o] :
( !! @ $o
@ ^ [Y19: $o] :
( ( Y17
=> ( Y18
=> Y19 ) )
=> Y19 ) )
@ ( ^ [Y17: $o] :
( Y17
=> c_False )
@ Y13 )
@ ( Y15 = Y16 ) ) ) )
@ ( c_In @ c_Empty @ Y12 )
@ Y10
@ Y11 ) )
@ Y9
@ Y9 )
@ c_Empty )
@ ( c_Repl @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y6 ) )
@ Y4 ) )
@ ( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ ( ^ [Y7: $i] :
( ^ [Y8: $i,Y9: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $i,Y13: $i] :
( c_Eps_i
@ ^ [Y14: $i] :
( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> Y17 )
=> ( ( Y16
=> Y17 )
=> Y17 ) ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ Y11
@ ( Y12 = Y14 ) )
@ ( ^ [Y15: $o,Y16: $o] :
( !! @ $o
@ ^ [Y17: $o] :
( ( Y15
=> ( Y16
=> Y17 ) )
=> Y17 ) )
@ ( ^ [Y15: $o] :
( Y15
=> c_False )
@ Y11 )
@ ( Y13 = Y14 ) ) ) )
@ ( c_In @ c_Empty @ Y10 )
@ Y8
@ Y9 ) )
@ Y7
@ Y7 )
@ c_Empty )
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) ) )
@ c_Empty
@ c_Empty ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f459,f510,f513,f509,f510,f513,f513,f513,f510,f509,f513,f513,f513]) ).
thf(f556,plain,
( $true
= ( sK9
@ ^ [Y0: $i] : Y0
@ ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] :
( ^ [Y2: $i > ( $i > $i ) > $i,Y3: $i] :
( c_Eps_i
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10 @ ( Y5 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
@ Y2
@ Y3
@ Y4 ) )
@ ^ [Y2: $i,Y3: $i > $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $i,Y10: $i] :
( c_Eps_i
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> Y14 )
=> ( ( Y13
=> Y14 )
=> Y14 ) ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ Y8
@ ( Y9 = Y11 ) )
@ ( ^ [Y12: $o,Y13: $o] :
( !! @ $o
@ ^ [Y14: $o] :
( ( Y12
=> ( Y13
=> Y14 ) )
=> Y14 ) )
@ ( ^ [Y12: $o] :
( Y12
=> c_False )
@ Y8 )
@ ( Y10 = Y11 ) ) ) )
@ ( c_In @ c_Empty @ Y7 )
@ Y5
@ Y6 ) )
@ Y4
@ Y4 )
@ c_Empty )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1 ) )
@ c_Empty ) ) ),
inference(definition_unfolding,[],[f458,f510]) ).
thf(f563,definition,
( sF13
= ( c_Power @ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
thf(f564,plain,
( ( c_Power @ c_Empty )
= sF13 ),
inference(reorient_equations,[],[f563]) ).
thf(f565,definition,
( sF14
= ( c_Power @ sF13 ) ),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
thf(f566,plain,
( ( c_Power @ sF13 )
= sF14 ),
inference(reorient_equations,[],[f565]) ).
thf(f567,definition,
( sF15
= ( ^ [Y0: $i] :
( ^ [Y1: $i,Y2: $i] :
( c_Repl @ sF14
@ ^ [Y3: $i] :
( ^ [Y4: $o,Y5: $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> Y10 )
=> ( ( Y9
=> Y10 )
=> Y10 ) ) )
@ ( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> ( Y9
=> Y10 ) )
=> Y10 ) )
@ Y4
@ ( Y5 = Y7 ) )
@ ( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> ( Y9
=> Y10 ) )
=> Y10 ) )
@ ( ^ [Y8: $o] :
( Y8
=> c_False )
@ Y4 )
@ ( Y6 = Y7 ) ) ) )
@ ( c_In @ c_Empty @ Y3 )
@ Y1
@ Y2 ) )
@ Y0
@ Y0 )
@ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
thf(f568,plain,
( ( ^ [Y0: $i] :
( ^ [Y1: $i,Y2: $i] :
( c_Repl @ sF14
@ ^ [Y3: $i] :
( ^ [Y4: $o,Y5: $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> Y10 )
=> ( ( Y9
=> Y10 )
=> Y10 ) ) )
@ ( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> ( Y9
=> Y10 ) )
=> Y10 ) )
@ Y4
@ ( Y5 = Y7 ) )
@ ( ^ [Y8: $o,Y9: $o] :
( !! @ $o
@ ^ [Y10: $o] :
( ( Y8
=> ( Y9
=> Y10 ) )
=> Y10 ) )
@ ( ^ [Y8: $o] :
( Y8
=> c_False )
@ Y4 )
@ ( Y6 = Y7 ) ) ) )
@ ( c_In @ c_Empty @ Y3 )
@ Y1
@ Y2 ) )
@ Y0
@ Y0 )
@ c_Empty )
= sF15 ),
inference(reorient_equations,[],[f567]) ).
thf(f569,definition,
( sF16
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] :
( ^ [Y2: $i > ( $i > $i ) > $i,Y3: $i] :
( c_Eps_i
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10 @ ( Y5 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
@ Y2
@ Y3
@ Y4 ) )
@ ^ [Y2: $i,Y3: $i > $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ sF14
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ sF15
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1 ) )
@ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
thf(f570,plain,
( ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] :
( ^ [Y2: $i > ( $i > $i ) > $i,Y3: $i] :
( c_Eps_i
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i,Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10 @ ( Y5 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
@ Y2
@ Y3
@ Y4 ) )
@ ^ [Y2: $i,Y3: $i > $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ sF14
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ sF15
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y1 ) )
@ c_Empty )
= sF16 ),
inference(reorient_equations,[],[f569]) ).
thf(f571,definition,
( sF17
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ ^ [Y0: $i,Y1: $i > $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ sF15
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sF16 ) ),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
thf(f572,plain,
( ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ ^ [Y0: $i,Y1: $i > $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ sF15
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sF16 )
= sF17 ),
inference(reorient_equations,[],[f571]) ).
thf(f573,definition,
( sF18
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ sF14
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ sF15
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ sF14
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ sF15
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ c_Empty
@ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
thf(f574,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ sF14
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ sF15
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ sF14
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ sF15
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ c_Empty
@ c_Empty )
= sF18 ),
inference(reorient_equations,[],[f573]) ).
thf(f575,definition,
( sF19
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ sF14
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ sF15
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ sF14
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ sF15
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ c_Empty
@ sF18 ) ),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
thf(f576,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ sF14
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ sF15
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ sF14
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ sF15
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ c_Empty
@ sF18 )
= sF19 ),
inference(reorient_equations,[],[f575]) ).
thf(f577,definition,
( sF20
= ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ ^ [Y0: $i,Y1: $i > $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ sF15
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
thf(f578,plain,
( ( ^ [Y0: $i > ( $i > $i ) > $i,Y1: $i] :
( c_Eps_i
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i,Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8 @ ( Y3 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ ^ [Y0: $i,Y1: $i > $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ sF15
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ c_Empty )
= sF20 ),
inference(reorient_equations,[],[f577]) ).
thf(f579,plain,
! [X6: $i > $i > $i > $i,X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i] :
( ( $true
= ( c_In @ sF16
@ ( X4
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) )
| ( $true
!= ( sK9
@ ^ [Y0: $i] : Y0
@ ( X6
@ ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ sF14
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ sF15
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ sF14
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ sF15
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ sF17
@ ( X5 @ c_Empty @ c_Empty ) )
@ ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( c_Union
@ ( ^ [Y4: $i,Y5: $i] :
( c_Repl @ sF14
@ ^ [Y6: $i] :
( ^ [Y7: $o,Y8: $i,Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> Y13 )
=> ( ( Y12
=> Y13 )
=> Y13 ) ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ Y7
@ ( Y8 = Y10 ) )
@ ( ^ [Y11: $o,Y12: $o] :
( !! @ $o
@ ^ [Y13: $o] :
( ( Y11
=> ( Y12
=> Y13 ) )
=> Y13 ) )
@ ( ^ [Y11: $o] :
( Y11
=> c_False )
@ Y7 )
@ ( Y9 = Y10 ) ) ) )
@ ( c_In @ c_Empty @ Y6 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ sF14
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ sF15
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] :
( ^ [Y3: $i > ( $i > $i ) > $i,Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( ^ [Y6: $i > ( $i > $i ) > $i,Y7: $i,Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11 @ ( Y6 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ ^ [Y3: $i,Y4: $i > $i] :
( ^ [Y5: $i,Y6: $i] :
( c_Union
@ ( ^ [Y7: $i,Y8: $i] :
( c_Repl @ sF14
@ ^ [Y9: $i] :
( ^ [Y10: $o,Y11: $i,Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> Y16 )
=> ( ( Y15
=> Y16 )
=> Y16 ) ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ Y10
@ ( Y11 = Y13 ) )
@ ( ^ [Y14: $o,Y15: $o] :
( !! @ $o
@ ^ [Y16: $o] :
( ( Y14
=> ( Y15
=> Y16 ) )
=> Y16 ) )
@ ( ^ [Y14: $o] :
( Y14
=> c_False )
@ Y10 )
@ ( Y12 = Y13 ) ) ) )
@ ( c_In @ c_Empty @ Y9 )
@ Y7
@ Y8 ) )
@ Y5
@ Y6 ) )
@ sF15
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2 ) ) )
@ sF19
@ ( X6 @ sF16 @ sF20 @ sF18 ) )
@ ( X4
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i] :
( c_Union
@ ( ^ [Y6: $i,Y7: $i] :
( c_Repl @ sF14
@ ^ [Y8: $i] :
( ^ [Y9: $o,Y10: $i,Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> Y15 )
=> ( ( Y14
=> Y15 )
=> Y15 ) ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ Y9
@ ( Y10 = Y12 ) )
@ ( ^ [Y13: $o,Y14: $o] :
( !! @ $o
@ ^ [Y15: $o] :
( ( Y13
=> ( Y14
=> Y15 ) )
=> Y15 ) )
@ ( ^ [Y13: $o] :
( Y13
=> c_False )
@ Y9 )
@ ( Y11 = Y12 ) ) ) )
@ ( c_In @ c_Empty @ Y8 )
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ ( c_Repl @ Y2
@ ^ [Y4: $i] :
( ^ [Y5: $i] :
( c_Repl @ Y5
@ ^ [Y6: $i] :
( ^ [Y7: $i > ( $i > $i ) > $i,Y8: $i] :
( c_Eps_i
@ ^ [Y9: $i] :
( ^ [Y10: $i > ( $i > $i ) > $i,Y11: $i,Y12: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y13: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y14: $i > $i] :
( !! @ $i
@ ^ [Y15: $i] :
( ( !! @ $i
@ ^ [Y16: $i] :
( ( c_In @ Y16 @ Y15 )
=> ( Y13 @ Y16 @ ( Y14 @ Y16 ) ) ) )
=> ( Y13 @ Y15 @ ( Y10 @ Y15 @ Y14 ) ) ) ) )
=> ( Y13 @ Y11 @ Y12 ) ) )
@ Y7
@ Y8
@ Y9 ) )
@ ^ [Y7: $i,Y8: $i > $i] :
( ^ [Y9: $i,Y10: $i] :
( c_Union
@ ( ^ [Y11: $i,Y12: $i] :
( c_Repl @ sF14
@ ^ [Y13: $i] :
( ^ [Y14: $o,Y15: $i,Y16: $i] :
( c_Eps_i
@ ^ [Y17: $i] :
( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> Y20 )
=> ( ( Y19
=> Y20 )
=> Y20 ) ) )
@ ( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> ( Y19
=> Y20 ) )
=> Y20 ) )
@ Y14
@ ( Y15 = Y17 ) )
@ ( ^ [Y18: $o,Y19: $o] :
( !! @ $o
@ ^ [Y20: $o] :
( ( Y18
=> ( Y19
=> Y20 ) )
=> Y20 ) )
@ ( ^ [Y18: $o] :
( Y18
=> c_False )
@ Y14 )
@ ( Y16 = Y17 ) ) ) )
@ ( c_In @ c_Empty @ Y13 )
@ Y11
@ Y12 ) )
@ Y9
@ Y10 ) )
@ sF15
@ ( c_Repl @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y6 ) )
@ Y4 ) )
@ ( c_Repl @ Y3
@ ^ [Y4: $i] :
( ^ [Y5: $i > ( $i > $i ) > $i,Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( ^ [Y8: $i > ( $i > $i ) > $i,Y9: $i,Y10: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y11: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( !! @ $i
@ ^ [Y13: $i] :
( ( !! @ $i
@ ^ [Y14: $i] :
( ( c_In @ Y14 @ Y13 )
=> ( Y11 @ Y14 @ ( Y12 @ Y14 ) ) ) )
=> ( Y11 @ Y13 @ ( Y8 @ Y13 @ Y12 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) )
@ Y5
@ Y6
@ Y7 ) )
@ ^ [Y5: $i,Y6: $i > $i] :
( ^ [Y7: $i,Y8: $i] :
( c_Union
@ ( ^ [Y9: $i,Y10: $i] :
( c_Repl @ sF14
@ ^ [Y11: $i] :
( ^ [Y12: $o,Y13: $i,Y14: $i] :
( c_Eps_i
@ ^ [Y15: $i] :
( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> Y18 )
=> ( ( Y17
=> Y18 )
=> Y18 ) ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ Y12
@ ( Y13 = Y15 ) )
@ ( ^ [Y16: $o,Y17: $o] :
( !! @ $o
@ ^ [Y18: $o] :
( ( Y16
=> ( Y17
=> Y18 ) )
=> Y18 ) )
@ ( ^ [Y16: $o] :
( Y16
=> c_False )
@ Y12 )
@ ( Y14 = Y15 ) ) ) )
@ ( c_In @ c_Empty @ Y11 )
@ Y9
@ Y10 ) )
@ Y7
@ Y8 ) )
@ sF15
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( Y6 @ Y7 ) ) )
@ Y4 ) ) )
@ Y1
@ sF18 ) ) ) ) ) ),
inference(definition_folding,[],[f555,f574,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f566,f564,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f566,f564,f574,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f566,f564,f578,f568,f566,f564,f566,f564,f570,f568,f566,f564,f566,f564,f576,f574,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f566,f564,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f566,f564,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f566,f564,f572,f570,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f568,f566,f564,f566,f564,f566,f564,f570,f568,f566,f564,f566,f564]) ).
thf(f580,definition,
( sF21
= ( sK9
@ ^ [Y0: $i] : Y0
@ sF16 ) ),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
thf(f581,plain,
( ( sK9
@ ^ [Y0: $i] : Y0
@ sF16 )
= sF21 ),
inference(reorient_equations,[],[f580]) ).
thf(f582,plain,
$true = sF21,
inference(definition_folding,[],[f556,f581,f570,f568,f566,f564,f566,f564]) ).
thf(f644,plain,
! [X6: $i > $i > $i > $i,X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i] :
( ( $true
!= ( sK9
@ ^ [Y0: $i] : Y0
@ ( X6
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y0: $i] :
( c_Eps_i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( ( !! @ $o
@ ^ [Y3: $o] :
( ( ( c_In @ c_Empty @ Y0 )
=> ( ( ( c_Repl @ sF17
@ ^ [Y4: $i] :
( c_Repl @ Y4
@ ^ [Y5: $i] :
( c_Eps_i
@ ^ [Y6: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y8: $i > $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( !! @ $i
@ ^ [Y10: $i] :
( ( c_In @ Y10 @ Y9 )
=> ( Y7 @ Y10 @ ( Y8 @ Y10 ) ) ) )
=> ( Y7 @ Y9
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y10: $i] :
( c_Eps_i
@ ^ [Y11: $i] :
( !! @ $o
@ ^ [Y12: $o] :
( ( ( !! @ $o
@ ^ [Y13: $o] :
( ( ( c_In @ c_Empty @ Y10 )
=> ( ( sF15 = Y11 )
=> Y13 ) )
=> Y13 ) )
=> Y12 )
=> ( ( ( !! @ $o
@ ^ [Y13: $o] :
( ( ( ( c_In @ c_Empty @ Y10 )
=> c_False )
=> ( ( ( c_Repl @ Y9 @ Y8 )
= Y11 )
=> Y13 ) )
=> Y13 ) )
=> Y12 )
=> Y12 ) ) ) ) ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) )
= Y1 )
=> Y3 ) )
=> Y3 ) )
=> Y2 )
=> ( ( ( !! @ $o
@ ^ [Y3: $o] :
( ( ( ( c_In @ c_Empty @ Y0 )
=> c_False )
=> ( ( ( c_Repl @ ( X5 @ c_Empty @ c_Empty )
@ ^ [Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( !! @ $o
@ ^ [Y11: $o] :
( ( ( !! @ $o
@ ^ [Y12: $o] :
( ( ( c_In @ c_Empty @ Y9 )
=> ( ( sF15 = Y10 )
=> Y12 ) )
=> Y12 ) )
=> Y11 )
=> ( ( ( !! @ $o
@ ^ [Y12: $o] :
( ( ( ( c_In @ c_Empty @ Y9 )
=> c_False )
=> ( ( ( c_Repl @ Y8 @ Y7 )
= Y10 )
=> Y12 ) )
=> Y12 ) )
=> Y11 )
=> Y11 ) ) ) ) ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
= Y1 )
=> Y3 ) )
=> Y3 ) )
=> Y2 )
=> Y2 ) ) ) ) ) )
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y0: $i] :
( c_Eps_i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( ( !! @ $o
@ ^ [Y3: $o] :
( ( ( c_In @ c_Empty @ Y0 )
=> ( ( ( c_Repl @ sF19
@ ^ [Y4: $i] :
( c_Repl @ Y4
@ ^ [Y5: $i] :
( c_Eps_i
@ ^ [Y6: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y8: $i > $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( !! @ $i
@ ^ [Y10: $i] :
( ( c_In @ Y10 @ Y9 )
=> ( Y7 @ Y10 @ ( Y8 @ Y10 ) ) ) )
=> ( Y7 @ Y9
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y10: $i] :
( c_Eps_i
@ ^ [Y11: $i] :
( !! @ $o
@ ^ [Y12: $o] :
( ( ( !! @ $o
@ ^ [Y13: $o] :
( ( ( c_In @ c_Empty @ Y10 )
=> ( ( sF15 = Y11 )
=> Y13 ) )
=> Y13 ) )
=> Y12 )
=> ( ( ( !! @ $o
@ ^ [Y13: $o] :
( ( ( ( c_In @ c_Empty @ Y10 )
=> c_False )
=> ( ( ( c_Repl @ Y9 @ Y8 )
= Y11 )
=> Y13 ) )
=> Y13 ) )
=> Y12 )
=> Y12 ) ) ) ) ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) )
= Y1 )
=> Y3 ) )
=> Y3 ) )
=> Y2 )
=> ( ( ( !! @ $o
@ ^ [Y3: $o] :
( ( ( ( c_In @ c_Empty @ Y0 )
=> c_False )
=> ( ( ( c_Repl @ ( X6 @ sF16 @ sF20 @ sF18 )
@ ^ [Y4: $i] :
( c_Eps_i
@ ^ [Y5: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( !! @ $i
@ ^ [Y9: $i] :
( ( c_In @ Y9 @ Y8 )
=> ( Y6 @ Y9 @ ( Y7 @ Y9 ) ) ) )
=> ( Y6 @ Y8
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y9: $i] :
( c_Eps_i
@ ^ [Y10: $i] :
( !! @ $o
@ ^ [Y11: $o] :
( ( ( !! @ $o
@ ^ [Y12: $o] :
( ( ( c_In @ c_Empty @ Y9 )
=> ( ( sF15 = Y10 )
=> Y12 ) )
=> Y12 ) )
=> Y11 )
=> ( ( ( !! @ $o
@ ^ [Y12: $o] :
( ( ( ( c_In @ c_Empty @ Y9 )
=> c_False )
=> ( ( ( c_Repl @ Y8 @ Y7 )
= Y10 )
=> Y12 ) )
=> Y12 ) )
=> Y11 )
=> Y11 ) ) ) ) ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
= Y1 )
=> Y3 ) )
=> Y3 ) )
=> Y2 )
=> Y2 ) ) ) ) ) )
@ ( X4
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] :
( c_Union
@ ( c_Repl @ sF14
@ ^ [Y2: $i] :
( c_Eps_i
@ ^ [Y3: $i] :
( !! @ $o
@ ^ [Y4: $o] :
( ( ( !! @ $o
@ ^ [Y5: $o] :
( ( ( c_In @ c_Empty @ Y2 )
=> ( ( ( c_Repl @ Y1
@ ^ [Y6: $i] :
( c_Repl @ Y6
@ ^ [Y7: $i] :
( c_Eps_i
@ ^ [Y8: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y9: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( !! @ $i
@ ^ [Y11: $i] :
( ( !! @ $i
@ ^ [Y12: $i] :
( ( c_In @ Y12 @ Y11 )
=> ( Y9 @ Y12 @ ( Y10 @ Y12 ) ) ) )
=> ( Y9 @ Y11
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y12: $i] :
( c_Eps_i
@ ^ [Y13: $i] :
( !! @ $o
@ ^ [Y14: $o] :
( ( ( !! @ $o
@ ^ [Y15: $o] :
( ( ( c_In @ c_Empty @ Y12 )
=> ( ( sF15 = Y13 )
=> Y15 ) )
=> Y15 ) )
=> Y14 )
=> ( ( ( !! @ $o
@ ^ [Y15: $o] :
( ( ( ( c_In @ c_Empty @ Y12 )
=> c_False )
=> ( ( ( c_Repl @ Y11 @ Y10 )
= Y13 )
=> Y15 ) )
=> Y15 ) )
=> Y14 )
=> Y14 ) ) ) ) ) ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) ) )
= Y3 )
=> Y5 ) )
=> Y5 ) )
=> Y4 )
=> ( ( ( !! @ $o
@ ^ [Y5: $o] :
( ( ( ( c_In @ c_Empty @ Y2 )
=> c_False )
=> ( ( ( c_Repl @ sF18
@ ^ [Y6: $i] :
( c_Eps_i
@ ^ [Y7: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y8: $i > $i > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( !! @ $i
@ ^ [Y11: $i] :
( ( c_In @ Y11 @ Y10 )
=> ( Y8 @ Y11 @ ( Y9 @ Y11 ) ) ) )
=> ( Y8 @ Y10
@ ( c_Union
@ ( c_Repl @ sF14
@ ^ [Y11: $i] :
( c_Eps_i
@ ^ [Y12: $i] :
( !! @ $o
@ ^ [Y13: $o] :
( ( ( !! @ $o
@ ^ [Y14: $o] :
( ( ( c_In @ c_Empty @ Y11 )
=> ( ( sF15 = Y12 )
=> Y14 ) )
=> Y14 ) )
=> Y13 )
=> ( ( ( !! @ $o
@ ^ [Y14: $o] :
( ( ( ( c_In @ c_Empty @ Y11 )
=> c_False )
=> ( ( ( c_Repl @ Y10 @ Y9 )
= Y12 )
=> Y14 ) )
=> Y14 ) )
=> Y13 )
=> Y13 ) ) ) ) ) ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) ) )
= Y3 )
=> Y5 ) )
=> Y5 ) )
=> Y4 )
=> Y4 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( c_In @ sF16
@ ( X4
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) ),
inference(beta-eta_normalization,[],[f579]) ).
thf(f734,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
=> c_False ) ),
inference(beta-eta_normalization,[],[f551]) ).
thf(f735,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
= $false )
| ( c_False = $true ) ),
inference(imp_proxy_clausification,[],[f734]) ).
thf(f736,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty )
@ X1 ) )
| ( c_False = $true ) ),
inference(pi_proxy_clausification,[],[f735]) ).
thf(f737,plain,
! [X1: $i] :
( ( $false
= ( c_In @ X1 @ c_Empty ) )
| ( c_False = $true ) ),
inference(beta-eta_normalization,[],[f736]) ).
thf(f796,plain,
( ( $true
= ( sK9
@ ^ [Y0: $i] : Y0
@ sF16 ) )
| ( $false = sF21 ) ),
inference(iff_proxy_clausification,[],[f581]) ).
thf(f828,plain,
! [X1: $i] :
( $false
= ( c_In @ X1 @ c_Empty ) ),
inference(forward_subsumption_resolution,[],[f737,f460]) ).
thf(f829,plain,
( ( $true = $false )
| ( $true
= ( sK9
@ ^ [Y0: $i] : Y0
@ sF16 ) ) ),
inference(forward_demodulation,[],[f796,f582]) ).
thf(f830,plain,
( $true
= ( sK9
@ ^ [Y0: $i] : Y0
@ sF16 ) ),
inference(trivial_inequality_removal,[],[f829]) ).
thf(f1518,plain,
! [X1: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true != $true )
| ( $true
= ( c_In @ sF16
@ ( X1
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) ),
inference(constrained_superposition,[],[f644,f830]) ).
thf(f1519,plain,
! [X1: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( $true
= ( c_In @ sF16
@ ( X1
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ),
inference(trivial_inequality_removal,[],[f1518]) ).
thf(f1807,plain,
$true = $false,
inference(constrained_superposition,[],[f828,f1519]) ).
thf(f1851,plain,
$false,
inference(trivial_inequality_removal,[],[f1807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV529^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:55:11 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.58/1.05 % (3542599)Will run a generic schedule for satisfiability detection.
% 5.58/1.05 % (3542606)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3980709738:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.58/1.05 % (3542605)% WARNING: option uhcvi not known.
% 5.58/1.05 % (3542604)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3528821783_2999 on theBenchmark for (2999ds/0Mi)
% 5.58/1.05 % (3542607)dis+10_1_sil=32000:sp=arity:random_seed=1340177581:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.58/1.05 % (3542605)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2530278822:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.58/1.05 % (3542608)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1515163754:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.58/1.05 % (3542609)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2540344020:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.58/1.05 % (3542610)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4067006739:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.58/1.05 % (3542605)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.58/1.05 % (3542608)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.58/1.05 % (3542607)Instruction limit reached!
% 5.58/1.05 % (3542607)------------------------------
% 5.58/1.05 % (3542607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.05 % (3542607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.05 % (3542607)CaDiCaL version: 2.1.3
% 5.58/1.05 % (3542607)Termination reason: Instruction limit
% 5.58/1.05 % (3542607)Termination phase: Property scanning
% 5.58/1.05 % (3542607)Time elapsed: 0.042 s
% 5.58/1.05 % (3542607)Peak memory usage: 11 MB
% 5.58/1.05 % (3542607)Instructions burned: 104 (million)
% 5.58/1.05 % (3542608)Instruction limit reached!
% 5.58/1.05 % (3542608)------------------------------
% 5.58/1.05 % (3542608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.05 % (3542608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.05 % (3542608)CaDiCaL version: 2.1.3
% 5.58/1.05 % (3542608)Termination reason: Instruction limit
% 5.58/1.05 % (3542608)Termination phase: Property scanning
% 5.58/1.05 % (3542608)Time elapsed: 0.047 s
% 5.58/1.05 % (3542608)Peak memory usage: 11 MB
% 5.58/1.05 % (3542608)Instructions burned: 117 (million)
% 5.58/1.05 % (3542609)Instruction limit reached!
% 5.58/1.05 % (3542609)------------------------------
% 5.58/1.05 % (3542609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.05 % (3542609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.05 % (3542609)CaDiCaL version: 2.1.3
% 5.58/1.05 % (3542609)Termination reason: Instruction limit
% 5.58/1.05 % (3542609)Termination phase: Property scanning
% 5.58/1.05 % (3542609)Time elapsed: 0.052 s
% 5.58/1.05 % (3542609)Peak memory usage: 11 MB
% 5.58/1.05 % (3542609)Instructions burned: 131 (million)
% 5.58/1.05 % (3542610)Instruction limit reached!
% 5.58/1.05 % (3542610)------------------------------
% 5.58/1.05 % (3542610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.05 % (3542610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.05 % (3542610)CaDiCaL version: 2.1.3
% 5.58/1.05 % (3542610)Termination reason: Instruction limit
% 5.58/1.05 % (3542610)Termination phase: Property scanning
% 5.58/1.05 % (3542610)Time elapsed: 0.063 s
% 5.58/1.05 % (3542610)Peak memory usage: 11 MB
% 5.58/1.05 % (3542610)Instructions burned: 160 (million)
% 5.58/1.05 % (3542619)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2928327542:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.58/1.05 % (3542618)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3198971589:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.58/1.05 % (3542620)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=597017014:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.58/1.05 % Exception at run slice level
% 5.58/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.58/1.05 % (3542605)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.76/1.44 % (3542621)ott-21_1_sil=16000:fs=off:random_seed=3280945054:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 7.76/1.44 % (3542620)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.76/1.44 % (3542625)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2535843562:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 7.76/1.44 % (3542619)Instruction limit reached!
% 7.76/1.44 % (3542619)------------------------------
% 7.76/1.44 % (3542619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542619)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542619)Termination reason: Instruction limit
% 7.76/1.44 % (3542619)Termination phase: Property scanning
% 7.76/1.44 % (3542619)Time elapsed: 0.052 s
% 7.76/1.44 % (3542619)Peak memory usage: 11 MB
% 7.76/1.44 % (3542619)Instructions burned: 132 (million)
% 7.76/1.44 % (3542628)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1030708368:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 7.76/1.44 % (3542620)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.76/1.44 % (3542621)Instruction limit reached!
% 7.76/1.44 % (3542621)------------------------------
% 7.76/1.44 % (3542621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542621)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542621)Termination reason: Instruction limit
% 7.76/1.44 % (3542621)Termination phase: Property scanning
% 7.76/1.44 % (3542621)Time elapsed: 0.070 s
% 7.76/1.44 % (3542621)Peak memory usage: 11 MB
% 7.76/1.44 % (3542621)Instructions burned: 180 (million)
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542630)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4265250564:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 7.76/1.44 % (3542631)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3981226176:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542634)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=228551275:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 7.76/1.44 % (3542634)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.76/1.44 % (3542625)Instruction limit reached!
% 7.76/1.44 % (3542625)------------------------------
% 7.76/1.44 % (3542625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542625)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542625)Termination reason: Instruction limit
% 7.76/1.44 % (3542625)Termination phase: Saturation
% 7.76/1.44 % (3542625)Time elapsed: 0.190 s
% 7.76/1.44 % (3542625)Peak memory usage: 12 MB
% 7.76/1.44 % (3542625)Instructions burned: 477 (million)
% 7.76/1.44 % (3542636)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3339848121:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 7.76/1.44 % (3542636)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542620)Instruction limit reached!
% 7.76/1.44 % (3542620)------------------------------
% 7.76/1.44 % (3542620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542620)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542620)Termination reason: Instruction limit
% 7.76/1.44 % (3542620)Termination phase: Saturation
% 7.76/1.44 % (3542620)Time elapsed: 0.275 s
% 7.76/1.44 % (3542620)Peak memory usage: 15 MB
% 7.76/1.44 % (3542620)Instructions burned: 686 (million)
% 7.76/1.44 % (3542638)fmb+10_1_sil=64000:random_seed=2921163567:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 7.76/1.44 % (3542639)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2635161650:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 7.76/1.44 % (3542638)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542642)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3507738806:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 7.76/1.44 % (3542643)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3575741095:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 7.76/1.44 % (3542643)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.76/1.44 % (3542634)Instruction limit reached!
% 7.76/1.44 % (3542634)------------------------------
% 7.76/1.44 % (3542634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542634)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542634)Termination reason: Instruction limit
% 7.76/1.44 % (3542634)Termination phase: Saturation
% 7.76/1.44 % (3542634)Time elapsed: 0.279 s
% 7.76/1.44 % (3542634)Peak memory usage: 17 MB
% 7.76/1.44 % (3542634)Instructions burned: 693 (million)
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542646)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1504694025:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 7.76/1.44 % (3542646)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.76/1.44 % (3542646)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.76/1.44 % (3542647)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=318694303:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542650)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1526639812:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 7.76/1.44 % (3542636)Instruction limit reached!
% 7.76/1.44 % (3542636)------------------------------
% 7.76/1.44 % (3542636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542636)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542636)Termination reason: Instruction limit
% 7.76/1.44 % (3542636)Termination phase: Saturation
% 7.76/1.44 % (3542636)Time elapsed: 0.359 s
% 7.76/1.44 % (3542636)Peak memory usage: 15 MB
% 7.76/1.44 % (3542636)Instructions burned: 882 (million)
% 7.76/1.44 % (3542652)ott-2_1_sil=16000:newcnf=on:random_seed=1543319639:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 7.76/1.44 % (3542630)Instruction limit reached!
% 7.76/1.44 % (3542630)------------------------------
% 7.76/1.44 % (3542630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542630)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542630)Termination reason: Instruction limit
% 7.76/1.44 % (3542630)Termination phase: Saturation
% 7.76/1.44 % (3542630)Time elapsed: 0.508 s
% 7.76/1.44 % (3542630)Peak memory usage: 19 MB
% 7.76/1.44 % (3542630)Instructions burned: 1180 (million)
% 7.76/1.44 % (3542652)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.76/1.44 % (3542654)ott+10_1_sil=32000:tgt=ground:random_seed=3602046643:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542656)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2843413038:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 7.76/1.44 % Exception at run slice level
% 7.76/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.76/1.44 % (3542658)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3739013393:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 7.76/1.44 % (3542658)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.76/1.44 % (3542652)Instruction limit reached!
% 7.76/1.44 % (3542652)------------------------------
% 7.76/1.44 % (3542652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.44 % (3542652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.44 % (3542652)CaDiCaL version: 2.1.3
% 7.76/1.44 % (3542652)Termination reason: Instruction limit
% 7.76/1.44 % (3542652)Termination phase: Saturation
% 7.76/1.44 % (3542652)Time elapsed: 0.355 s
% 7.76/1.44 % (3542652)Peak memory usage: 16 MB
% 7.76/1.44 % (3542652)Instructions burned: 871 (million)
% 7.76/1.44 % (3542660)dis+21_1_sil=32000:sas=cadical:random_seed=269653774:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 7.76/1.44 % (3542654) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3542599-3542654"...
% 7.76/1.44 % (3542654)...printing done.
% 7.76/1.44 % (3542654)Refutation found. Thanks to Tanya!
% 7.76/1.44 % SZS status Theorem for theBenchmark
% 7.76/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 7.76/1.45 % (3542654)------------------------------
% 7.76/1.45 % (3542654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.45 % (3542654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.45 % (3542654)CaDiCaL version: 2.1.3
% 7.76/1.45 % (3542654)Termination reason: Refutation
% 7.76/1.45 % (3542654)Time elapsed: 0.455 s
% 7.76/1.45 % (3542654)Peak memory usage: 18 MB
% 7.76/1.45 % (3542654)Instructions burned: 1085 (million)
% 7.76/1.45 % (3542599)Success in time 1.204 s
% 7.76/1.45 % Vampire exiting
%------------------------------------------------------------------------------