%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV524^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:38:47 AM UTC 2026
% Result : Theorem 42.84s 6.51s
% Output : Refutation 42.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 8
% Syntax : Number of formulae : 136 ( 40 unt; 0 typ; 4 def)
% Number of atoms : 6914 ( 390 equ; 0 cnn)
% Maximal formula atoms : 88 ( 50 avg)
% Number of connectives : 31438 ( 192 ~; 348 |; 0 &;28899 @)
% ( 4 <=>; 926 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10629 (10629 >; 0 *; 0 +; 0 <<)
% Number of symbols : 166 ( 162 usr; 14 con; 0-14 aty)
% (1069 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 7952 (3694 sgn 297 !; 0 ?;7952 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c_Eps_i: ( $i > $o ) > $i ).
thf(func_def_1,type,
c_False: $o ).
thf(func_def_2,type,
c_True: $o ).
thf(func_def_3,type,
c_not: $o > $o ).
thf(func_def_4,type,
c_and: $o > $o > $o ).
thf(func_def_5,type,
c_or: $o > $o > $o ).
thf(func_def_6,type,
c_iff: $o > $o > $o ).
thf(func_def_7,type,
c_In: $i > $i > $o ).
thf(func_def_8,type,
c_Subq: $i > $i > $o ).
thf(func_def_10,type,
c_Union: $i > $i ).
thf(func_def_11,type,
c_Power: $i > $i ).
thf(func_def_12,type,
c_Repl: $i > ( $i > $i ) > $i ).
thf(func_def_13,type,
c_TransSet: $i > $o ).
thf(func_def_14,type,
c_atleast2: $i > $o ).
thf(func_def_15,type,
c_atleast3: $i > $o ).
thf(func_def_16,type,
c_atleast4: $i > $o ).
thf(func_def_17,type,
c_atleast5: $i > $o ).
thf(func_def_18,type,
c_atleast6: $i > $o ).
thf(func_def_19,type,
c_exactly2: $i > $o ).
thf(func_def_20,type,
c_exactly3: $i > $o ).
thf(func_def_21,type,
c_exactly4: $i > $o ).
thf(func_def_22,type,
c_exactly5: $i > $o ).
thf(func_def_23,type,
c_exu_i: ( $i > $o ) > $o ).
thf(func_def_24,type,
c_reflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
c_irreflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
c_symmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
c_antisymmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
c_transitive_i: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
c_eqreln_i: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
c_per_i: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
c_linear_i: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
c_partialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_34,type,
c_totalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_37,type,
c_If_i: $o > $i > $i > $i ).
thf(func_def_38,type,
c_exactly1of2: $o > $o > $o ).
thf(func_def_39,type,
c_exactly1of3: $o > $o > $o > $o ).
thf(func_def_40,type,
c_nIn: $i > $i > $o ).
thf(func_def_41,type,
c_nSubq: $i > $i > $o ).
thf(func_def_42,type,
c_UPair: $i > $i > $i ).
thf(func_def_43,type,
c_Sing: $i > $i ).
thf(func_def_44,type,
c_binunion: $i > $i > $i ).
thf(func_def_45,type,
c_SetAdjoin: $i > $i > $i ).
thf(func_def_46,type,
c_famunion: $i > ( $i > $i ) > $i ).
thf(func_def_47,type,
c_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_49,type,
c_binintersect: $i > $i > $i ).
thf(func_def_50,type,
c_setminus: $i > $i > $i ).
thf(func_def_51,type,
c_inj: $i > $i > ( $i > $i ) > $o ).
thf(func_def_52,type,
c_bij: $i > $i > ( $i > $i ) > $o ).
thf(func_def_53,type,
c_atleastp: $i > $i > $o ).
thf(func_def_54,type,
c_equip: $i > $i > $o ).
thf(func_def_55,type,
c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_56,type,
c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_57,type,
c_ordsucc: $i > $i ).
thf(func_def_58,type,
c_nat_p: $i > $o ).
thf(func_def_59,type,
c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
thf(func_def_60,type,
c_add_nat: $i > $i > $i ).
thf(func_def_61,type,
c_mul_nat: $i > $i > $i ).
thf(func_def_62,type,
c_ordinal: $i > $o ).
thf(func_def_63,type,
c_V_: $i > $i ).
thf(func_def_64,type,
c_Inj1: $i > $i ).
thf(func_def_65,type,
c_Inj0: $i > $i ).
thf(func_def_66,type,
c_Unj: $i > $i ).
thf(func_def_67,type,
c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_68,type,
c_setsum: $i > $i > $i ).
thf(func_def_69,type,
c_proj0: $i > $i ).
thf(func_def_70,type,
c_proj1: $i > $i ).
thf(func_def_71,type,
c_binrep: $i > $i > $i ).
thf(func_def_72,type,
c_lam: $i > ( $i > $i ) > $i ).
thf(func_def_73,type,
c_setprod: $i > $i > $i ).
thf(func_def_74,type,
c_ap: $i > $i > $i ).
thf(func_def_75,type,
c_setsum_p: $i > $o ).
thf(func_def_76,type,
c_tuple_p: $i > $i > $o ).
thf(func_def_77,type,
c_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_78,type,
c_setexp: $i > $i > $i ).
thf(func_def_79,type,
c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
c_set_of_pairs: $i > $o ).
thf(func_def_81,type,
c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_82,type,
c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_83,type,
c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_84,type,
c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_85,type,
c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_86,type,
c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_87,type,
c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_88,type,
c_SNoElts_: $i > $i ).
thf(func_def_89,type,
c_SNo_: $i > $i > $o ).
thf(func_def_90,type,
c_PSNo: $i > ( $i > $o ) > $i ).
thf(func_def_91,type,
c_SNo: $i > $o ).
thf(func_def_92,type,
c_SNoLev: $i > $i ).
thf(func_def_93,type,
c_SNoEq_: $i > $i > $i > $o ).
thf(func_def_94,type,
c_SNoLt: $i > $i > $o ).
thf(func_def_95,type,
c_SNoLe: $i > $i > $o ).
thf(func_def_96,type,
c_binop_on: $i > ( $i > $i > $i ) > $o ).
thf(func_def_97,type,
c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
thf(func_def_98,type,
c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_99,type,
c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_100,type,
c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_101,type,
c_combinator: $i > $o ).
thf(func_def_102,type,
c_combinator_equiv: $i > $i > $o ).
thf(func_def_103,type,
c_equip_mod: $i > $i > $i > $o ).
thf(func_def_105,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_106,type,
vIMP: $o > $o > $o ).
thf(func_def_107,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_108,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_109,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_110,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_111,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_112,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_115,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_116,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_117,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_118,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_120,type,
db13:
!>[X0: $tType] : X0 ).
thf(func_def_121,type,
db12:
!>[X0: $tType] : X0 ).
thf(func_def_122,type,
db11:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
db10:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db14:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db15:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db16:
!>[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,
vNOT: $o > $o ).
thf(func_def_132,type,
sK0: $o ).
thf(func_def_133,type,
sK1: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i > $i ).
thf(func_def_134,type,
sK2: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_138,type,
sK6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i ).
thf(func_def_139,type,
sK7: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > $i ).
thf(func_def_140,type,
sK8: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > $i ).
thf(func_def_141,type,
sK9: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i ).
thf(func_def_142,type,
sK10: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_143,type,
sK11: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i ).
thf(func_def_144,type,
sK12: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > ( ( ( $i > $i ) > $i > $i ) > $i ) > $i ).
thf(func_def_145,type,
sK13: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_146,type,
sK14: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i ).
thf(func_def_147,type,
sK15: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > $i ).
thf(func_def_148,type,
sK16: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i > $i ).
thf(func_def_149,type,
sK17: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_151,type,
sK19: $i > $i ).
thf(func_def_152,type,
sK20: $i > $i > $i ).
thf(func_def_153,type,
sK21: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i ).
thf(func_def_154,type,
sK22: ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o ) > ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o ) > $i ).
thf(func_def_157,type,
sK25: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i ).
thf(func_def_158,type,
sK26: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > $i > ( ( $i > $i ) > $i > $i ) > $i ).
thf(func_def_159,type,
sK27: ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o ) > ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i ).
thf(func_def_160,type,
sK28: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i ).
thf(func_def_161,type,
sK29: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i ).
thf(func_def_162,type,
sK30: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o ) > $i ).
thf(f13,axiom,
( ( ^ [X0: $o] :
( X0
=> c_False ) )
= c_not ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
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,
( ( ^ [X0: $i,X1: $i] :
( c_binunion
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
@ ( c_Repl @ X1
@ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) )
= c_setsum ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(f109,conjecture,
( c_not
@ ! [X1: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X0: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X2: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( ! [X7: $i,X4: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i,X6: $i,X5: $i] :
( ( c_In @ ( c_Inj0 @ X6 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ X6 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X2
@ ^ [X8: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum
@ ( X4
@ ^ [X8: $i > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : ( c_Inj0 @ X8 )
@ X5
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( ! [X4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X6: $i,X5: $i > $i,X7: $i] :
( ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : c_Empty
@ X7
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : X7
@ ( c_setsum
@ ( X4
@ ^ [X8: ( $i > $i ) > $i > $i] : X7 )
@ X6 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ! [X5: $i > ( ( $i > $i ) > $i > $i ) > $i,X7: $i,X6: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i,X4: $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( c_setsum @ c_Empty
@ ( X5 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ c_Empty ) ) ) )
=> ( ( X0
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : X8
@ X7
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj1 @ c_Empty )
@ ^ [X8: $i,X9: $i] : c_Empty ) )
=> ( X2
@ ^ [X8: $i] : X8
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ c_Empty )
@ ^ [X8: $i,X9: $i] : X9 ) ) ) ) )
=> ( ! [X7: $i > $i,X4: $i > $i > $i,X5: $i > $i,X6: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( X4 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X2
@ ^ [X8: $i] : c_Empty
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ X6 ) ) )
=> ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( X4 @ c_Empty @ ( X5 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X7: $i,X5: $i > $i,X6: $i > $i,X4: $i] :
( ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] :
( X9
@ ^ [X10: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ! [X5: $i,X7: $i,X4: $i,X6: $i] :
( ( c_In @ ( c_Inj0 @ X6 ) @ ( c_setsum @ ( c_setsum @ X4 @ ( c_setsum @ X5 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ X5 @ c_Empty ) ) ) )
=> ( ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : X7
@ c_Empty )
=> ( X2
@ ^ [X8: $i] : c_Empty
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ X5 ) ) )
=> ( ! [X5: $i,X6: $i,X7: $i,X4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ X5 )
=> ( ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X0
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( X4
@ ^ [X8: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) )
=> ( ! [X7: $i,X5: $i,X4: $i > $i,X6: $i > $i] :
( ( X0
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : c_Empty
@ ( X4 @ c_Empty )
@ X7 )
=> c_False )
=> c_False ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f110,negated_conjecture,
~ ( c_not
@ ! [X1: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X0: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X2: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( ! [X7: $i,X4: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i,X6: $i,X5: $i] :
( ( c_In @ ( c_Inj0 @ X6 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ X6 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X2
@ ^ [X8: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum
@ ( X4
@ ^ [X8: $i > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : ( c_Inj0 @ X8 )
@ X5
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( ! [X4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X6: $i,X5: $i > $i,X7: $i] :
( ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : c_Empty
@ X7
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : X7
@ ( c_setsum
@ ( X4
@ ^ [X8: ( $i > $i ) > $i > $i] : X7 )
@ X6 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ! [X5: $i > ( ( $i > $i ) > $i > $i ) > $i,X7: $i,X6: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i,X4: $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( c_setsum @ c_Empty
@ ( X5 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ c_Empty ) ) ) )
=> ( ( X0
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : X8
@ X7
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj1 @ c_Empty )
@ ^ [X8: $i,X9: $i] : c_Empty ) )
=> ( X2
@ ^ [X8: $i] : X8
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : X10
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( X6
@ ^ [X8: ( $i > $i ) > $i > $i,X9: $i > $i,X10: $i] : ( c_Inj0 @ c_Empty )
@ ^ [X8: $i,X9: $i] : X9 ) ) ) ) )
=> ( ! [X7: $i > $i,X4: $i > $i > $i,X5: $i > $i,X6: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( X4 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X2
@ ^ [X8: $i] : c_Empty
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ X6 ) ) )
=> ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( X4 @ c_Empty @ ( X5 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X7: $i,X5: $i > $i,X6: $i > $i,X4: $i] :
( ( X3
@ ^ [X8: $i,X9: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] :
( X9
@ ^ [X10: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ! [X5: $i,X7: $i,X4: $i,X6: $i] :
( ( c_In @ ( c_Inj0 @ X6 ) @ ( c_setsum @ ( c_setsum @ X4 @ ( c_setsum @ X5 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ X5 @ c_Empty ) ) ) )
=> ( ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : X7
@ c_Empty )
=> ( X2
@ ^ [X8: $i] : c_Empty
@ ^ [X8: ( ( $i > $i ) > $i ) > $i,X9: $i > $i > $i,X10: $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ X5 ) ) )
=> ( ! [X5: $i,X6: $i,X7: $i,X4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ X5 )
=> ( ( X1
@ ^ [X8: $i,X9: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X0
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( X4
@ ^ [X8: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) )
=> ( ! [X7: $i,X5: $i,X4: $i > $i,X6: $i > $i] :
( ( X0
@ ^ [X8: $i,X9: $i,X10: ( $i > $i ) > $i > $i] : c_Empty
@ ( X4 @ c_Empty )
@ X7 )
=> c_False )
=> c_False ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
thf(f161,plain,
( ( ^ [X0: $o] :
( X0
=> c_False ) )
= c_not ),
inference(rectify,[],[f13]) ).
thf(f162,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(fool_elimination,[],[f161]) ).
thf(f194,plain,
( c_Inj0
= ( ^ [X0: $i] :
( c_Repl @ X0
@ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f195,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f194]) ).
thf(f260,plain,
( ( ^ [X0: $i,X1: $i] :
( c_binunion
@ ( c_Repl @ X0
@ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
@ ( c_Repl @ X1
@ ^ [X3: $i] : ( c_Inj1 @ X3 ) ) ) )
= c_setsum ),
inference(rectify,[],[f73]) ).
thf(f261,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,[],[f260]) ).
thf(f292,plain,
~ ( c_not
@ ! [X0: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X1: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( ! [X5: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i,X6: $i,X7: $i] :
( ( c_In @ ( c_Inj0 @ X6 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ X6 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X3
@ ^ [X8: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [X9: ( ( $i > $i ) > $i ) > $i,X10: $i > $i > $i,X11: $i,X12: $i] : X11
@ ( c_setsum
@ ( X5
@ ^ [X13: $i > $i > $i,X14: $i > $i,X15: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( X2
@ ^ [X16: $i,X17: $i > $i > $i] : ( c_Inj0 @ X16 )
@ X7
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( ! [X18: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i,X19: $i,X21: $i] :
( ( X2
@ ^ [X22: $i,X23: $i > $i > $i] : c_Empty
@ X21
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( X2
@ ^ [X24: $i,X25: $i > $i > $i] : X21
@ ( c_setsum
@ ( X18
@ ^ [X26: ( $i > $i ) > $i > $i] : X21 )
@ X19 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ! [X27: $i > ( ( $i > $i ) > $i > $i ) > $i,X28: $i,X29: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( c_setsum @ c_Empty
@ ( X27 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [X31: $i > $i,X32: $i] : ( c_Inj0 @ c_Empty ) ) ) )
=> ( ( X1
@ ^ [X33: $i,X34: $i,X35: ( $i > $i ) > $i > $i] : X33
@ X28
@ ( X29
@ ^ [X36: ( $i > $i ) > $i > $i,X37: $i > $i,X38: $i] : ( c_Inj1 @ c_Empty )
@ ^ [X39: $i,X40: $i] : c_Empty ) )
=> ( X3
@ ^ [X41: $i] : X41
@ ^ [X42: ( ( $i > $i ) > $i ) > $i,X43: $i > $i > $i,X44: $i,X45: $i] : X44
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( X29
@ ^ [X46: ( $i > $i ) > $i > $i,X47: $i > $i,X48: $i] : ( c_Inj0 @ c_Empty )
@ ^ [X49: $i,X50: $i] : X50 ) ) ) ) )
=> ( ! [X52: $i > $i > $i,X53: $i > $i,X54: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( X52 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X3
@ ^ [X55: $i] : c_Empty
@ ^ [X56: ( ( $i > $i ) > $i ) > $i,X57: $i > $i > $i,X58: $i,X59: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ X54 ) ) )
=> ( X0
@ ^ [X60: $i,X61: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( X52 @ c_Empty @ ( X53 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ( ( X2
@ ^ [X66: $i,X67: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X0
@ ^ [X68: $i,X69: ( $i > $i ) > $i] :
( X69
@ ^ [X70: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ! [X71: $i,X72: $i,X73: $i,X74: $i] :
( ( c_In @ ( c_Inj0 @ X74 ) @ ( c_setsum @ ( c_setsum @ X73 @ ( c_setsum @ X71 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ X71 @ c_Empty ) ) ) )
=> ( ( X0
@ ^ [X75: $i,X76: ( $i > $i ) > $i] : X72
@ c_Empty )
=> ( X3
@ ^ [X77: $i] : c_Empty
@ ^ [X78: ( ( $i > $i ) > $i ) > $i,X79: $i > $i > $i,X80: $i,X81: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ X71 ) ) )
=> ( ! [X82: $i,X85: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ X82 )
=> ( ( X0
@ ^ [X86: $i,X87: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X1
@ ^ [X88: $i,X89: $i,X90: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( X85
@ ^ [X91: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) )
=> ( ! [X92: $i,X94: $i > $i] :
( ( X1
@ ^ [X96: $i,X97: $i,X98: ( $i > $i ) > $i > $i] : c_Empty
@ ( X94 @ c_Empty )
@ X92 )
=> c_False )
=> c_False ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f293,plain,
( ( ~ ( c_not
@ ( !! @ ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o )
@ ^ [Y0: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y3: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Inj0 @ Y5 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ Y5 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_setsum
@ ( Y6
@ ^ [Y7: $i > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : ( c_Inj0 @ Y7 )
@ Y4
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : c_Empty
@ Y4
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : Y4
@ ( c_setsum
@ ( Y6
@ ^ [Y7: ( $i > $i ) > $i > $i] : Y4 )
@ Y5 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( c_setsum @ c_Empty
@ ( Y6 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [Y7: $i > $i,Y8: $i] : ( c_Inj0 @ c_Empty ) ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: $i,Y9: ( $i > $i ) > $i > $i] : Y7
@ Y5
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : c_Empty ) )
=> ( Y0
@ ^ [Y7: $i] : Y7
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj0 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : Y8 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y6: $i > $i > $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( Y6 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ Y4 ) ) )
=> ( Y3
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( Y6 @ c_Empty @ ( Y5 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( ( Y1
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y3
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] :
( Y5
@ ^ [Y6: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_Inj0 @ Y4 ) @ ( c_setsum @ ( c_setsum @ Y5 @ ( c_setsum @ Y7 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ Y7 @ c_Empty ) ) ) )
=> ( ( Y3
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i] : Y6
@ c_Empty )
=> ( Y0
@ ^ [Y8: $i] : c_Empty
@ ^ [Y8: ( ( $i > $i ) > $i ) > $i,Y9: $i > $i > $i,Y10: $i,Y11: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ Y7 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y5 )
=> ( ( Y3
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y4 @ c_Empty )
@ Y5 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f292]) ).
thf(f313,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,[],[f261]) ).
thf(f315,plain,
( c_Inj0
= ( ^ [Y0: $i] :
( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Inj1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f195]) ).
thf(f316,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(cnf_transformation,[],[f162]) ).
thf(f319,plain,
( ( ~ ( c_not
@ ( !! @ ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o )
@ ^ [Y0: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y3: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Inj0 @ Y5 ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ Y5 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_setsum
@ ( Y6
@ ^ [Y7: $i > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : ( c_Inj0 @ Y7 )
@ Y4
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ c_Empty ) ) @ c_Empty ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : c_Empty
@ Y4
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : Y4
@ ( c_setsum
@ ( Y6
@ ^ [Y7: ( $i > $i ) > $i > $i] : Y4 )
@ Y5 )
@ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( c_setsum @ c_Empty
@ ( Y6 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [Y7: $i > $i,Y8: $i] : ( c_Inj0 @ c_Empty ) ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: $i,Y9: ( $i > $i ) > $i > $i] : Y7
@ Y5
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : c_Empty ) )
=> ( Y0
@ ^ [Y7: $i] : Y7
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj0 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : Y8 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y6: $i > $i > $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( Y6 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) ) @ ( c_Inj1 @ Y4 ) ) )
=> ( Y3
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : ( c_Inj0 @ c_Empty )
@ ( Y6 @ c_Empty @ ( Y5 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( ( Y1
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y3
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] :
( Y5
@ ^ [Y6: $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_Inj0 @ Y4 ) @ ( c_setsum @ ( c_setsum @ Y5 @ ( c_setsum @ Y7 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_Inj1 @ ( c_setsum @ Y7 @ c_Empty ) ) ) )
=> ( ( Y3
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i] : Y6
@ c_Empty )
=> ( Y0
@ ^ [Y8: $i] : c_Empty
@ ^ [Y8: ( ( $i > $i ) > $i ) > $i,Y9: $i > $i > $i,Y10: $i,Y11: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ Y7 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y5 )
=> ( ( Y3
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y4 @ c_Empty )
@ Y5 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f293]) ).
thf(f322,plain,
( c_setsum
= ( ^ [Y0: $i,Y1: $i] :
( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] :
( ^ [Y3: $i] :
( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Inj1 @ Y4 ) )
@ Y2 ) )
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Inj1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f313,f315]) ).
thf(f326,plain,
( $true
= ( ~ ( ^ [Y0: $o] :
( Y0
=> c_False )
@ ( !! @ ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o )
@ ^ [Y0: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y3: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ Y5 )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ Y5
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) ) ) ) )
=> ( ( Y0
@ ^ [Y7: $i] :
( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ c_Empty ) )
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( Y6
@ ^ [Y7: $i > $i > $i,Y8: $i > $i,Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ ( ^ [Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ Y10
@ ^ [Y12: $i] :
( ^ [Y13: $i] :
( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) )
@ Y12 ) )
@ ( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ c_Empty ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ Y7 )
@ Y4
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty ) )
@ c_Empty ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : c_Empty
@ Y4
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( c_Inj1
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) ) ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : Y4
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( Y6
@ ^ [Y7: ( $i > $i ) > $i > $i] : Y4 )
@ Y5 )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ ( c_Inj1
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( Y6
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) )
@ ^ [Y7: $i > $i,Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ c_Empty ) ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: $i,Y9: ( $i > $i ) > $i > $i] : Y7
@ Y5
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : c_Empty ) )
=> ( Y0
@ ^ [Y7: $i] : Y7
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty )
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ c_Empty )
@ ^ [Y7: $i,Y8: $i] : Y8 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y6: $i > $i > $i] :
( ( c_In
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ ( c_Inj1 @ c_Empty ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty )
@ ( Y6 @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty )
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty ) ) )
@ ( c_Inj1 @ Y4 ) ) )
=> ( Y3
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ c_Empty )
@ ( Y6 @ c_Empty
@ ( Y5
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( c_Inj1 @ c_Empty )
@ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( ( Y1
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y3
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] :
( Y5
@ ^ [Y6: $i] :
( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ ( c_Inj1
@ ( ^ [Y7: $i] :
( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) )
@ c_Empty ) )
@ ( ^ [Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y9: $i] :
( ^ [Y10: $i] :
( c_Repl @ Y10
@ ^ [Y11: $i] : ( c_Inj1 @ Y11 ) )
@ Y9 ) )
@ ( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In
@ ( ^ [Y8: $i] :
( c_Repl @ Y8
@ ^ [Y9: $i] : ( c_Inj1 @ Y9 ) )
@ Y4 )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ Y5
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ Y7
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ c_Empty
@ c_Empty ) ) )
@ ( c_Inj1
@ ( ^ [Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ Y8
@ ^ [Y10: $i] :
( ^ [Y11: $i] :
( c_Repl @ Y11
@ ^ [Y12: $i] : ( c_Inj1 @ Y12 ) )
@ Y10 ) )
@ ( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) ) )
@ Y7
@ c_Empty ) ) ) )
=> ( ( Y3
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i] : Y6
@ c_Empty )
=> ( Y0
@ ^ [Y8: $i] : c_Empty
@ ^ [Y8: ( ( $i > $i ) > $i ) > $i,Y9: $i > $i > $i,Y10: $i,Y11: $i] :
( ^ [Y12: $i,Y13: $i] :
( c_binunion
@ ( c_Repl @ Y12
@ ^ [Y14: $i] :
( ^ [Y15: $i] :
( c_Repl @ Y15
@ ^ [Y16: $i] : ( c_Inj1 @ Y16 ) )
@ Y14 ) )
@ ( c_Repl @ Y13
@ ^ [Y14: $i] : ( c_Inj1 @ Y14 ) ) )
@ c_Empty
@ c_Empty )
@ Y7 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y5 )
=> ( ( Y3
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( ^ [Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ Y8 ) )
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) ) )
@ ( ^ [Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y8: $i] :
( ^ [Y9: $i] :
( c_Repl @ Y9
@ ^ [Y10: $i] : ( c_Inj1 @ Y10 ) )
@ Y8 ) )
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Inj1 @ Y8 ) ) )
@ ( ^ [Y6: $i] :
( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) )
@ c_Empty )
@ c_Empty )
@ ( c_Inj1
@ ( ^ [Y6: $i] :
( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Inj1 @ Y7 ) )
@ c_Empty ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y4 @ c_Empty )
@ Y5 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f319,f316,f315,f322,f322,f322,f315,f322,f315,f315,f322,f315,f322,f315,f322,f322,f322,f322,f315,f322,f322,f322,f322,f322,f322,f315,f322,f322,f322,f315,f322,f322,f322,f315,f322,f315,f322,f315,f322,f315,f315,f315,f322,f322,f315,f322,f322,f322,f322,f322,f315,f322,f322,f322,f322,f315,f315,f322,f322,f315,f322,f315,f322,f322,f322,f322,f322,f322,f322,f322,f315,f315]) ).
thf(f331,plain,
( $true
= ( ~ ( ( !! @ ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o )
@ ^ [Y0: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y3: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i > $i > $i,Y8: $i > $i,Y9: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : ( c_Repl @ Y7 @ c_Inj1 )
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : c_Empty
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: ( $i > $i ) > $i > $i] : Y4 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y7: $i > $i,Y8: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: $i,Y9: ( $i > $i ) > $i > $i] : Y7
@ Y5
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : c_Empty ) )
=> ( Y0
@ ^ [Y7: $i] : Y7
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i,Y8: $i] : Y8 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y6: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( Y6 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y4 ) @ c_Inj1 ) ) )
=> ( Y3
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y6 @ c_Empty
@ ( Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( Y1
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y3
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y3
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i] : Y6
@ c_Empty )
=> ( Y0
@ ^ [Y8: $i] : c_Empty
@ ^ [Y8: ( ( $i > $i ) > $i ) > $i,Y9: $i > $i > $i,Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y12: $i] : ( c_Repl @ Y12 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y7 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y5 )
=> ( ( Y3
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y4 @ c_Empty )
@ Y5 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) )
=> c_False ) ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f332,plain,
( ( ( !! @ ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o )
@ ^ [Y0: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y3: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i > $i > $i,Y8: $i > $i,Y9: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : ( c_Repl @ Y7 @ c_Inj1 )
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : c_Empty
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: ( $i > $i ) > $i > $i] : Y4 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y7: $i > $i,Y8: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: $i,Y9: ( $i > $i ) > $i > $i] : Y7
@ Y5
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : c_Empty ) )
=> ( Y0
@ ^ [Y7: $i] : Y7
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i,Y8: $i] : Y8 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y6: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( Y6 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y4 ) @ c_Inj1 ) ) )
=> ( Y3
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y6 @ c_Empty
@ ( Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( Y1
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y3
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y3
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i] : Y6
@ c_Empty )
=> ( Y0
@ ^ [Y8: $i] : c_Empty
@ ^ [Y8: ( ( $i > $i ) > $i ) > $i,Y9: $i > $i > $i,Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y12: $i] : ( c_Repl @ Y12 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y7 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y5 )
=> ( ( Y3
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y4 @ c_Empty )
@ Y5 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) )
=> c_False )
= $false ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f333,plain,
c_False = $false,
inference(imp_proxy_clausification,[],[f332]) ).
thf(f334,plain,
( ( !! @ ( ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o )
@ ^ [Y0: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y3: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i > $i > $i,Y8: $i > $i,Y9: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : ( c_Repl @ Y7 @ c_Inj1 )
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : c_Empty
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: ( $i > $i ) > $i > $i] : Y4 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y7: $i > $i,Y8: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: $i,Y9: ( $i > $i ) > $i > $i] : Y7
@ Y5
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : c_Empty ) )
=> ( Y0
@ ^ [Y7: $i] : Y7
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i,Y8: $i] : Y8 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y6: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( Y6 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y4 ) @ c_Inj1 ) ) )
=> ( Y3
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y6 @ c_Empty
@ ( Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( Y1
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y3
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y3
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i] : Y6
@ c_Empty )
=> ( Y0
@ ^ [Y8: $i] : c_Empty
@ ^ [Y8: ( ( $i > $i ) > $i ) > $i,Y9: $i > $i > $i,Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y12: $i] : ( c_Repl @ Y12 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y7 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y5 )
=> ( ( Y3
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y4 @ c_Empty )
@ Y5 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f332]) ).
thf(f353,plain,
! [X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( $true
= ( ^ [Y0: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y2: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y3: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y5 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: $i > $i > $i,Y8: $i > $i,Y9: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : ( c_Repl @ Y7 @ c_Inj1 )
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y6: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : c_Empty
@ Y4
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y7: $i,Y8: $i > $i > $i] : Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y6
@ ^ [Y7: ( $i > $i ) > $i > $i] : Y4 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y6: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y6
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y7: $i > $i,Y8: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: $i,Y9: ( $i > $i ) > $i > $i] : Y7
@ Y5
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i,Y8: $i] : c_Empty ) )
=> ( Y0
@ ^ [Y7: $i] : Y7
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : Y9
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ^ [Y7: ( $i > $i ) > $i > $i,Y8: $i > $i,Y9: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i,Y8: $i] : Y8 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y6: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( Y6 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y4 ) @ c_Inj1 ) ) )
=> ( Y3
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y6 @ c_Empty
@ ( Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( Y1
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y3
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] :
( Y5
@ ^ [Y6: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( c_In @ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y7
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y3
@ ^ [Y8: $i,Y9: ( $i > $i ) > $i] : Y6
@ c_Empty )
=> ( Y0
@ ^ [Y8: $i] : c_Empty
@ ^ [Y8: ( ( $i > $i ) > $i ) > $i,Y9: $i > $i > $i,Y10: $i,Y11: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y12: $i] : ( c_Repl @ Y12 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y7 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y5 )
=> ( ( Y3
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y4
@ ^ [Y6: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y4 @ c_Empty )
@ Y5 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f334]) ).
thf(f354,plain,
! [X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( $true
= ( !! @ ( ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y0: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y5: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y6: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] : Y8
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ^ [Y6: $i > $i > $i,Y7: $i > $i,Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y6: $i,Y7: $i > $i > $i] : ( c_Repl @ Y6 @ c_Inj1 )
@ Y3
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y0
@ ^ [Y6: $i,Y7: $i > $i > $i] : c_Empty
@ Y3
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y6: $i,Y7: $i > $i > $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ^ [Y6: ( $i > $i ) > $i > $i] : Y3 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y5: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y5
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y6: $i > $i,Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y1
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : Y6
@ Y4
@ ( Y3
@ ^ [Y6: ( $i > $i ) > $i > $i,Y7: $i > $i,Y8: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i,Y7: $i] : c_Empty ) )
=> ( X1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] : Y8
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ^ [Y6: ( $i > $i ) > $i > $i,Y7: $i > $i,Y8: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i,Y7: $i] : Y7 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( Y5 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y6: $i] : c_Empty
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y3 ) @ c_Inj1 ) ) )
=> ( Y2
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y5 @ c_Empty
@ ( Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( Y0
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] :
( Y4
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Repl @ Y3 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : Y5
@ c_Empty )
=> ( X1
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y11: $i] : ( c_Repl @ Y11 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y6 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y4 )
=> ( ( Y2
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y1
@ ^ [Y5: $i,Y6: $i,Y7: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y3
@ ^ [Y5: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1
@ ^ [Y5: $i,Y6: $i,Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y3 @ c_Empty )
@ Y4 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f355,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( $true
= ( ^ [Y0: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y1: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y2: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y5: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y4 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y6: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] : Y8
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ^ [Y6: $i > $i > $i,Y7: $i > $i,Y8: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y6: $i,Y7: $i > $i > $i] : ( c_Repl @ Y6 @ c_Inj1 )
@ Y3
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y5: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( Y0
@ ^ [Y6: $i,Y7: $i > $i > $i] : c_Empty
@ Y3
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y6: $i,Y7: $i > $i > $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y5
@ ^ [Y6: ( $i > $i ) > $i > $i] : Y3 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y5: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y5
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y6: $i > $i,Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y1
@ ^ [Y6: $i,Y7: $i,Y8: ( $i > $i ) > $i > $i] : Y6
@ Y4
@ ( Y3
@ ^ [Y6: ( $i > $i ) > $i > $i,Y7: $i > $i,Y8: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i,Y7: $i] : c_Empty ) )
=> ( X1
@ ^ [Y6: $i] : Y6
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] : Y8
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ^ [Y6: ( $i > $i ) > $i > $i,Y7: $i > $i,Y8: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i,Y7: $i] : Y7 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( Y5 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y6: $i] : c_Empty
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y3 ) @ c_Inj1 ) ) )
=> ( Y2
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y5 @ c_Empty
@ ( Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( Y0
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y2
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] :
( Y4
@ ^ [Y5: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( c_In @ ( c_Repl @ Y3 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y6
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y2
@ ^ [Y7: $i,Y8: ( $i > $i ) > $i] : Y5
@ c_Empty )
=> ( X1
@ ^ [Y7: $i] : c_Empty
@ ^ [Y7: ( ( $i > $i ) > $i ) > $i,Y8: $i > $i > $i,Y9: $i,Y10: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y11: $i] : ( c_Repl @ Y11 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y6 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y4 )
=> ( ( Y2
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y1
@ ^ [Y5: $i,Y6: $i,Y7: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y3
@ ^ [Y5: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1
@ ^ [Y5: $i,Y6: $i,Y7: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y3 @ c_Empty )
@ Y4 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( $true
= ( !! @ ( ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o )
@ ^ [Y0: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y1: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y4: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y3 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y5: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] : Y7
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: $i > $i > $i,Y6: $i > $i,Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y5: $i,Y6: $i > $i > $i] : ( c_Repl @ Y5 @ c_Inj1 )
@ Y2
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y5: $i,Y6: $i > $i > $i] : c_Empty
@ Y2
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y5: $i,Y6: $i > $i > $i] : Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y2 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y4: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y5: $i > $i,Y6: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y5: $i,Y6: $i,Y7: ( $i > $i ) > $i > $i] : Y5
@ Y3
@ ( Y2
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i,Y7: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i,Y6: $i] : c_Empty ) )
=> ( X1
@ ^ [Y5: $i] : Y5
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] : Y7
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i,Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i,Y6: $i] : Y6 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y4: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( Y4 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y2 ) @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y4 @ c_Empty
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y2: $i,Y3: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y1
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] :
( Y3
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Repl @ Y2 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y1
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : Y4
@ c_Empty )
=> ( X1
@ ^ [Y6: $i] : c_Empty
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y3 )
=> ( ( Y1
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y0
@ ^ [Y4: $i,Y5: $i,Y6: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y2
@ ^ [Y4: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0
@ ^ [Y4: $i,Y5: $i,Y6: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y2 @ c_Empty )
@ Y3 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f355]) ).
thf(f357,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( $true
= ( ^ [Y0: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y1: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y4: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y3 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y5: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] : Y7
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: $i > $i > $i,Y6: $i > $i,Y7: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y5: $i,Y6: $i > $i > $i] : ( c_Repl @ Y5 @ c_Inj1 )
@ Y2
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y4: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y5: $i,Y6: $i > $i > $i] : c_Empty
@ Y2
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y5: $i,Y6: $i > $i > $i] : Y2
@ ( c_binunion
@ ( c_Repl
@ ( Y4
@ ^ [Y5: ( $i > $i ) > $i > $i] : Y2 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y4: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y4
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y5: $i > $i,Y6: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y5: $i,Y6: $i,Y7: ( $i > $i ) > $i > $i] : Y5
@ Y3
@ ( Y2
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i,Y7: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i,Y6: $i] : c_Empty ) )
=> ( X1
@ ^ [Y5: $i] : Y5
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] : Y7
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ^ [Y5: ( $i > $i ) > $i > $i,Y6: $i > $i,Y7: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i,Y6: $i] : Y6 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y4: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( Y4 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y2 ) @ c_Inj1 ) ) )
=> ( Y1
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y4 @ c_Empty
@ ( Y3
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y2: $i,Y3: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y1
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] :
( Y3
@ ^ [Y4: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( c_In @ ( c_Repl @ Y2 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y5
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y1
@ ^ [Y6: $i,Y7: ( $i > $i ) > $i] : Y4
@ c_Empty )
=> ( X1
@ ^ [Y6: $i] : c_Empty
@ ^ [Y6: ( ( $i > $i ) > $i ) > $i,Y7: $i > $i > $i,Y8: $i,Y9: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y10: $i] : ( c_Repl @ Y10 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y3 )
=> ( ( Y1
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( Y0
@ ^ [Y4: $i,Y5: $i,Y6: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y2
@ ^ [Y4: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0
@ ^ [Y4: $i,Y5: $i,Y6: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y2 @ c_Empty )
@ Y3 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
( $true
= ( !! @ ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o )
@ ^ [Y0: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y3: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y2 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y4: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] : Y6
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y4: $i > $i > $i,Y5: $i > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y4: $i,Y5: $i > $i > $i] : ( c_Repl @ Y4 @ c_Inj1 )
@ Y1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ Y1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y4: $i,Y5: $i > $i > $i] : Y1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y4: ( $i > $i ) > $i > $i] : Y1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y3: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y4: $i,Y5: $i,Y6: ( $i > $i ) > $i > $i] : Y4
@ Y2
@ ( Y1
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i,Y6: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i,Y5: $i] : c_Empty ) )
=> ( X1
@ ^ [Y4: $i] : Y4
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] : Y6
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i,Y6: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i,Y5: $i] : Y5 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y3: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( Y3 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y1 ) @ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y3 @ c_Empty
@ ( Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y1: $i,Y2: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y0
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] :
( Y2
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i] : Y3
@ c_Empty )
=> ( X1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y2 )
=> ( ( Y0
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y1
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y1 @ c_Empty )
@ Y2 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f357]) ).
thf(f359,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( $true
= ( ^ [Y0: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y3: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y2 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y4: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] : Y6
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y4: $i > $i > $i,Y5: $i > $i,Y6: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y4: $i,Y5: $i > $i > $i] : ( c_Repl @ Y4 @ c_Inj1 )
@ Y1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y3: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y4: $i,Y5: $i > $i > $i] : c_Empty
@ Y1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y4: $i,Y5: $i > $i > $i] : Y1
@ ( c_binunion
@ ( c_Repl
@ ( Y3
@ ^ [Y4: ( $i > $i ) > $i > $i] : Y1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y3: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y3
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y4: $i,Y5: $i,Y6: ( $i > $i ) > $i > $i] : Y4
@ Y2
@ ( Y1
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i,Y6: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i,Y5: $i] : c_Empty ) )
=> ( X1
@ ^ [Y4: $i] : Y4
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] : Y6
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ^ [Y4: ( $i > $i ) > $i > $i,Y5: $i > $i,Y6: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i,Y5: $i] : Y5 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y3: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( Y3 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y1 ) @ c_Inj1 ) ) )
=> ( Y0
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y3 @ c_Empty
@ ( Y2
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y1: $i,Y2: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( Y0
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] :
( Y2
@ ^ [Y3: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y4
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( Y0
@ ^ [Y5: $i,Y6: ( $i > $i ) > $i] : Y3
@ c_Empty )
=> ( X1
@ ^ [Y5: $i] : c_Empty
@ ^ [Y5: ( ( $i > $i ) > $i ) > $i,Y6: $i > $i > $i,Y7: $i,Y8: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y9: $i] : ( c_Repl @ Y9 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y2 )
=> ( ( Y0
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y1
@ ^ [Y3: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y1 @ c_Empty )
@ Y2 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 )
=> c_False ) ) )
=> c_False ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f361,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 )
=> $false ) ) )
=> $false ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[],[f360,f333]) ).
thf(f362,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 )
=> $false ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f361]) ).
thf(f363,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f362]) ).
thf(f364,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
=> ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
=> ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] :
( Y1
@ ^ [Y2: $i] :
( c_binunion
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Empty ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f367]) ).
thf(f370,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f368]) ).
thf(f372,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
=> ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f374,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
= $true )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f372]) ).
thf(f376,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f374]) ).
thf(f377,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
= $true )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : c_Empty
@ ( Y0 @ c_Empty )
@ Y1 ) )
@ ( sK1 @ X3 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f376]) ).
thf(f380,plain,
! [X2: ( $i > ( $i > $i > $i ) > $i ) > $i > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( X2
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( X2
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f377]) ).
thf(f385,plain,
! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i > ( $i > $i > $i ) > $i,Y1: $i,Y2: $i] : $false
@ ^ [Y0: $i,Y1: $i > $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
= $true )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( ( ^ [Y3: $i > ( $i > $i > $i ) > $i,Y4: $i,Y5: $i] : $false
@ ^ [Y3: $i,Y4: $i > $i > $i] : c_Empty
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ^ [Y3: $i > ( $i > $i > $i ) > $i,Y4: $i,Y5: $i] : $false
@ ^ [Y3: $i,Y4: $i > $i > $i] : Y0
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: ( $i > $i ) > $i > $i] : Y0 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
@ c_Inj1 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> ( ^ [Y3: $i > ( $i > $i > $i ) > $i,Y4: $i,Y5: $i] : $false
@ ^ [Y3: $i,Y4: $i > $i > $i] : ( c_Repl @ Y3 @ c_Inj1 )
@ Y0
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) )
= $false ) ),
inference(primitive_instantiation,[],[f380]) ).
thf(f396,plain,
! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( $false
=> $false ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $true = $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> $false ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f385]) ).
thf(f397,plain,
! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( $false
=> $false ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> $false ) ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f396]) ).
thf(f398,plain,
! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
=> $false ) ) ) ) )
= $false ) ),
inference(boolean_simplification,[],[f397]) ).
thf(f399,plain,
! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f398]) ).
thf(f410,definition,
( spl3_3
<=> ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f411,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f410]) ).
thf(f413,definition,
( spl3_4
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f415,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true ) ) )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f413]) ).
thf(f416,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f399,f413,f410]) ).
thf(f435,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y1 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y3: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl
@ ( Y2
@ ^ [Y3: $i > $i > $i,Y4: $i > $i,Y5: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y6: $i] : ( c_Repl @ Y6 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
@ ( sK7 @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f411]) ).
thf(f437,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y2: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y2: $i > $i > $i,Y3: $i > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f435]) ).
thf(f439,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( ^ [Y0: $i] :
( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y2: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl
@ ( Y1
@ ^ [Y2: $i > $i > $i,Y3: $i > $i,Y4: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y5: $i] : ( c_Repl @ Y5 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
@ ( sK8 @ X1 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f437]) ).
thf(f441,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f439]) ).
thf(f443,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( Y2 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ Y0 ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y2 @ c_Empty
@ ( Y1
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
@ ( sK9 @ X1 @ X4 ) ) ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f441]) ).
thf(f446,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f443]) ).
thf(f467,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > ( $i > $i > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y2: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y2
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y3: $i,Y4: $i,Y5: ( $i > $i ) > $i > $i] : Y3
@ Y1
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y3: $i,Y4: $i] : c_Empty ) )
=> ( X1
@ ^ [Y3: $i] : Y3
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] : Y5
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ^ [Y3: ( $i > $i ) > $i > $i,Y4: $i > $i,Y5: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y3: $i,Y4: $i] : Y4 )
@ c_Inj1 ) ) ) ) ) ) )
@ ( sK10 @ X3 @ X1 ) ) ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f446]) ).
thf(f470,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f467]) ).
thf(f471,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( c_In @ ( c_Repl @ Y0 @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y3
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y4: $i,Y5: ( $i > $i ) > $i] : Y2
@ c_Empty )
=> ( X1
@ ^ [Y4: $i] : c_Empty
@ ^ [Y4: ( ( $i > $i ) > $i ) > $i,Y5: $i > $i > $i,Y6: $i,Y7: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y8: $i] : ( c_Repl @ Y8 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y3 ) ) ) ) ) )
@ ( sK11 @ X1 @ X4 ) )
= $false )
| ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f470]) ).
thf(f473,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) ) )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f471]) ).
thf(f475,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( ( ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y1 )
=> ( ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( Y0
@ ^ [Y2: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
@ ( sK12 @ X3 @ X4 ) )
= $false )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f473]) ).
thf(f478,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f475]) ).
thf(f479,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ Y0 )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f478]) ).
thf(f481,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ~ ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f479]) ).
thf(f483,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(not_proxy_clausification,[],[f481]) ).
thf(f484,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( ^ [Y0: ( ( $i > $i > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y1: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y1: ( ( $i > $i ) > $i ) > $i,Y2: $i > $i > $i,Y3: $i,Y4: $i] : Y3
@ ( c_binunion
@ ( c_Repl
@ ( Y0
@ ^ [Y1: $i > $i > $i,Y2: $i > $i,Y3: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y4: $i] : ( c_Repl @ Y4 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
@ ( sK14 @ X1 ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) ) )
| ~ spl3_3 ),
inference(sigma_proxy_clausification,[],[f483]) ).
thf(f487,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( ( c_In @ ( c_Repl @ ( sK8 @ X1 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK8 @ X1 )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X1
@ ^ [Y0: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y0: ( ( $i > $i ) > $i ) > $i,Y1: $i > $i > $i,Y2: $i,Y3: $i] : Y2
@ ( c_binunion
@ ( c_Repl
@ ( sK14 @ X1
@ ^ [Y0: $i > $i > $i,Y1: $i > $i,Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f484]) ).
thf(f488,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( ~ ( X1
@ ^ [Y0: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y0: ( ( $i > $i ) > $i ) > $i,Y1: $i > $i > $i,Y2: $i,Y3: $i] : Y2
@ ( c_binunion
@ ( c_Repl
@ ( sK14 @ X1
@ ^ [Y0: $i > $i > $i,Y1: $i > $i,Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(imp_proxy_clausification,[],[f487]) ).
thf(f490,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X1: ( $i > $i ) > ( ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i ) > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( X1
@ ^ [Y0: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y0: ( ( $i > $i ) > $i ) > $i,Y1: $i > $i > $i,Y2: $i,Y3: $i] : Y2
@ ( c_binunion
@ ( c_Repl
@ ( sK14 @ X1
@ ^ [Y0: $i > $i > $i,Y1: $i > $i,Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X1
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( sK9 @ X1 @ X4 ) ) @ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( X1
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3 @ X1
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In @ ( c_Repl @ ( sK11 @ X1 @ X4 ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( X1
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(not_proxy_clausification,[],[f488]) ).
thf(f495,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: $i] : ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 )
@ ^ [Y0: ( ( $i > $i ) > $i ) > $i,Y1: $i > $i > $i,Y2: $i,Y3: $i] : Y2
@ ( c_binunion
@ ( c_Repl
@ ( sK14
@ ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: $i > $i > $i,Y1: $i > $i,Y2: $i] :
( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> ( ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ ^ [Y3: $i] : c_Empty
@ ^ [Y3: ( ( $i > $i ) > $i ) > $i,Y4: $i > $i > $i,Y5: $i,Y6: $i] :
( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y7: $i] : ( c_Repl @ Y7 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ Y2 ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> ( ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: $i] : Y2
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : Y4
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i,Y3: $i] : Y3 )
@ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: $i] : c_Empty
@ ^ [Y2: ( ( $i > $i ) > $i ) > $i,Y3: $i > $i > $i,Y4: $i,Y5: $i] : c_Empty
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( sK9
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ X4 ) )
@ c_Inj1 ) ) )
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(primitive_instantiation,[],[f490]) ).
thf(f499,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> $false ) ) ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( $false
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> $false ) ) ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true = $false ) )
| ~ spl3_3 ),
inference(beta-eta_normalization,[],[f495]) ).
thf(f500,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ( ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty )
=> $false ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> $false ) ) ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( $false
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f499]) ).
thf(f501,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) )
=> $false ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( $false
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false ) )
| ~ spl3_3 ),
inference(boolean_simplification,[],[f500]) ).
thf(f502,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) ) ) ) ) )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ( $false
=> ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : ( c_Repl @ c_Empty @ c_Inj1 )
@ ( Y1 @ c_Empty
@ ( Y0
@ ( c_binunion
@ ( c_Repl @ ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) ) )
| ~ spl3_3 ),
inference(boolean_simplification,[],[f501]) ).
thf(f503,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( ( c_In @ ( c_Repl @ ( c_Inj1 @ c_Empty ) @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ ( Y1 @ c_Empty @ c_Empty ) @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) ) )
=> $true ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(boolean_simplification,[],[f502]) ).
thf(f504,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] : $true ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) ) )
| ~ spl3_3 ),
inference(boolean_simplification,[],[f503]) ).
thf(f507,definition,
( spl3_5
<=> ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o,X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o] :
( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f508,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f507]) ).
thf(f510,definition,
( spl3_6
<=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] : $true ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f512,plain,
( ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] : $true ) )
= $false )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f510]) ).
thf(f513,plain,
( spl3_5
| spl3_6
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f504,f410,f510,f507]) ).
thf(f515,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y1: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y1
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y2: $i > $i,Y3: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y2: $i,Y3: $i,Y4: ( $i > $i ) > $i > $i] : Y2
@ Y0
@ ( sK10 @ X3
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ ^ [Y2: ( $i > $i ) > $i > $i,Y3: $i > $i,Y4: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y2: $i,Y3: $i] : c_Empty ) ) ) )
@ ( sK17 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) ) )
| ~ spl3_5 ),
inference(sigma_proxy_clausification,[],[f508]) ).
thf(f518,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: $i > $i,Y2: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : Y1
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i,Y2: $i] : c_Empty ) ) ) )
= $false ) )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f515]) ).
thf(f548,plain,
( ( ( ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] : $true )
@ sK19 )
= $false )
| ~ spl3_6 ),
inference(sigma_proxy_clausification,[],[f512]) ).
thf(f550,plain,
( ( $false
= ( !! @ ( $i > $i > $i )
@ ^ [Y0: $i > $i > $i] : $true ) )
| ~ spl3_6 ),
inference(beta-eta_normalization,[],[f548]) ).
thf(f552,plain,
( ( $false
= ( ^ [Y0: $i > $i > $i] : $true
@ sK20 ) )
| ~ spl3_6 ),
inference(sigma_proxy_clausification,[],[f550]) ).
thf(f554,plain,
( ( $true = $false )
| ~ spl3_6 ),
inference(beta-eta_normalization,[],[f552]) ).
thf(f555,plain,
( $false
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f554]) ).
thf(f556,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f555]) ).
thf(f569,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: $i > $i,Y2: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : Y1
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i,Y2: $i] : c_Empty ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y3: $i > $i,Y4: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y5: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y2
@ ^ [Y3: $i] : ( c_Repl @ Y3 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y3: $i,Y4: ( $i > $i ) > $i] : Y1
@ c_Empty ) ) ) )
@ ( sK21 @ X4 ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false ) )
| ~ spl3_5 ),
inference(sigma_proxy_clausification,[],[f518]) ).
thf(f571,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ ( $i > ( ( $i > $i ) > $i > $i ) > $i )
@ ^ [Y0: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: $i > $i,Y2: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : Y1
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i,Y2: $i] : c_Empty ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : Y0
@ c_Empty ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) ) )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f569]) ).
thf(f597,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y2: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true ) )
@ sK23 )
= $false )
| ~ spl3_4 ),
inference(sigma_proxy_clausification,[],[f415]) ).
thf(f599,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true ) )
= $false )
| ~ spl3_4 ),
inference(beta-eta_normalization,[],[f597]) ).
thf(f601,plain,
( ( ( ^ [Y0: $i] :
( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y1: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true )
@ sK24 )
= $false )
| ~ spl3_4 ),
inference(sigma_proxy_clausification,[],[f599]) ).
thf(f604,plain,
( ( ( !! @ ( ( ( ( $i > $i ) > $i > $i ) > $i ) > $i )
@ ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true )
= $false )
| ~ spl3_4 ),
inference(beta-eta_normalization,[],[f601]) ).
thf(f605,plain,
( ( ( ^ [Y0: ( ( ( $i > $i ) > $i > $i ) > $i ) > $i] : $true
@ sK25 )
= $false )
| ~ spl3_4 ),
inference(sigma_proxy_clausification,[],[f604]) ).
thf(f608,plain,
( ( $true = $false )
| ~ spl3_4 ),
inference(beta-eta_normalization,[],[f605]) ).
thf(f609,plain,
( $false
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f610,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f609]) ).
thf(f618,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : Y0
@ c_Empty ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( Y0
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y1: $i > $i,Y2: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : Y1
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y1: $i,Y2: $i] : c_Empty ) ) )
@ ( sK26 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false ) )
| ~ spl3_5 ),
inference(sigma_proxy_clausification,[],[f571]) ).
thf(f620,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( ( c_In @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl
@ ( sK26 @ X3
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y0: $i] : ( c_Repl @ Y0 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) ) )
=> ~ ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : Y0
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i,Y2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y0: $i,Y1: $i] : c_Empty ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : Y0
@ c_Empty ) ) ) )
= $false ) )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f618]) ).
thf(f622,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : Y0
@ c_Empty ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ~ ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : Y0
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i,Y2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y0: $i,Y1: $i] : c_Empty ) ) ) ) )
| ~ spl3_5 ),
inference(imp_proxy_clausification,[],[f620]) ).
thf(f624,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : Y0
@ c_Empty ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : Y0
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i,Y2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y0: $i,Y1: $i] : c_Empty ) ) ) )
| ~ spl3_5 ),
inference(not_proxy_clausification,[],[f622]) ).
thf(f655,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : Y0
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i,Y2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y0: $i,Y1: $i] : c_Empty ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y2: $i > $i,Y3: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y4: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y1
@ ^ [Y2: $i] : ( c_Repl @ Y2 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y2: $i,Y3: ( $i > $i ) > $i] : Y0
@ c_Empty ) ) )
@ ( sK28 @ X4 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false ) )
| ~ spl3_5 ),
inference(sigma_proxy_clausification,[],[f624]) ).
thf(f657,plain,
( ! [X3: ( $i > $i > ( ( $i > $i ) > $i > $i ) > $i ) > $i > $i > $o,X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : Y0
@ ( sK17 @ X3 )
@ ( sK10 @ X3
@ ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i,Y2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y0: $i,Y1: $i] : c_Empty ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1 @ X3 @ c_Empty )
@ ( sK13 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( X3
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12 @ X3 @ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) )
= $false ) )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f655]) ).
thf(f663,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( ^ [Y0: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i] : $false
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : c_Empty
@ ( sK1
@ ^ [Y0: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i] : $false
@ c_Empty )
@ ( sK13
@ ^ [Y0: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i] : $false ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> ( ^ [Y1: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i] : $false
@ ^ [Y1: $i,Y2: $i,Y3: ( $i > $i ) > $i > $i] : ( c_Inj1 @ c_Empty )
@ ( c_Inj1
@ ( c_Inj1
@ ( sK12
@ ^ [Y1: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y2: $i,Y3: $i] : $false
@ X4
@ ^ [Y1: ( $i > $i ) > $i > $i] : c_Empty ) ) )
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( c_Repl @ c_Empty @ c_Inj1 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ ( c_Inj1 @ ( c_Repl @ c_Empty @ c_Inj1 ) ) @ c_Inj1 ) ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i] : $false
@ ^ [Y0: $i,Y1: $i,Y2: ( $i > $i ) > $i > $i] : Y0
@ ( sK17
@ ^ [Y0: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i] : $false )
@ ( sK10
@ ^ [Y0: $i > $i > ( ( $i > $i ) > $i > $i ) > $i,Y1: $i,Y2: $i] : $false
@ ^ [Y0: $i > $i,Y1: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y2: $i] : $false
@ ^ [Y0: ( $i > $i ) > $i > $i,Y1: $i > $i,Y2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Y0: $i,Y1: $i] : c_Empty ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false ) )
| ~ spl3_5 ),
inference(primitive_instantiation,[],[f657]) ).
thf(f668,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true = $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> $false ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false )
| ( $true = $false ) )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f663]) ).
thf(f669,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> $false ) ) ) )
| ( $true = $false ) )
| ~ spl3_5 ),
inference(duplicate_literal_removal,[],[f668]) ).
thf(f670,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ( ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
=> $false ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false ) )
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f669]) ).
thf(f671,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false ) )
| ~ spl3_5 ),
inference(boolean_simplification,[],[f670]) ).
thf(f710,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( c_In @ ( c_Inj1 @ c_Empty ) @ Y0 )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : c_Empty
@ c_Empty ) )
@ ( sK30 @ X4 ) )
= $false ) )
| ~ spl3_5 ),
inference(sigma_proxy_clausification,[],[f671]) ).
thf(f713,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( sK30 @ X4 ) )
=> ~ ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] : c_Empty
@ c_Empty ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false ) )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f710]) ).
thf(f714,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $false
= ( ~ ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] : c_Empty
@ c_Empty ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false ) )
| ~ spl3_5 ),
inference(imp_proxy_clausification,[],[f713]) ).
thf(f716,plain,
( ! [X4: ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $o] :
( ( $true
= ( X4
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] : c_Empty
@ c_Empty ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ X4 )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ ( sK21 @ X4 )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( X4
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] : ( sK28 @ X4 )
@ c_Empty ) ) )
= $false ) )
| ~ spl3_5 ),
inference(not_proxy_clausification,[],[f714]) ).
thf(f746,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK21
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ ( ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false
@ ^ [Y1: $i,Y2: ( $i > $i ) > $i] :
( sK28
@ ^ [Y3: $i > ( ( $i > $i ) > $i ) > $i,Y4: $i] : $false )
@ c_Empty ) ) )
= $false )
| ( ( ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i] : $false
@ ^ [Y0: $i,Y1: ( $i > $i ) > $i] : c_Empty
@ c_Empty )
= $true )
| ~ spl3_5 ),
inference(primitive_instantiation,[],[f716]) ).
thf(f751,plain,
( ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK21
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ $false ) )
= $false )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f746]) ).
thf(f752,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK21
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> ~ $false ) )
= $false )
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f751]) ).
thf(f753,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( c_In
@ ( c_Repl
@ ( sK11
@ ^ [Y1: $i > $i,Y2: ( ( ( $i > $i ) > $i ) > $i ) > ( $i > $i > $i ) > $i > $i > $i,Y3: $i] : $false
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ c_Inj1 )
@ ( c_binunion
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl
@ ( sK21
@ ^ [Y1: $i > ( ( $i > $i ) > $i ) > $i,Y2: $i] : $false )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_binunion
@ ( c_Repl @ c_Empty
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) )
@ c_Inj1 ) )
@ c_Inj1 ) )
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl
@ ( c_Inj1
@ ( c_binunion
@ ( c_Repl @ Y0
@ ^ [Y1: $i] : ( c_Repl @ Y1 @ c_Inj1 ) )
@ ( c_Repl @ c_Empty @ c_Inj1 ) ) )
@ c_Inj1 ) ) )
=> $true ) )
= $false )
| ~ spl3_5 ),
inference(boolean_simplification,[],[f752]) ).
thf(f754,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) )
| ~ spl3_5 ),
inference(boolean_simplification,[],[f753]) ).
thf(f760,plain,
( ( ( ^ [Y0: $i] : $true
@ sK31 )
= $false )
| ~ spl3_5 ),
inference(sigma_proxy_clausification,[],[f754]) ).
thf(f762,plain,
( ( $true = $false )
| ~ spl3_5 ),
inference(beta-eta_normalization,[],[f760]) ).
thf(f763,plain,
( $false
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f762]) ).
thf(f764,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f763]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f416]) ).
cnf(s3,plain,
( ~ spl3_3
| spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f513]) ).
cnf(s6,plain,
~ spl3_6,
inference(sat_conversion,[],[f556]) ).
cnf(s8,plain,
~ spl3_4,
inference(sat_conversion,[],[f610]) ).
cnf(s12,plain,
~ spl3_5,
inference(sat_conversion,[],[f764]) ).
cnf(s16,plain,
~ spl3_3,
inference(rat,[],[s3,s6,s12]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s2,s8,s16]) ).
thf(f766,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV524^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:55:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.38 % (961194)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.78/0.38 % (961202)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=238298912:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.78/0.38 % (961205)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.78/0.38 % (961205)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.78/0.38 % (961201)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1796620020:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.78/0.38 % (961203)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3684114951:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.78/0.38 % (961199)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4031126363:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.78/0.38 % (961200)lrs+10_16_si=on:nwc=1.5:random_seed=3341463658:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.78/0.38 % (961204)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=620410063:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.78/0.38 % (961205)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1420658486:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.78/0.38 % (961201)Instruction limit reached!
% 0.78/0.38 % (961201)------------------------------
% 0.78/0.38 % (961201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.38 % (961201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.38 % (961201)CaDiCaL version: 2.1.3
% 0.78/0.38 % (961201)Termination reason: Instruction limit
% 0.78/0.38 % (961201)Termination phase: shuffling
% 0.78/0.38 % (961201)Time elapsed: 0.004 s
% 0.78/0.38 % (961201)Peak memory usage: 10 MB
% 0.78/0.38 % (961201)Instructions burned: 8 (million)
% 0.78/0.38 % (961200)Instruction limit reached!
% 0.78/0.38 % (961200)------------------------------
% 0.78/0.38 % (961200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.38 % (961200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.38 % (961200)CaDiCaL version: 2.1.3
% 0.78/0.38 % (961200)Termination reason: Instruction limit
% 0.78/0.38 % (961200)Termination phase: Property scanning
% 0.78/0.38 % (961200)Time elapsed: 0.009 s
% 0.78/0.38 % (961200)Peak memory usage: 10 MB
% 0.78/0.38 % (961200)Instructions burned: 20 (million)
% 0.78/0.38 % (961203)Instruction limit reached!
% 0.78/0.38 % (961203)------------------------------
% 0.78/0.38 % (961203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.38 % (961203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.38 % (961203)CaDiCaL version: 2.1.3
% 0.78/0.38 % (961203)Termination reason: Instruction limit
% 0.78/0.38 % (961203)Termination phase: Property scanning
% 0.78/0.38 % (961203)Time elapsed: 0.011 s
% 0.78/0.38 % (961203)Peak memory usage: 10 MB
% 0.78/0.38 % (961203)Instructions burned: 25 (million)
% 0.78/0.38 % (961213)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2441404834:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.78/0.38 % (961215)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.78/0.38 % (961213)Instruction limit reached!
% 0.78/0.38 % (961213)------------------------------
% 0.78/0.38 % (961213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.38 % (961213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.38 % (961213)CaDiCaL version: 2.1.3
% 0.78/0.38 % (961213)Termination reason: Instruction limit
% 0.78/0.38 % (961213)Termination phase: shuffling
% 0.78/0.38 % (961213)Time elapsed: 0.003 s
% 0.78/0.38 % (961213)Peak memory usage: 10 MB
% 0.78/0.38 % (961213)Instructions burned: 6 (million)
% 0.78/0.38 % (961214)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3462738704:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.78/0.42 % (961215)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3668521095:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.78/0.42 % (961214)Instruction limit reached!
% 0.78/0.42 % (961214)------------------------------
% 0.78/0.42 % (961214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (961214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (961214)CaDiCaL version: 2.1.3
% 0.78/0.42 % (961214)Termination reason: Instruction limit
% 0.78/0.42 % (961214)Termination phase: shuffling
% 0.78/0.42 % (961214)Time elapsed: 0.003 s
% 0.78/0.42 % (961214)Peak memory usage: 10 MB
% 0.78/0.42 % (961214)Instructions burned: 6 (million)
% 0.78/0.42 % (961204)Instruction limit reached!
% 0.78/0.42 % (961204)------------------------------
% 0.78/0.42 % (961204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (961204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (961204)CaDiCaL version: 2.1.3
% 0.78/0.42 % (961204)Termination reason: Instruction limit
% 0.78/0.42 % (961204)Termination phase: Function definition elimination
% 0.78/0.42 % (961204)Time elapsed: 0.033 s
% 0.78/0.42 % (961204)Peak memory usage: 11 MB
% 0.78/0.42 % (961204)Instructions burned: 77 (million)
% 0.78/0.42 % (961215)Instruction limit reached!
% 0.78/0.42 % (961215)------------------------------
% 0.78/0.42 % (961215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (961215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (961215)CaDiCaL version: 2.1.3
% 0.78/0.42 % (961215)Termination reason: Instruction limit
% 0.78/0.42 % (961215)Termination phase: shuffling
% 0.78/0.42 % (961215)Time elapsed: 0.004 s
% 0.78/0.42 % (961215)Peak memory usage: 10 MB
% 0.78/0.42 % (961215)Instructions burned: 9 (million)
% 0.78/0.42 % (961199)Instruction limit reached!
% 0.78/0.42 % (961199)------------------------------
% 0.78/0.42 % (961199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (961199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (961199)CaDiCaL version: 2.1.3
% 0.78/0.42 % (961199)Termination reason: Instruction limit
% 0.78/0.42 % (961199)Termination phase: Function definition elimination
% 0.78/0.42 % (961199)Time elapsed: 0.037 s
% 0.78/0.42 % (961199)Peak memory usage: 11 MB
% 0.78/0.42 % (961199)Instructions burned: 89 (million)
% 0.78/0.42 % (961217)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4155054464:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.78/0.42 % (961217)Instruction limit reached!
% 0.78/0.42 % (961217)------------------------------
% 0.78/0.42 % (961217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (961217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (961221)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2552673044:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.78/0.42 % (961217)CaDiCaL version: 2.1.3
% 0.78/0.42 % (961217)Termination reason: Instruction limit
% 0.78/0.42 % (961217)Termination phase: shuffling
% 0.78/0.42 % (961217)Time elapsed: 0.006 s
% 0.78/0.42 % (961217)Peak memory usage: 10 MB
% 0.78/0.42 % (961217)Instructions burned: 13 (million)
% 0.78/0.42 % (961223)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.78/0.42 % (961222)lrs+10_1_si=on:cs=on:random_seed=379173453:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.78/0.42 % (961220)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.78/0.42 % (961220)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.78/0.42 % (961223)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=890468631:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.78/0.45 % (961222)Instruction limit reached!
% 0.78/0.45 % (961222)------------------------------
% 0.78/0.45 % (961222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.45 % (961222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.45 % (961222)CaDiCaL version: 2.1.3
% 0.78/0.45 % (961222)Termination reason: Instruction limit
% 0.78/0.45 % (961222)Termination phase: shuffling
% 0.78/0.45 % (961222)Time elapsed: 0.004 s
% 0.78/0.45 % (961222)Peak memory usage: 10 MB
% 0.78/0.45 % (961222)Instructions burned: 8 (million)
% 0.78/0.45 % (961223)Instruction limit reached!
% 0.78/0.45 % (961223)------------------------------
% 0.78/0.45 % (961223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.45 % (961223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.45 % (961223)CaDiCaL version: 2.1.3
% 0.78/0.45 % (961223)Termination reason: Instruction limit
% 0.78/0.45 % (961223)Termination phase: shuffling
% 0.78/0.45 % (961223)Time elapsed: 0.002 s
% 0.78/0.45 % (961223)Peak memory usage: 10 MB
% 0.78/0.45 % (961223)Instructions burned: 4 (million)
% 0.78/0.45 % (961220)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1905473743:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.78/0.45 % (961205)Instruction limit reached!
% 0.78/0.45 % (961205)------------------------------
% 0.78/0.45 % (961205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.45 % (961205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.45 % (961205)CaDiCaL version: 2.1.3
% 0.78/0.45 % (961205)Termination reason: Instruction limit
% 0.78/0.45 % (961205)Termination phase: Twee Goal Transformation
% 0.78/0.45 % (961205)Time elapsed: 0.063 s
% 0.78/0.45 % (961205)Peak memory usage: 11 MB
% 0.78/0.45 % (961205)Instructions burned: 163 (million)
% 0.78/0.45 % (961227)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1300573453:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.78/0.45 % (961229)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3821569225:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.78/0.45 % (961230)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3193474753:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.78/0.45 % (961232)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4224818461:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.78/0.45 % (961220)Instruction limit reached!
% 0.78/0.45 % (961220)------------------------------
% 0.78/0.45 % (961220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.45 % (961220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.45 % (961220)CaDiCaL version: 2.1.3
% 0.78/0.45 % (961220)Termination reason: Instruction limit
% 0.78/0.45 % (961220)Termination phase: shuffling
% 0.78/0.45 % (961220)Time elapsed: 0.023 s
% 0.78/0.45 % (961220)Peak memory usage: 10 MB
% 0.78/0.45 % (961220)Instructions burned: 28 (million)
% 0.78/0.45 % (961221)Instruction limit reached!
% 0.78/0.45 % (961221)------------------------------
% 0.78/0.45 % (961221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.45 % (961221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.45 % (961221)CaDiCaL version: 2.1.3
% 0.78/0.45 % (961221)Termination reason: Instruction limit
% 0.78/0.45 % (961221)Termination phase: Function definition elimination
% 0.78/0.45 % (961221)Time elapsed: 0.035 s
% 0.78/0.45 % (961221)Peak memory usage: 10 MB
% 0.78/0.45 % (961221)Instructions burned: 87 (million)
% 0.78/0.45 % (961227)Instruction limit reached!
% 0.78/0.45 % (961227)------------------------------
% 0.78/0.45 % (961227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.45 % (961227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.45 % (961227)CaDiCaL version: 2.1.3
% 0.78/0.45 % (961227)Termination reason: Instruction limit
% 0.78/0.45 % (961227)Termination phase: Property scanning
% 0.78/0.45 % (961227)Time elapsed: 0.018 s
% 0.78/0.45 % (961227)Peak memory usage: 11 MB
% 0.78/0.45 % (961227)Instructions burned: 40 (million)
% 1.36/0.50 % (961230)Instruction limit reached!
% 1.36/0.50 % (961230)------------------------------
% 1.36/0.50 % (961230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.50 % (961230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.50 % (961230)CaDiCaL version: 2.1.3
% 1.36/0.50 % (961230)Termination reason: Instruction limit
% 1.36/0.50 % (961230)Termination phase: Property scanning
% 1.36/0.50 % (961230)Time elapsed: 0.012 s
% 1.36/0.50 % (961230)Peak memory usage: 10 MB
% 1.36/0.50 % (961230)Instructions burned: 27 (million)
% 1.36/0.50 % (961232)Instruction limit reached!
% 1.36/0.50 % (961232)------------------------------
% 1.36/0.50 % (961232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.50 % (961232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.50 % (961232)CaDiCaL version: 2.1.3
% 1.36/0.50 % (961232)Termination reason: Instruction limit
% 1.36/0.50 % (961232)Termination phase: shuffling
% 1.36/0.50 % (961232)Time elapsed: 0.007 s
% 1.36/0.50 % (961232)Peak memory usage: 10 MB
% 1.36/0.50 % (961232)Instructions burned: 16 (million)
% 1.36/0.50 % (961237)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1872048375:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.36/0.50 % (961238)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=702382135:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.36/0.50 % (961239)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1564753982:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.36/0.50 % (961240)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=837752673:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.36/0.50 % (961241)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1553698872:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.36/0.50 % (961239)Instruction limit reached!
% 1.36/0.50 % (961239)------------------------------
% 1.36/0.50 % (961239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.50 % (961239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.50 % (961239)CaDiCaL version: 2.1.3
% 1.36/0.50 % (961239)Termination reason: Instruction limit
% 1.36/0.50 % (961239)Termination phase: shuffling
% 1.36/0.50 % (961239)Time elapsed: 0.001 s
% 1.36/0.50 % (961239)Peak memory usage: 10 MB
% 1.36/0.50 % (961239)Instructions burned: 3 (million)
% 1.36/0.50 % (961238)Instruction limit reached!
% 1.36/0.50 % (961238)------------------------------
% 1.36/0.50 % (961238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.50 % (961238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.50 % (961238)CaDiCaL version: 2.1.3
% 1.36/0.50 % (961238)Termination reason: Instruction limit
% 1.36/0.50 % (961238)Termination phase: shuffling
% 1.36/0.50 % (961238)Time elapsed: 0.007 s
% 1.36/0.50 % (961238)Peak memory usage: 10 MB
% 1.36/0.50 % (961238)Instructions burned: 15 (million)
% 1.36/0.50 % (961241)Instruction limit reached!
% 1.36/0.50 % (961241)------------------------------
% 1.36/0.50 % (961241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.50 % (961241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.50 % (961241)CaDiCaL version: 2.1.3
% 1.36/0.50 % (961241)Termination reason: Instruction limit
% 1.36/0.50 % (961241)Termination phase: Property scanning
% 1.36/0.50 % (961241)Time elapsed: 0.010 s
% 1.36/0.50 % (961241)Peak memory usage: 10 MB
% 1.36/0.50 % (961241)Instructions burned: 23 (million)
% 1.36/0.50 % (961240)Instruction limit reached!
% 1.36/0.50 % (961240)------------------------------
% 1.36/0.50 % (961240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.50 % (961240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.50 % (961240)CaDiCaL version: 2.1.3
% 1.36/0.50 % (961240)Termination reason: Instruction limit
% 1.36/0.50 % (961240)Termination phase: Clausification
% 1.36/0.50 % (961240)Time elapsed: 0.012 s
% 1.36/0.50 % (961240)Peak memory usage: 10 MB
% 1.36/0.50 % (961240)Instructions burned: 28 (million)
% 1.36/0.50 % (961248)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.36/0.53 % (961248)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.36/0.53 % (961247)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3548903527:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.36/0.53 % (961248)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2304224461:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.36/0.53 % (961249)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.36/0.53 % (961202)Instruction limit reached!
% 1.36/0.53 % (961202)------------------------------
% 1.36/0.53 % (961202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (961202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (961202)CaDiCaL version: 2.1.3
% 1.36/0.53 % (961202)Termination reason: Instruction limit
% 1.36/0.53 % (961202)Termination phase: Saturation
% 1.36/0.53 % (961202)Time elapsed: 0.145 s
% 1.36/0.53 % (961202)Peak memory usage: 16 MB
% 1.36/0.53 % (961202)Instructions burned: 638 (million)
% 1.36/0.53 % (961249)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3362717377:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.36/0.53 % (961248)Instruction limit reached!
% 1.36/0.53 % (961248)------------------------------
% 1.36/0.53 % (961248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (961248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (961248)CaDiCaL version: 2.1.3
% 1.36/0.53 % (961248)Termination reason: Instruction limit
% 1.36/0.53 % (961248)Termination phase: shuffling
% 1.36/0.53 % (961248)Time elapsed: 0.006 s
% 1.36/0.53 % (961248)Peak memory usage: 10 MB
% 1.36/0.53 % (961248)Instructions burned: 14 (million)
% 1.36/0.53 % (961250)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=783366703:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.36/0.53 % (961249)Instruction limit reached!
% 1.36/0.53 % (961249)------------------------------
% 1.36/0.53 % (961249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (961249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (961249)CaDiCaL version: 2.1.3
% 1.36/0.53 % (961249)Termination reason: Instruction limit
% 1.36/0.53 % (961249)Termination phase: shuffling
% 1.36/0.53 % (961249)Time elapsed: 0.004 s
% 1.36/0.53 % (961249)Peak memory usage: 10 MB
% 1.36/0.53 % (961249)Instructions burned: 8 (million)
% 1.36/0.53 % (961256)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3523156611:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.36/0.53 % (961250)Instruction limit reached!
% 1.36/0.53 % (961250)------------------------------
% 1.36/0.53 % (961250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (961250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (961250)CaDiCaL version: 2.1.3
% 1.36/0.53 % (961250)Termination reason: Instruction limit
% 1.36/0.53 % (961250)Termination phase: Property scanning
% 1.36/0.53 % (961250)Time elapsed: 0.014 s
% 1.36/0.53 % (961250)Peak memory usage: 10 MB
% 1.36/0.53 % (961250)Instructions burned: 32 (million)
% 1.36/0.53 % (961247)Instruction limit reached!
% 1.36/0.53 % (961247)------------------------------
% 1.36/0.53 % (961247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (961247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (961247)CaDiCaL version: 2.1.3
% 1.36/0.53 % (961247)Termination reason: Instruction limit
% 1.36/0.53 % (961247)Termination phase: Saturation
% 1.36/0.53 % (961247)Time elapsed: 0.027 s
% 1.36/0.53 % (961247)Peak memory usage: 12 MB
% 1.36/0.53 % (961247)Instructions burned: 61 (million)
% 1.36/0.53 % (961256)Instruction limit reached!
% 1.36/0.53 % (961256)------------------------------
% 1.36/0.53 % (961256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.61 % (961256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.61 % (961256)CaDiCaL version: 2.1.3
% 2.20/0.61 % (961256)Termination reason: Instruction limit
% 2.20/0.61 % (961256)Termination phase: Property scanning
% 2.20/0.61 % (961256)Time elapsed: 0.005 s
% 2.20/0.61 % (961256)Peak memory usage: 10 MB
% 2.20/0.61 % (961256)Instructions burned: 25 (million)
% 2.20/0.61 % (961257)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1918853655:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.20/0.61 % (961253)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3205109607:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.20/0.61 % (961261)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3984873499:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.20/0.61 % (961253)Instruction limit reached!
% 2.20/0.61 % (961253)------------------------------
% 2.20/0.61 % (961253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.61 % (961253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.61 % (961253)CaDiCaL version: 2.1.3
% 2.20/0.61 % (961253)Termination reason: Instruction limit
% 2.20/0.61 % (961253)Termination phase: shuffling
% 2.20/0.61 % (961253)Time elapsed: 0.006 s
% 2.20/0.61 % (961253)Peak memory usage: 10 MB
% 2.20/0.61 % (961253)Instructions burned: 7 (million)
% 2.20/0.61 % (961257)Instruction limit reached!
% 2.20/0.61 % (961257)------------------------------
% 2.20/0.61 % (961257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.61 % (961257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.61 % (961257)CaDiCaL version: 2.1.3
% 2.20/0.61 % (961257)Termination reason: Instruction limit
% 2.20/0.61 % (961257)Termination phase: Property scanning
% 2.20/0.61 % (961257)Time elapsed: 0.009 s
% 2.20/0.61 % (961257)Peak memory usage: 10 MB
% 2.20/0.61 % (961257)Instructions burned: 21 (million)
% 2.20/0.61 % (961229)Instruction limit reached!
% 2.20/0.61 % (961229)------------------------------
% 2.20/0.61 % (961229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.61 % (961229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.61 % (961229)CaDiCaL version: 2.1.3
% 2.20/0.61 % (961229)Termination reason: Instruction limit
% 2.20/0.61 % (961229)Termination phase: Saturation
% 2.20/0.61 % (961229)Time elapsed: 0.095 s
% 2.20/0.61 % (961229)Peak memory usage: 12 MB
% 2.20/0.61 % (961229)Instructions burned: 250 (million)
% 2.20/0.61 % (961259)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=190286483:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.20/0.61 % (961260)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1189561191:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.20/0.61 % (961266)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.20/0.61 % (961265)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2098581311:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.20/0.61 % (961266)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3481259859:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.20/0.61 % (961267)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2571696401:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.20/0.61 % (961266)Instruction limit reached!
% 2.20/0.61 % (961266)------------------------------
% 2.20/0.61 % (961266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.61 % (961266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.61 % (961266)CaDiCaL version: 2.1.3
% 2.20/0.61 % (961266)Termination reason: Instruction limit
% 2.20/0.61 % (961266)Termination phase: shuffling
% 2.20/0.61 % (961266)Time elapsed: 0.003 s
% 2.20/0.61 % (961266)Peak memory usage: 10 MB
% 2.20/0.61 % (961266)Instructions burned: 7 (million)
% 2.20/0.61 % (961261)Instruction limit reached!
% 2.20/0.61 % (961261)------------------------------
% 2.20/0.61 % (961261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.67 % (961261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.67 % (961261)CaDiCaL version: 2.1.3
% 2.57/0.67 % (961261)Termination reason: Instruction limit
% 2.57/0.67 % (961261)Termination phase: Saturation
% 2.57/0.67 % (961261)Time elapsed: 0.040 s
% 2.57/0.67 % (961261)Peak memory usage: 12 MB
% 2.57/0.67 % (961261)Instructions burned: 197 (million)
% 2.57/0.67 % (961265)Instruction limit reached!
% 2.57/0.67 % (961265)------------------------------
% 2.57/0.67 % (961265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.67 % (961265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.67 % (961265)CaDiCaL version: 2.1.3
% 2.57/0.67 % (961265)Termination reason: Instruction limit
% 2.57/0.67 % (961265)Termination phase: Function definition elimination
% 2.57/0.67 % (961265)Time elapsed: 0.018 s
% 2.57/0.67 % (961265)Peak memory usage: 11 MB
% 2.57/0.67 % (961265)Instructions burned: 43 (million)
% 2.57/0.67 % (961273)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=4122645850:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.57/0.67 % (961274)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.57/0.67 % (961274)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1094785202:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.57/0.67 % (961274)Instruction limit reached!
% 2.57/0.67 % (961274)------------------------------
% 2.57/0.67 % (961274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.67 % (961274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.67 % (961274)CaDiCaL version: 2.1.3
% 2.57/0.67 % (961274)Termination reason: Instruction limit
% 2.57/0.67 % (961274)Termination phase: shuffling
% 2.57/0.67 % (961274)Time elapsed: 0.002 s
% 2.57/0.67 % (961274)Peak memory usage: 10 MB
% 2.57/0.67 % (961274)Instructions burned: 9 (million)
% 2.57/0.67 % (961275)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2511629197:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.57/0.67 % (961278)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1134059876:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.57/0.67 % (961237)Instruction limit reached!
% 2.57/0.67 % (961237)------------------------------
% 2.57/0.67 % (961237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.67 % (961237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.67 % (961237)CaDiCaL version: 2.1.3
% 2.57/0.67 % (961237)Termination reason: Instruction limit
% 2.57/0.67 % (961237)Termination phase: Saturation
% 2.57/0.67 % (961237)Time elapsed: 0.131 s
% 2.57/0.67 % (961237)Peak memory usage: 13 MB
% 2.57/0.67 % (961237)Instructions burned: 328 (million)
% 2.57/0.67 % (961260)Instruction limit reached!
% 2.57/0.67 % (961260)------------------------------
% 2.57/0.67 % (961260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.67 % (961260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.67 % (961260)CaDiCaL version: 2.1.3
% 2.57/0.67 % (961260)Termination reason: Instruction limit
% 2.57/0.67 % (961260)Termination phase: Twee Goal Transformation
% 2.57/0.67 % (961260)Time elapsed: 0.057 s
% 2.57/0.67 % (961260)Peak memory usage: 11 MB
% 2.57/0.67 % (961260)Instructions burned: 144 (million)
% 2.57/0.67 % (961278)Instruction limit reached!
% 2.57/0.67 % (961278)------------------------------
% 2.57/0.67 % (961278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.67 % (961278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.67 % (961278)CaDiCaL version: 2.1.3
% 2.57/0.67 % (961278)Termination reason: Instruction limit
% 2.57/0.67 % (961278)Termination phase: Property scanning
% 2.57/0.67 % (961278)Time elapsed: 0.004 s
% 2.57/0.67 % (961278)Peak memory usage: 10 MB
% 2.57/0.67 % (961278)Instructions burned: 20 (million)
% 2.57/0.67 % (961275)Instruction limit reached!
% 2.57/0.67 % (961275)------------------------------
% 2.57/0.67 % (961275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.67 % (961275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.76 % (961275)CaDiCaL version: 2.1.3
% 3.10/0.76 % (961275)Termination reason: Instruction limit
% 3.10/0.76 % (961275)Termination phase: Property scanning
% 3.10/0.76 % (961275)Time elapsed: 0.010 s
% 3.10/0.76 % (961275)Peak memory usage: 10 MB
% 3.10/0.76 % (961275)Instructions burned: 22 (million)
% 3.10/0.76 % (961283)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=913110338:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 3.10/0.76 % (961281)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1519123032:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.10/0.76 % (961282)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=280512128:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 3.10/0.76 % (961284)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2276956760:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 3.10/0.76 % (961283)Instruction limit reached!
% 3.10/0.76 % (961283)------------------------------
% 3.10/0.76 % (961283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.76 % (961283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.76 % (961283)CaDiCaL version: 2.1.3
% 3.10/0.76 % (961283)Termination reason: Instruction limit
% 3.10/0.76 % (961283)Termination phase: Property scanning
% 3.10/0.76 % (961283)Time elapsed: 0.011 s
% 3.10/0.76 % (961283)Peak memory usage: 11 MB
% 3.10/0.76 % (961283)Instructions burned: 48 (million)
% 3.10/0.76 % (961289)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3648400081:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.10/0.76 % (961273)Instruction limit reached!
% 3.10/0.76 % (961273)------------------------------
% 3.10/0.76 % (961273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.76 % (961273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.76 % (961273)CaDiCaL version: 2.1.3
% 3.10/0.76 % (961273)Termination reason: Instruction limit
% 3.10/0.76 % (961273)Termination phase: Property scanning
% 3.10/0.76 % (961273)Time elapsed: 0.067 s
% 3.10/0.76 % (961273)Peak memory usage: 11 MB
% 3.10/0.76 % (961273)Instructions burned: 170 (million)
% 3.10/0.76 % (961267)Instruction limit reached!
% 3.10/0.76 % (961267)------------------------------
% 3.10/0.76 % (961267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.76 % (961267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.76 % (961267)CaDiCaL version: 2.1.3
% 3.10/0.76 % (961267)Termination reason: Instruction limit
% 3.10/0.76 % (961267)Termination phase: Saturation
% 3.10/0.76 % (961267)Time elapsed: 0.096 s
% 3.10/0.76 % (961267)Peak memory usage: 12 MB
% 3.10/0.76 % (961267)Instructions burned: 181 (million)
% 3.10/0.76 % (961289)Instruction limit reached!
% 3.10/0.76 % (961289)------------------------------
% 3.10/0.76 % (961289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.76 % (961289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.76 % (961289)CaDiCaL version: 2.1.3
% 3.10/0.76 % (961289)Termination reason: Instruction limit
% 3.10/0.76 % (961289)Termination phase: Property scanning
% 3.10/0.76 % (961289)Time elapsed: 0.018 s
% 3.10/0.76 % (961289)Peak memory usage: 10 MB
% 3.10/0.76 % (961289)Instructions burned: 21 (million)
% 3.10/0.76 % (961291)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.10/0.76 % (961291)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=918635343:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.10/0.76 % (961293)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=691186502:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 4.12/0.93 % (961292)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1669845936:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 4.12/0.93 % (961292)Instruction limit reached!
% 4.12/0.93 % (961292)------------------------------
% 4.12/0.93 % (961292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.93 % (961292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.93 % (961292)CaDiCaL version: 2.1.3
% 4.12/0.93 % (961292)Termination reason: Instruction limit
% 4.12/0.93 % (961292)Termination phase: shuffling
% 4.12/0.93 % (961292)Time elapsed: 0.006 s
% 4.12/0.93 % (961292)Peak memory usage: 10 MB
% 4.12/0.93 % (961292)Instructions burned: 14 (million)
% 4.12/0.93 % (961297)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2342098889:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 4.12/0.93 % (961293)Instruction limit reached!
% 4.12/0.93 % (961293)------------------------------
% 4.12/0.93 % (961293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.93 % (961293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.93 % (961293)CaDiCaL version: 2.1.3
% 4.12/0.93 % (961293)Termination reason: Instruction limit
% 4.12/0.93 % (961293)Termination phase: Function definition elimination
% 4.12/0.93 % (961293)Time elapsed: 0.033 s
% 4.12/0.93 % (961293)Peak memory usage: 11 MB
% 4.12/0.93 % (961293)Instructions burned: 67 (million)
% 4.12/0.93 % (961284)Instruction limit reached!
% 4.12/0.93 % (961284)------------------------------
% 4.12/0.93 % (961284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.93 % (961284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.93 % (961284)CaDiCaL version: 2.1.3
% 4.12/0.93 % (961284)Termination reason: Instruction limit
% 4.12/0.93 % (961284)Termination phase: Saturation
% 4.12/0.93 % (961284)Time elapsed: 0.104 s
% 4.12/0.93 % (961284)Peak memory usage: 14 MB
% 4.12/0.93 % (961284)Instructions burned: 482 (million)
% 4.12/0.93 % (961297)Instruction limit reached!
% 4.12/0.93 % (961297)------------------------------
% 4.12/0.93 % (961297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.93 % (961297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.93 % (961297)CaDiCaL version: 2.1.3
% 4.12/0.93 % (961297)Termination reason: Instruction limit
% 4.12/0.93 % (961297)Termination phase: Function definition elimination
% 4.12/0.93 % (961297)Time elapsed: 0.022 s
% 4.12/0.93 % (961297)Peak memory usage: 11 MB
% 4.12/0.93 % (961297)Instructions burned: 53 (million)
% 4.12/0.93 % (961299)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=64242656:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 4.12/0.93 % (961300)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=484480329:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 4.12/0.93 % (961281)Instruction limit reached!
% 4.12/0.93 % (961281)------------------------------
% 4.12/0.93 % (961281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.93 % (961281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.93 % (961281)CaDiCaL version: 2.1.3
% 4.12/0.93 % (961281)Termination reason: Instruction limit
% 4.12/0.93 % (961281)Termination phase: Saturation
% 4.12/0.93 % (961281)Time elapsed: 0.125 s
% 4.12/0.93 % (961281)Peak memory usage: 12 MB
% 4.12/0.93 % (961281)Instructions burned: 318 (million)
% 4.12/0.93 % (961291)Instruction limit reached!
% 4.12/0.93 % (961291)------------------------------
% 4.12/0.93 % (961291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.93 % (961291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.93 % (961291)CaDiCaL version: 2.1.3
% 4.12/0.93 % (961291)Termination reason: Instruction limit
% 4.12/0.93 % (961291)Termination phase: Property scanning
% 4.12/0.93 % (961291)Time elapsed: 0.078 s
% 4.12/0.93 % (961291)Peak memory usage: 11 MB
% 4.12/0.93 % (961291)Instructions burned: 200 (million)
% 4.12/0.93 % (961299)Instruction limit reached!
% 4.12/0.93 % (961299)------------------------------
% 4.12/0.93 % (961299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.93 % (961299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.01 % (961299)CaDiCaL version: 2.1.3
% 4.12/1.01 % (961299)Termination reason: Instruction limit
% 4.12/1.01 % (961299)Termination phase: Property scanning
% 4.12/1.01 % (961299)Time elapsed: 0.013 s
% 4.12/1.01 % (961299)Peak memory usage: 10 MB
% 4.12/1.01 % (961299)Instructions burned: 31 (million)
% 4.12/1.01 % (961301)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3022973301:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 4.12/1.01 % (961305)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 4.12/1.01 % (961304)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1911107252:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 4.12/1.01 % (961305)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3774084953:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 4.12/1.01 % (961301)Instruction limit reached!
% 4.12/1.01 % (961301)------------------------------
% 4.12/1.01 % (961301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/1.01 % (961301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.01 % (961301)CaDiCaL version: 2.1.3
% 4.12/1.01 % (961301)Termination reason: Instruction limit
% 4.12/1.01 % (961301)Termination phase: Property scanning
% 4.12/1.01 % (961301)Time elapsed: 0.014 s
% 4.12/1.01 % (961301)Peak memory usage: 10 MB
% 4.12/1.01 % (961301)Instructions burned: 34 (million)
% 4.12/1.01 % (961300)Instruction limit reached!
% 4.12/1.01 % (961300)------------------------------
% 4.12/1.01 % (961300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/1.01 % (961300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.01 % (961300)CaDiCaL version: 2.1.3
% 4.12/1.01 % (961300)Termination reason: Instruction limit
% 4.12/1.01 % (961300)Termination phase: Saturation
% 4.12/1.01 % (961300)Time elapsed: 0.029 s
% 4.12/1.01 % (961300)Peak memory usage: 12 MB
% 4.12/1.01 % (961300)Instructions burned: 139 (million)
% 4.12/1.01 % (961306)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1149097853:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 4.12/1.01 % (961312)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3227821927:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 4.12/1.01 % (961311)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3721672243:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 4.12/1.01 % (961304)Instruction limit reached!
% 4.12/1.01 % (961304)------------------------------
% 4.12/1.01 % (961304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/1.01 % (961304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.01 % (961304)CaDiCaL version: 2.1.3
% 4.12/1.01 % (961304)Termination reason: Instruction limit
% 4.12/1.01 % (961304)Termination phase: Function definition elimination
% 4.12/1.01 % (961304)Time elapsed: 0.028 s
% 4.12/1.01 % (961304)Peak memory usage: 11 MB
% 4.12/1.01 % (961304)Instructions burned: 68 (million)
% 4.12/1.01 % (961315)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=983118000:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 4.12/1.01 % (961311)Instruction limit reached!
% 4.12/1.01 % (961311)------------------------------
% 4.12/1.01 % (961311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/1.01 % (961311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.01 % (961311)CaDiCaL version: 2.1.3
% 4.12/1.01 % (961311)Termination reason: Instruction limit
% 4.12/1.01 % (961311)Termination phase: Twee Goal Transformation
% 4.12/1.01 % (961311)Time elapsed: 0.040 s
% 4.12/1.01 % (961311)Peak memory usage: 11 MB
% 4.12/1.01 % (961311)Instructions burned: 98 (million)
% 4.12/1.01 % (961305)Instruction limit reached!
% 4.12/1.01 % (961305)------------------------------
% 4.12/1.01 % (961305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/1.01 % (961305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.01 % (961305)CaDiCaL version: 2.1.3
% 4.12/1.01 % (961305)Termination reason: Instruction limit
% 4.12/1.01 % (961305)Termination phase: Property scanning
% 4.12/1.01 % (961305)Time elapsed: 0.071 s
% 4.12/1.01 % (961305)Peak memory usage: 10 MB
% 5.57/1.09 % (961305)Instructions burned: 181 (million)
% 5.57/1.09 % (961317)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3106493695:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.57/1.09 % (961318)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3746251382:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.57/1.09 % (961312)Instruction limit reached!
% 5.57/1.09 % (961312)------------------------------
% 5.57/1.09 % (961312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.09 % (961312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.09 % (961312)CaDiCaL version: 2.1.3
% 5.57/1.09 % (961312)Termination reason: Instruction limit
% 5.57/1.09 % (961312)Termination phase: Saturation
% 5.57/1.09 % (961312)Time elapsed: 0.085 s
% 5.57/1.09 % (961312)Peak memory usage: 13 MB
% 5.57/1.09 % (961312)Instructions burned: 431 (million)
% 5.57/1.09 % (961321)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2015221533:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.57/1.09 % (961321)Instruction limit reached!
% 5.57/1.09 % (961321)------------------------------
% 5.57/1.09 % (961321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.09 % (961321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.09 % (961321)CaDiCaL version: 2.1.3
% 5.57/1.09 % (961321)Termination reason: Instruction limit
% 5.57/1.09 % (961321)Termination phase: Function definition elimination
% 5.57/1.09 % (961321)Time elapsed: 0.011 s
% 5.57/1.09 % (961321)Peak memory usage: 10 MB
% 5.57/1.09 % (961321)Instructions burned: 48 (million)
% 5.57/1.09 % (961323)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2931186208:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 5.57/1.09 % (961318)Instruction limit reached!
% 5.57/1.09 % (961318)------------------------------
% 5.57/1.09 % (961318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.09 % (961318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.09 % (961318)CaDiCaL version: 2.1.3
% 5.57/1.09 % (961318)Termination reason: Instruction limit
% 5.57/1.09 % (961318)Termination phase: Saturation
% 5.57/1.09 % (961318)Time elapsed: 0.060 s
% 5.57/1.09 % (961318)Peak memory usage: 15 MB
% 5.57/1.09 % (961318)Instructions burned: 132 (million)
% 5.57/1.09 % (961325)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3024152631:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 5.57/1.09 % (961306)Instruction limit reached!
% 5.57/1.09 % (961306)------------------------------
% 5.57/1.09 % (961306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.09 % (961306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.09 % (961306)CaDiCaL version: 2.1.3
% 5.57/1.09 % (961306)Termination reason: Instruction limit
% 5.57/1.09 % (961306)Termination phase: Saturation
% 5.57/1.09 % (961306)Time elapsed: 0.175 s
% 5.57/1.09 % (961306)Peak memory usage: 12 MB
% 5.57/1.09 % (961306)Instructions burned: 247 (million)
% 5.57/1.09 % (961327)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1864851525:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 5.57/1.09 % (961282)Instruction limit reached!
% 5.57/1.09 % (961282)------------------------------
% 5.57/1.09 % (961282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.09 % (961282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.09 % (961282)CaDiCaL version: 2.1.3
% 5.57/1.09 % (961282)Termination reason: Instruction limit
% 5.57/1.09 % (961282)Termination phase: Saturation
% 5.57/1.09 % (961282)Time elapsed: 0.350 s
% 5.57/1.09 % (961282)Peak memory usage: 15 MB
% 5.57/1.09 % (961282)Instructions burned: 855 (million)
% 5.57/1.09 % (961329)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=253620451:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 5.57/1.09 % (961327)Instruction limit reached!
% 5.57/1.09 % (961327)------------------------------
% 5.57/1.09 % (961327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.09 % (961327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.17 % (961327)CaDiCaL version: 2.1.3
% 6.01/1.17 % (961327)Termination reason: Instruction limit
% 6.01/1.17 % (961327)Termination phase: Property scanning
% 6.01/1.17 % (961327)Time elapsed: 0.041 s
% 6.01/1.17 % (961327)Peak memory usage: 11 MB
% 6.01/1.17 % (961327)Instructions burned: 97 (million)
% 6.01/1.17 % (961329)Instruction limit reached!
% 6.01/1.17 % (961329)------------------------------
% 6.01/1.17 % (961329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.01/1.17 % (961329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.17 % (961329)CaDiCaL version: 2.1.3
% 6.01/1.17 % (961329)Termination reason: Instruction limit
% 6.01/1.17 % (961329)Termination phase: Function definition elimination
% 6.01/1.17 % (961329)Time elapsed: 0.028 s
% 6.01/1.17 % (961329)Peak memory usage: 11 MB
% 6.01/1.17 % (961329)Instructions burned: 67 (million)
% 6.01/1.17 % (961331)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=125588273:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 6.01/1.17 % (961259)Instruction limit reached!
% 6.01/1.17 % (961259)------------------------------
% 6.01/1.17 % (961259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.01/1.17 % (961259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.17 % (961259)CaDiCaL version: 2.1.3
% 6.01/1.17 % (961259)Termination reason: Instruction limit
% 6.01/1.17 % (961259)Termination phase: Saturation
% 6.01/1.17 % (961259)Time elapsed: 0.493 s
% 6.01/1.17 % (961259)Peak memory usage: 18 MB
% 6.01/1.17 % (961259)Instructions burned: 1240 (million)
% 6.01/1.17 % (961323)Instruction limit reached!
% 6.01/1.17 % (961323)------------------------------
% 6.01/1.17 % (961323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.01/1.17 % (961323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.17 % (961323)CaDiCaL version: 2.1.3
% 6.01/1.17 % (961323)Termination reason: Instruction limit
% 6.01/1.17 % (961323)Termination phase: Saturation
% 6.01/1.17 % (961323)Time elapsed: 0.138 s
% 6.01/1.17 % (961323)Peak memory usage: 17 MB
% 6.01/1.17 % (961323)Instructions burned: 576 (million)
% 6.01/1.17 % (961332)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3928502535:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 6.01/1.17 % (961335)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1927401471:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.01/1.17 % (961317)Instruction limit reached!
% 6.01/1.17 % (961317)------------------------------
% 6.01/1.17 % (961317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.01/1.17 % (961317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.17 % (961317)CaDiCaL version: 2.1.3
% 6.01/1.17 % (961317)Termination reason: Instruction limit
% 6.01/1.17 % (961317)Termination phase: Saturation
% 6.01/1.17 % (961317)Time elapsed: 0.207 s
% 6.01/1.17 % (961317)Peak memory usage: 13 MB
% 6.01/1.17 % (961317)Instructions burned: 516 (million)
% 6.01/1.17 % (961334)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2299109312:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 6.01/1.17 % (961331)Instruction limit reached!
% 6.01/1.17 % (961331)------------------------------
% 6.01/1.17 % (961331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.01/1.17 % (961331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.17 % (961331)CaDiCaL version: 2.1.3
% 6.01/1.17 % (961331)Termination reason: Instruction limit
% 6.01/1.17 % (961331)Termination phase: Property scanning
% 6.01/1.17 % (961331)Time elapsed: 0.043 s
% 6.01/1.17 % (961331)Peak memory usage: 11 MB
% 6.01/1.17 % (961331)Instructions burned: 106 (million)
% 6.01/1.17 % (961339)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3440778919:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 6.01/1.17 % (961339)Instruction limit reached!
% 6.40/1.25 % (961339)------------------------------
% 6.40/1.25 % (961339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.40/1.25 % (961339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.25 % (961339)CaDiCaL version: 2.1.3
% 6.40/1.25 % (961339)Termination reason: Instruction limit
% 6.40/1.25 % (961339)Termination phase: Property scanning
% 6.40/1.25 % (961339)Time elapsed: 0.015 s
% 6.40/1.25 % (961339)Peak memory usage: 10 MB
% 6.40/1.25 % (961339)Instructions burned: 36 (million)
% 6.40/1.25 % (961340)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=4186714631:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 6.40/1.25 % (961342)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3405311157:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2992 on theBenchmark for (2992ds/66Mi)
% 6.40/1.25 % (961325)Instruction limit reached!
% 6.40/1.25 % (961325)------------------------------
% 6.40/1.25 % (961325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.40/1.25 % (961325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.25 % (961325)CaDiCaL version: 2.1.3
% 6.40/1.25 % (961325)Termination reason: Instruction limit
% 6.40/1.25 % (961325)Termination phase: Saturation
% 6.40/1.25 % (961325)Time elapsed: 0.180 s
% 6.40/1.25 % (961325)Peak memory usage: 13 MB
% 6.40/1.25 % (961325)Instructions burned: 452 (million)
% 6.40/1.25 % (961345)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2193622373:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2992 on theBenchmark for (2992ds/22Mi)
% 6.40/1.25 % (961342)Instruction limit reached!
% 6.40/1.25 % (961342)------------------------------
% 6.40/1.25 % (961342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.40/1.25 % (961342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.25 % (961342)CaDiCaL version: 2.1.3
% 6.40/1.25 % (961342)Termination reason: Instruction limit
% 6.40/1.25 % (961342)Termination phase: Saturation
% 6.40/1.25 % (961342)Time elapsed: 0.037 s
% 6.40/1.25 % (961342)Peak memory usage: 13 MB
% 6.40/1.25 % (961342)Instructions burned: 72 (million)
% 6.40/1.25 % (961340)Instruction limit reached!
% 6.40/1.25 % (961340)------------------------------
% 6.40/1.25 % (961340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.40/1.25 % (961340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.25 % (961340)CaDiCaL version: 2.1.3
% 6.40/1.25 % (961340)Termination reason: Instruction limit
% 6.40/1.25 % (961340)Termination phase: Twee Goal Transformation
% 6.40/1.25 % (961340)Time elapsed: 0.047 s
% 6.40/1.25 % (961340)Peak memory usage: 11 MB
% 6.40/1.25 % (961340)Instructions burned: 94 (million)
% 6.40/1.25 % (961345)Instruction limit reached!
% 6.40/1.25 % (961345)------------------------------
% 6.40/1.25 % (961345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.40/1.25 % (961345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.25 % (961345)CaDiCaL version: 2.1.3
% 6.40/1.25 % (961345)Termination reason: Instruction limit
% 6.40/1.25 % (961345)Termination phase: Property scanning
% 6.40/1.25 % (961345)Time elapsed: 0.011 s
% 6.40/1.25 % (961345)Peak memory usage: 10 MB
% 6.40/1.25 % (961345)Instructions burned: 24 (million)
% 6.40/1.25 % (961335)Instruction limit reached!
% 6.40/1.25 % (961335)------------------------------
% 6.40/1.25 % (961335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.40/1.25 % (961335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.25 % (961335)CaDiCaL version: 2.1.3
% 6.40/1.25 % (961335)Termination reason: Instruction limit
% 6.40/1.25 % (961335)Termination phase: Saturation
% 6.40/1.25 % (961335)Time elapsed: 0.105 s
% 6.40/1.25 % (961335)Peak memory usage: 12 MB
% 6.40/1.25 % (961335)Instructions burned: 505 (million)
% 6.40/1.25 % (961315)Instruction limit reached!
% 6.40/1.25 % (961315)------------------------------
% 6.40/1.25 % (961315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.40/1.25 % (961315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.25 % (961315)CaDiCaL version: 2.1.3
% 6.40/1.25 % (961315)Termination reason: Instruction limit
% 6.40/1.25 % (961315)Termination phase: Saturation
% 6.40/1.25 % (961315)Time elapsed: 0.350 s
% 6.40/1.25 % (961315)Peak memory usage: 13 MB
% 6.40/1.25 % (961315)Instructions burned: 876 (million)
% 7.32/1.43 % (961347)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=1567198516:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 7.32/1.43 % (961350)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=2640541459:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/340Mi)
% 7.32/1.43 % (961349)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 7.32/1.43 % (961348)lrs+10_1_sil=128000:si=on:urr=on:random_seed=4212677380:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 7.32/1.43 % (961349)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=4248422969:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/137Mi)
% 7.32/1.43 % (961351)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=4884470:i=227:sd=1:bd=all:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/227Mi)
% 7.32/1.43 % (961348)Instruction limit reached!
% 7.32/1.43 % (961348)------------------------------
% 7.32/1.43 % (961348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.32/1.43 % (961348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.32/1.43 % (961348)CaDiCaL version: 2.1.3
% 7.32/1.43 % (961348)Termination reason: Instruction limit
% 7.32/1.43 % (961348)Termination phase: SInE selection
% 7.32/1.43 % (961348)Time elapsed: 0.013 s
% 7.32/1.43 % (961348)Peak memory usage: 10 MB
% 7.32/1.43 % (961348)Instructions burned: 29 (million)
% 7.32/1.43 % (961334)Instruction limit reached!
% 7.32/1.43 % (961334)------------------------------
% 7.32/1.43 % (961334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.32/1.43 % (961334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.32/1.43 % (961334)CaDiCaL version: 2.1.3
% 7.32/1.43 % (961334)Termination reason: Instruction limit
% 7.32/1.43 % (961334)Termination phase: Saturation
% 7.32/1.43 % (961334)Time elapsed: 0.141 s
% 7.32/1.43 % (961334)Peak memory usage: 12 MB
% 7.32/1.43 % (961334)Instructions burned: 377 (million)
% 7.32/1.43 % (961357)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 7.32/1.43 % (961357)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2436164163:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/373Mi)
% 7.32/1.43 % (961358)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1538052121:i=116:ep=RSTC:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/116Mi)
% 7.32/1.43 % (961349)Instruction limit reached!
% 7.32/1.43 % (961349)------------------------------
% 7.32/1.43 % (961349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.32/1.43 % (961349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.32/1.43 % (961349)CaDiCaL version: 2.1.3
% 7.32/1.43 % (961349)Termination reason: Instruction limit
% 7.32/1.43 % (961349)Termination phase: Property scanning
% 7.32/1.43 % (961349)Time elapsed: 0.055 s
% 7.32/1.43 % (961349)Peak memory usage: 11 MB
% 7.32/1.43 % (961349)Instructions burned: 138 (million)
% 7.32/1.43 % (961350)Instruction limit reached!
% 7.32/1.43 % (961350)------------------------------
% 7.32/1.43 % (961350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.32/1.43 % (961350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.32/1.43 % (961350)CaDiCaL version: 2.1.3
% 7.32/1.43 % (961350)Termination reason: Instruction limit
% 7.32/1.43 % (961350)Termination phase: Saturation
% 7.32/1.43 % (961350)Time elapsed: 0.069 s
% 7.32/1.43 % (961350)Peak memory usage: 12 MB
% 7.32/1.43 % (961350)Instructions burned: 340 (million)
% 7.32/1.43 % (961362)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2662619097:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2990 on theBenchmark for (2990ds/270Mi)
% 7.32/1.43 % (961361)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2797944357:i=575:rtra=on_2990 on theBenchmark for (2990ds/575Mi)
% 8.72/1.61 % (961358)Instruction limit reached!
% 8.72/1.61 % (961358)------------------------------
% 8.72/1.61 % (961358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.61 % (961358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.61 % (961358)CaDiCaL version: 2.1.3
% 8.72/1.61 % (961358)Termination reason: Instruction limit
% 8.72/1.61 % (961358)Termination phase: Property scanning
% 8.72/1.61 % (961358)Time elapsed: 0.047 s
% 8.72/1.61 % (961358)Peak memory usage: 11 MB
% 8.72/1.61 % (961358)Instructions burned: 116 (million)
% 8.72/1.61 % (961351)Instruction limit reached!
% 8.72/1.61 % (961351)------------------------------
% 8.72/1.61 % (961351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.61 % (961351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.61 % (961351)CaDiCaL version: 2.1.3
% 8.72/1.61 % (961351)Termination reason: Instruction limit
% 8.72/1.61 % (961351)Termination phase: Saturation
% 8.72/1.61 % (961351)Time elapsed: 0.087 s
% 8.72/1.61 % (961351)Peak memory usage: 12 MB
% 8.72/1.61 % (961351)Instructions burned: 228 (million)
% 8.72/1.61 % (961365)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=184177432:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2990 on theBenchmark for (2990ds/9840Mi)
% 8.72/1.61 % (961366)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=3570188640:i=421:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/421Mi)
% 8.72/1.61 % (961347)Instruction limit reached!
% 8.72/1.61 % (961347)------------------------------
% 8.72/1.61 % (961347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.61 % (961347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.61 % (961347)CaDiCaL version: 2.1.3
% 8.72/1.61 % (961347)Termination reason: Instruction limit
% 8.72/1.61 % (961347)Termination phase: Saturation
% 8.72/1.61 % (961347)Time elapsed: 0.134 s
% 8.72/1.61 % (961347)Peak memory usage: 12 MB
% 8.72/1.61 % (961347)Instructions burned: 339 (million)
% 8.72/1.61 % (961362)Instruction limit reached!
% 8.72/1.61 % (961362)------------------------------
% 8.72/1.61 % (961362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.61 % (961362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.61 % (961362)CaDiCaL version: 2.1.3
% 8.72/1.61 % (961362)Termination reason: Instruction limit
% 8.72/1.61 % (961362)Termination phase: Saturation
% 8.72/1.61 % (961362)Time elapsed: 0.056 s
% 8.72/1.61 % (961362)Peak memory usage: 12 MB
% 8.72/1.61 % (961362)Instructions burned: 274 (million)
% 8.72/1.61 % (961370)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2322127967:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/31Mi)
% 8.72/1.61 % (961369)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.72/1.61 % (961369)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3854822607:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/270Mi)
% 8.72/1.61 % (961370)Instruction limit reached!
% 8.72/1.61 % (961370)------------------------------
% 8.72/1.61 % (961370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.61 % (961370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.61 % (961370)CaDiCaL version: 2.1.3
% 8.72/1.61 % (961370)Termination reason: Instruction limit
% 8.72/1.61 % (961370)Termination phase: Property scanning
% 8.72/1.61 % (961370)Time elapsed: 0.008 s
% 8.72/1.61 % (961370)Peak memory usage: 10 MB
% 8.72/1.61 % (961370)Instructions burned: 36 (million)
% 8.72/1.61 % (961373)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 8.72/1.61 % (961373)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.72/1.61 % (961373)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4164654362:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2990 on theBenchmark for (2990ds/1440Mi)
% 8.96/1.77 % (961357)Instruction limit reached!
% 8.96/1.77 % (961357)------------------------------
% 8.96/1.77 % (961357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.96/1.77 % (961357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.96/1.77 % (961357)CaDiCaL version: 2.1.3
% 8.96/1.77 % (961357)Termination reason: Instruction limit
% 8.96/1.77 % (961357)Termination phase: Saturation
% 8.96/1.77 % (961357)Time elapsed: 0.148 s
% 8.96/1.77 % (961357)Peak memory usage: 12 MB
% 8.96/1.77 % (961357)Instructions burned: 375 (million)
% 8.96/1.77 % (961375)dis+10_2_sil=128000:si=on:random_seed=3363800121:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2989 on theBenchmark for (2989ds/339Mi)
% 8.96/1.77 % (961369)Instruction limit reached!
% 8.96/1.77 % (961369)------------------------------
% 8.96/1.77 % (961369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.96/1.77 % (961369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.96/1.77 % (961369)CaDiCaL version: 2.1.3
% 8.96/1.77 % (961369)Termination reason: Instruction limit
% 8.96/1.77 % (961369)Termination phase: Saturation
% 8.96/1.77 % (961369)Time elapsed: 0.106 s
% 8.96/1.77 % (961369)Peak memory usage: 12 MB
% 8.96/1.77 % (961369)Instructions burned: 270 (million)
% 8.96/1.77 % (961377)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2392530253:i=111:add=on:fgj=on:rtra=on:fdi=1024_2988 on theBenchmark for (2988ds/111Mi)
% 8.96/1.77 % (961366)Instruction limit reached!
% 8.96/1.77 % (961366)------------------------------
% 8.96/1.77 % (961366)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.96/1.77 % (961366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.96/1.77 % (961366)CaDiCaL version: 2.1.3
% 8.96/1.77 % (961366)Termination reason: Instruction limit
% 8.96/1.77 % (961366)Termination phase: Saturation
% 8.96/1.77 % (961366)Time elapsed: 0.159 s
% 8.96/1.77 % (961366)Peak memory usage: 13 MB
% 8.96/1.77 % (961366)Instructions burned: 423 (million)
% 8.96/1.77 % (961379)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1475983048:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/122Mi)
% 8.96/1.77 % (961361)Instruction limit reached!
% 8.96/1.77 % (961361)------------------------------
% 8.96/1.77 % (961361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.96/1.77 % (961361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.96/1.77 % (961361)CaDiCaL version: 2.1.3
% 8.96/1.77 % (961361)Termination reason: Instruction limit
% 8.96/1.77 % (961361)Termination phase: Saturation
% 8.96/1.77 % (961361)Time elapsed: 0.234 s
% 8.96/1.77 % (961361)Peak memory usage: 13 MB
% 8.96/1.77 % (961361)Instructions burned: 577 (million)
% 8.96/1.77 % (961377)Instruction limit reached!
% 8.96/1.77 % (961377)------------------------------
% 8.96/1.77 % (961377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.96/1.77 % (961377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.96/1.77 % (961377)CaDiCaL version: 2.1.3
% 8.96/1.77 % (961377)Termination reason: Instruction limit
% 8.96/1.77 % (961377)Termination phase: Property scanning
% 8.96/1.77 % (961377)Time elapsed: 0.045 s
% 8.96/1.77 % (961377)Peak memory usage: 11 MB
% 8.96/1.77 % (961377)Instructions burned: 113 (million)
% 8.96/1.77 % (961381)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=869800647:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/136Mi)
% 8.96/1.77 % (961375)Instruction limit reached!
% 8.96/1.77 % (961375)------------------------------
% 8.96/1.77 % (961375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.96/1.77 % (961375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.96/1.77 % (961375)CaDiCaL version: 2.1.3
% 8.96/1.77 % (961375)Termination reason: Instruction limit
% 8.96/1.77 % (961375)Termination phase: Saturation
% 8.96/1.77 % (961375)Time elapsed: 0.130 s
% 8.96/1.77 % (961375)Peak memory usage: 12 MB
% 8.96/1.77 % (961375)Instructions burned: 339 (million)
% 8.96/1.77 % (961382)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=151888045:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/232Mi)
% 9.78/1.97 % (961379)Instruction limit reached!
% 9.78/1.97 % (961379)------------------------------
% 9.78/1.97 % (961379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.78/1.97 % (961379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/1.97 % (961379)CaDiCaL version: 2.1.3
% 9.78/1.97 % (961379)Termination reason: Instruction limit
% 9.78/1.97 % (961379)Termination phase: Property scanning
% 9.78/1.97 % (961379)Time elapsed: 0.049 s
% 9.78/1.97 % (961379)Peak memory usage: 11 MB
% 9.78/1.97 % (961379)Instructions burned: 122 (million)
% 9.78/1.97 % (961384)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=2359464312:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2988 on theBenchmark for (2988ds/1254Mi)
% 9.78/1.97 % (961386)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 9.78/1.97 % (961386)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=1854533930:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2988 on theBenchmark for (2988ds/281Mi)
% 9.78/1.97 % (961381)Instruction limit reached!
% 9.78/1.97 % (961381)------------------------------
% 9.78/1.97 % (961381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.78/1.97 % (961381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/1.97 % (961381)CaDiCaL version: 2.1.3
% 9.78/1.97 % (961381)Termination reason: Instruction limit
% 9.78/1.97 % (961381)Termination phase: Property scanning
% 9.78/1.97 % (961381)Time elapsed: 0.055 s
% 9.78/1.97 % (961381)Peak memory usage: 11 MB
% 9.78/1.97 % (961381)Instructions burned: 138 (million)
% 9.78/1.97 % (961389)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1600672603:i=619:add=on:rtra=on_2987 on theBenchmark for (2987ds/619Mi)
% 9.78/1.97 % (961382)Instruction limit reached!
% 9.78/1.97 % (961382)------------------------------
% 9.78/1.97 % (961382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.78/1.97 % (961382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/1.97 % (961382)CaDiCaL version: 2.1.3
% 9.78/1.97 % (961382)Termination reason: Instruction limit
% 9.78/1.97 % (961382)Termination phase: Saturation
% 9.78/1.97 % (961382)Time elapsed: 0.106 s
% 9.78/1.97 % (961382)Peak memory usage: 13 MB
% 9.78/1.97 % (961382)Instructions burned: 234 (million)
% 9.78/1.97 % (961373)Instruction limit reached!
% 9.78/1.97 % (961373)------------------------------
% 9.78/1.97 % (961373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.78/1.97 % (961373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/1.97 % (961373)CaDiCaL version: 2.1.3
% 9.78/1.97 % (961373)Termination reason: Instruction limit
% 9.78/1.97 % (961373)Termination phase: Saturation
% 9.78/1.97 % (961373)Time elapsed: 0.295 s
% 9.78/1.97 % (961373)Peak memory usage: 13 MB
% 9.78/1.97 % (961373)Instructions burned: 1443 (million)
% 9.78/1.97 % (961391)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4012550597:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/865Mi)
% 9.78/1.97 % (961392)lrs+10_1_sil=128000:si=on:urr=on:random_seed=31849338:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/212Mi)
% 9.78/1.97 % (961386)Instruction limit reached!
% 9.78/1.97 % (961386)------------------------------
% 9.78/1.97 % (961386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.78/1.97 % (961386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/1.97 % (961386)CaDiCaL version: 2.1.3
% 9.78/1.97 % (961386)Termination reason: Instruction limit
% 9.78/1.97 % (961386)Termination phase: Saturation
% 9.78/1.97 % (961386)Time elapsed: 0.111 s
% 9.78/1.97 % (961386)Peak memory usage: 12 MB
% 9.78/1.97 % (961386)Instructions burned: 282 (million)
% 9.78/1.97 % (961395)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=2803205497:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/130Mi)
% 9.78/1.97 % (961392)Instruction limit reached!
% 9.78/1.97 % (961392)------------------------------
% 13.32/2.18 % (961392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.32/2.18 % (961392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.18 % (961392)CaDiCaL version: 2.1.3
% 13.32/2.18 % (961392)Termination reason: Instruction limit
% 13.32/2.18 % (961392)Termination phase: Saturation
% 13.32/2.18 % (961392)Time elapsed: 0.046 s
% 13.32/2.18 % (961392)Peak memory usage: 12 MB
% 13.32/2.18 % (961392)Instructions burned: 217 (million)
% 13.32/2.18 % (961397)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3385015984:st=1.5:i=346:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/346Mi)
% 13.32/2.18 % (961395)Instruction limit reached!
% 13.32/2.18 % (961395)------------------------------
% 13.32/2.18 % (961395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.32/2.18 % (961395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.18 % (961395)CaDiCaL version: 2.1.3
% 13.32/2.18 % (961395)Termination reason: Instruction limit
% 13.32/2.18 % (961395)Termination phase: Saturation
% 13.32/2.18 % (961395)Time elapsed: 0.053 s
% 13.32/2.18 % (961395)Peak memory usage: 12 MB
% 13.32/2.18 % (961395)Instructions burned: 132 (million)
% 13.32/2.18 % (961399)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=295833946:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2986 on theBenchmark for (2986ds/152Mi)
% 13.32/2.18 % (961397)Instruction limit reached!
% 13.32/2.18 % (961397)------------------------------
% 13.32/2.18 % (961397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.32/2.18 % (961397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.18 % (961397)CaDiCaL version: 2.1.3
% 13.32/2.18 % (961397)Termination reason: Instruction limit
% 13.32/2.18 % (961397)Termination phase: Saturation
% 13.32/2.18 % (961397)Time elapsed: 0.081 s
% 13.32/2.18 % (961397)Peak memory usage: 17 MB
% 13.32/2.18 % (961397)Instructions burned: 350 (million)
% 13.32/2.18 % (961401)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1896538339:i=75:ep=R:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/75Mi)
% 13.32/2.18 % (961399)Instruction limit reached!
% 13.32/2.18 % (961399)------------------------------
% 13.32/2.18 % (961399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.32/2.18 % (961399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.18 % (961399)CaDiCaL version: 2.1.3
% 13.32/2.18 % (961399)Termination reason: Instruction limit
% 13.32/2.18 % (961399)Termination phase: Property scanning
% 13.32/2.18 % (961399)Time elapsed: 0.061 s
% 13.32/2.18 % (961399)Peak memory usage: 12 MB
% 13.32/2.18 % (961399)Instructions burned: 152 (million)
% 13.32/2.18 % (961401)Instruction limit reached!
% 13.32/2.18 % (961401)------------------------------
% 13.32/2.18 % (961401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.32/2.18 % (961401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.18 % (961401)CaDiCaL version: 2.1.3
% 13.32/2.18 % (961401)Termination reason: Instruction limit
% 13.32/2.18 % (961401)Termination phase: Function definition elimination
% 13.32/2.18 % (961401)Time elapsed: 0.016 s
% 13.32/2.18 % (961401)Peak memory usage: 10 MB
% 13.32/2.18 % (961401)Instructions burned: 77 (million)
% 13.32/2.18 % (961404)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1593550469:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2985 on theBenchmark for (2985ds/148Mi)
% 13.32/2.18 % (961403)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=526048586:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/387Mi)
% 13.32/2.18 % (961389)Instruction limit reached!
% 13.32/2.18 % (961389)------------------------------
% 13.32/2.18 % (961389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.32/2.18 % (961389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.18 % (961389)CaDiCaL version: 2.1.3
% 13.32/2.18 % (961389)Termination reason: Instruction limit
% 13.32/2.18 % (961389)Termination phase: Saturation
% 13.32/2.18 % (961389)Time elapsed: 0.250 s
% 13.32/2.18 % (961389)Peak memory usage: 13 MB
% 13.32/2.18 % (961389)Instructions burned: 621 (million)
% 13.32/2.18 % (961407)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3666883193:i=161:piset=and:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/161Mi)
% 14.16/2.40 % (961404)Instruction limit reached!
% 14.16/2.40 % (961404)------------------------------
% 14.16/2.40 % (961404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.16/2.40 % (961404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.16/2.40 % (961404)CaDiCaL version: 2.1.3
% 14.16/2.40 % (961404)Termination reason: Instruction limit
% 14.16/2.40 % (961404)Termination phase: Saturation
% 14.16/2.40 % (961404)Time elapsed: 0.037 s
% 14.16/2.40 % (961404)Peak memory usage: 13 MB
% 14.16/2.40 % (961404)Instructions burned: 149 (million)
% 14.16/2.40 % (961409)lrs+10_1_sil=128000:si=on:random_seed=3528796743:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/888Mi)
% 14.16/2.40 % (961407)Instruction limit reached!
% 14.16/2.40 % (961407)------------------------------
% 14.16/2.40 % (961407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.16/2.40 % (961407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.16/2.40 % (961407)CaDiCaL version: 2.1.3
% 14.16/2.40 % (961407)Termination reason: Instruction limit
% 14.16/2.40 % (961407)Termination phase: Property scanning
% 14.16/2.40 % (961407)Time elapsed: 0.065 s
% 14.16/2.40 % (961407)Peak memory usage: 11 MB
% 14.16/2.40 % (961407)Instructions burned: 161 (million)
% 14.16/2.40 % (961411)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=3052851523:i=136:add=on:ins=4:rtra=on:sup=off_2984 on theBenchmark for (2984ds/136Mi)
% 14.16/2.40 % (961403)Instruction limit reached!
% 14.16/2.40 % (961403)------------------------------
% 14.16/2.40 % (961403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.16/2.40 % (961403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.16/2.40 % (961403)CaDiCaL version: 2.1.3
% 14.16/2.40 % (961403)Termination reason: Instruction limit
% 14.16/2.40 % (961403)Termination phase: Saturation
% 14.16/2.40 % (961403)Time elapsed: 0.171 s
% 14.16/2.40 % (961403)Peak memory usage: 12 MB
% 14.16/2.40 % (961403)Instructions burned: 388 (million)
% 14.16/2.40 % (961391)Instruction limit reached!
% 14.16/2.40 % (961391)------------------------------
% 14.16/2.40 % (961391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.16/2.40 % (961391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.16/2.40 % (961391)CaDiCaL version: 2.1.3
% 14.16/2.40 % (961391)Termination reason: Instruction limit
% 14.16/2.40 % (961391)Termination phase: Saturation
% 14.16/2.40 % (961391)Time elapsed: 0.360 s
% 14.16/2.40 % (961391)Peak memory usage: 22 MB
% 14.16/2.40 % (961391)Instructions burned: 866 (million)
% 14.16/2.40 % (961411)Instruction limit reached!
% 14.16/2.40 % (961411)------------------------------
% 14.16/2.40 % (961411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.16/2.40 % (961411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.16/2.40 % (961411)CaDiCaL version: 2.1.3
% 14.16/2.40 % (961411)Termination reason: Instruction limit
% 14.16/2.40 % (961411)Termination phase: Property scanning
% 14.16/2.40 % (961411)Time elapsed: 0.056 s
% 14.16/2.40 % (961411)Peak memory usage: 11 MB
% 14.16/2.40 % (961411)Instructions burned: 138 (million)
% 14.16/2.40 % (961413)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2026909981:i=88:s2at=3:nm=2:rtra=on:rawr=on_2983 on theBenchmark for (2983ds/88Mi)
% 14.16/2.40 % (961414)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2313906279:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2983 on theBenchmark for (2983ds/93Mi)
% 14.16/2.40 % (961415)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3979100968:i=2186:rtra=on:ixr=off_2983 on theBenchmark for (2983ds/2186Mi)
% 14.16/2.40 % (961409)Instruction limit reached!
% 14.16/2.40 % (961409)------------------------------
% 14.16/2.40 % (961409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.16/2.40 % (961409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.16/2.40 % (961409)CaDiCaL version: 2.1.3
% 14.16/2.40 % (961409)Termination reason: Instruction limit
% 14.16/2.40 % (961409)Termination phase: Saturation
% 14.16/2.40 % (961409)Time elapsed: 0.183 s
% 14.16/2.40 % (961409)Peak memory usage: 13 MB
% 14.16/2.40 % (961409)Instructions burned: 890 (million)
% 14.16/2.40 % (961413)Instruction limit reached!
% 16.01/2.60 % (961413)------------------------------
% 16.01/2.60 % (961413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.01/2.60 % (961413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.01/2.60 % (961413)CaDiCaL version: 2.1.3
% 16.01/2.60 % (961413)Termination reason: Instruction limit
% 16.01/2.60 % (961413)Termination phase: Function definition elimination
% 16.01/2.60 % (961413)Time elapsed: 0.037 s
% 16.01/2.60 % (961413)Peak memory usage: 11 MB
% 16.01/2.60 % (961413)Instructions burned: 89 (million)
% 16.01/2.60 % (961414)Instruction limit reached!
% 16.01/2.60 % (961414)------------------------------
% 16.01/2.60 % (961414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.01/2.60 % (961414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.01/2.60 % (961414)CaDiCaL version: 2.1.3
% 16.01/2.60 % (961414)Termination reason: Instruction limit
% 16.01/2.60 % (961414)Termination phase: Property scanning
% 16.01/2.60 % (961414)Time elapsed: 0.039 s
% 16.01/2.60 % (961414)Peak memory usage: 11 MB
% 16.01/2.60 % (961414)Instructions burned: 95 (million)
% 16.01/2.60 % (961419)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2449057361:s2a=on:i=240:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/240Mi)
% 16.01/2.60 % (961420)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=1565505326:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2982 on theBenchmark for (2982ds/805Mi)
% 16.01/2.60 % (961421)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 16.01/2.60 % (961421)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=4153730973:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2982 on theBenchmark for (2982ds/391Mi)
% 16.01/2.60 % (961419)Instruction limit reached!
% 16.01/2.60 % (961419)------------------------------
% 16.01/2.60 % (961419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.01/2.60 % (961419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.01/2.60 % (961419)CaDiCaL version: 2.1.3
% 16.01/2.60 % (961419)Termination reason: Instruction limit
% 16.01/2.60 % (961419)Termination phase: Saturation
% 16.01/2.60 % (961419)Time elapsed: 0.051 s
% 16.01/2.60 % (961419)Peak memory usage: 12 MB
% 16.01/2.60 % (961419)Instructions burned: 242 (million)
% 16.01/2.60 % (961425)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=4176908103:i=355:av=off:fsr=off:rtra=on:ixr=off_2982 on theBenchmark for (2982ds/355Mi)
% 16.01/2.60 % (961384)Instruction limit reached!
% 16.01/2.60 % (961384)------------------------------
% 16.01/2.60 % (961384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.01/2.60 % (961384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.01/2.60 % (961384)CaDiCaL version: 2.1.3
% 16.01/2.60 % (961384)Termination reason: Instruction limit
% 16.01/2.60 % (961384)Termination phase: Saturation
% 16.01/2.60 % (961384)Time elapsed: 0.647 s
% 16.01/2.60 % (961384)Peak memory usage: 19 MB
% 16.01/2.60 % (961384)Instructions burned: 1254 (million)
% 16.01/2.60 % (961427)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=3928269907:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2981 on theBenchmark for (2981ds/314Mi)
% 16.01/2.60 % (961425)Instruction limit reached!
% 16.01/2.60 % (961425)------------------------------
% 16.01/2.60 % (961425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.01/2.60 % (961425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.01/2.60 % (961425)CaDiCaL version: 2.1.3
% 16.01/2.60 % (961425)Termination reason: Instruction limit
% 16.01/2.60 % (961425)Termination phase: Saturation
% 16.01/2.60 % (961425)Time elapsed: 0.076 s
% 16.01/2.60 % (961425)Peak memory usage: 12 MB
% 16.01/2.60 % (961425)Instructions burned: 356 (million)
% 16.01/2.60 % (961429)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=4061018859:s2a=on:i=251:fsr=off:rtra=on_2981 on theBenchmark for (2981ds/251Mi)
% 16.01/2.60 % (961429)Instruction limit reached!
% 16.01/2.60 % (961429)------------------------------
% 16.01/2.60 % (961429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.01/2.60 % (961429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.01/2.60 % (961429)CaDiCaL version: 2.1.3
% 17.54/2.84 % (961429)Termination reason: Instruction limit
% 17.54/2.84 % (961429)Termination phase: Saturation
% 17.54/2.84 % (961429)Time elapsed: 0.052 s
% 17.54/2.84 % (961429)Peak memory usage: 12 MB
% 17.54/2.84 % (961429)Instructions burned: 252 (million)
% 17.54/2.84 % (961421)Instruction limit reached!
% 17.54/2.84 % (961421)------------------------------
% 17.54/2.84 % (961421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.54/2.84 % (961421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.54/2.84 % (961421)CaDiCaL version: 2.1.3
% 17.54/2.84 % (961421)Termination reason: Instruction limit
% 17.54/2.84 % (961421)Termination phase: Saturation
% 17.54/2.84 % (961421)Time elapsed: 0.186 s
% 17.54/2.84 % (961421)Peak memory usage: 12 MB
% 17.54/2.84 % (961421)Instructions burned: 391 (million)
% 17.54/2.84 % (961431)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=3534886797:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2980 on theBenchmark for (2980ds/2470Mi)
% 17.54/2.84 % (961433)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=4163746175:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2980 on theBenchmark for (2980ds/673Mi)
% 17.54/2.84 % (961427)Instruction limit reached!
% 17.54/2.84 % (961427)------------------------------
% 17.54/2.84 % (961427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.54/2.84 % (961427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.54/2.84 % (961427)CaDiCaL version: 2.1.3
% 17.54/2.84 % (961427)Termination reason: Instruction limit
% 17.54/2.84 % (961427)Termination phase: Saturation
% 17.54/2.84 % (961427)Time elapsed: 0.120 s
% 17.54/2.84 % (961427)Peak memory usage: 12 MB
% 17.54/2.84 % (961427)Instructions burned: 314 (million)
% 17.54/2.84 % (961435)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1652867590:i=116:ep=RSTC:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/116Mi)
% 17.54/2.84 % (961435)Instruction limit reached!
% 17.54/2.84 % (961435)------------------------------
% 17.54/2.84 % (961435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.54/2.84 % (961435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.54/2.84 % (961435)CaDiCaL version: 2.1.3
% 17.54/2.84 % (961435)Termination reason: Instruction limit
% 17.54/2.84 % (961435)Termination phase: Property scanning
% 17.54/2.84 % (961435)Time elapsed: 0.048 s
% 17.54/2.84 % (961435)Peak memory usage: 11 MB
% 17.54/2.84 % (961435)Instructions burned: 120 (million)
% 17.54/2.84 % (961437)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2616047263:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2979 on theBenchmark for (2979ds/270Mi)
% 17.54/2.84 % (961420)Instruction limit reached!
% 17.54/2.84 % (961420)------------------------------
% 17.54/2.84 % (961420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.54/2.84 % (961420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.54/2.84 % (961420)CaDiCaL version: 2.1.3
% 17.54/2.84 % (961420)Termination reason: Instruction limit
% 17.54/2.84 % (961420)Termination phase: Saturation
% 17.54/2.84 % (961420)Time elapsed: 0.349 s
% 17.54/2.84 % (961420)Peak memory usage: 13 MB
% 17.54/2.84 % (961420)Instructions burned: 806 (million)
% 17.54/2.84 % (961439)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3517260834:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2978 on theBenchmark for (2978ds/30Mi)
% 17.54/2.84 % (961439)Instruction limit reached!
% 17.54/2.84 % (961439)------------------------------
% 17.54/2.84 % (961439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.54/2.84 % (961439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.54/2.84 % (961439)CaDiCaL version: 2.1.3
% 17.54/2.84 % (961439)Termination reason: Instruction limit
% 17.54/2.84 % (961439)Termination phase: Property scanning
% 17.54/2.84 % (961439)Time elapsed: 0.013 s
% 17.54/2.84 % (961439)Peak memory usage: 10 MB
% 17.54/2.84 % (961439)Instructions burned: 30 (million)
% 17.54/2.84 % (961441)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 18.20/3.04 % (961441)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3034900239:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2978 on theBenchmark for (2978ds/39Mi)
% 18.20/3.04 % (961441)Instruction limit reached!
% 18.20/3.04 % (961441)------------------------------
% 18.20/3.04 % (961441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.20/3.04 % (961441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.20/3.04 % (961441)CaDiCaL version: 2.1.3
% 18.20/3.04 % (961441)Termination reason: Instruction limit
% 18.20/3.04 % (961441)Termination phase: Property scanning
% 18.20/3.04 % (961441)Time elapsed: 0.016 s
% 18.20/3.04 % (961441)Peak memory usage: 10 MB
% 18.20/3.04 % (961441)Instructions burned: 39 (million)
% 18.20/3.04 % (961437)Instruction limit reached!
% 18.20/3.04 % (961437)------------------------------
% 18.20/3.04 % (961437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.20/3.04 % (961437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.20/3.04 % (961437)CaDiCaL version: 2.1.3
% 18.20/3.04 % (961437)Termination reason: Instruction limit
% 18.20/3.04 % (961437)Termination phase: Saturation
% 18.20/3.04 % (961437)Time elapsed: 0.106 s
% 18.20/3.04 % (961437)Peak memory usage: 12 MB
% 18.20/3.04 % (961437)Instructions burned: 271 (million)
% 18.20/3.04 % (961443)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=794161612:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2978 on theBenchmark for (2978ds/365Mi)
% 18.20/3.04 % (961444)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3394265368:i=158:av=off:rtra=on_2978 on theBenchmark for (2978ds/158Mi)
% 18.20/3.04 % (961433)Instruction limit reached!
% 18.20/3.04 % (961433)------------------------------
% 18.20/3.04 % (961433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.20/3.04 % (961433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.20/3.04 % (961433)CaDiCaL version: 2.1.3
% 18.20/3.04 % (961433)Termination reason: Instruction limit
% 18.20/3.04 % (961433)Termination phase: Saturation
% 18.20/3.04 % (961433)Time elapsed: 0.269 s
% 18.20/3.04 % (961433)Peak memory usage: 13 MB
% 18.20/3.04 % (961433)Instructions burned: 675 (million)
% 18.20/3.04 % (961447)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 18.20/3.04 % (961447)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3349287277:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2977 on theBenchmark for (2977ds/252Mi)
% 18.20/3.04 % (961444)Instruction limit reached!
% 18.20/3.04 % (961444)------------------------------
% 18.20/3.04 % (961444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.20/3.04 % (961444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.20/3.04 % (961444)CaDiCaL version: 2.1.3
% 18.20/3.04 % (961444)Termination reason: Instruction limit
% 18.20/3.04 % (961444)Termination phase: Saturation
% 18.20/3.04 % (961444)Time elapsed: 0.078 s
% 18.20/3.04 % (961444)Peak memory usage: 13 MB
% 18.20/3.04 % (961444)Instructions burned: 160 (million)
% 18.20/3.04 % (961449)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=103821435:i=213:rtra=on:ss=axioms_2977 on theBenchmark for (2977ds/213Mi)
% 18.20/3.04 % (961443)Instruction limit reached!
% 18.20/3.04 % (961443)------------------------------
% 18.20/3.04 % (961443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.20/3.04 % (961443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.20/3.04 % (961443)CaDiCaL version: 2.1.3
% 18.20/3.04 % (961443)Termination reason: Instruction limit
% 18.20/3.04 % (961443)Termination phase: Saturation
% 18.20/3.04 % (961443)Time elapsed: 0.145 s
% 18.20/3.04 % (961443)Peak memory usage: 13 MB
% 18.20/3.04 % (961443)Instructions burned: 366 (million)
% 18.20/3.04 % (961449)Refutation not found, incomplete strategy
% 18.20/3.04 % (961449)------------------------------
% 18.20/3.04 % (961449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.20/3.04 % (961449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.20/3.04 % (961449)CaDiCaL version: 2.1.3
% 18.20/3.04 % (961449)Termination reason: Refutation not found, incomplete strategy
% 19.71/3.13 % (961449)Time elapsed: 0.057 s
% 19.71/3.13 % (961449)Peak memory usage: 14 MB
% 19.71/3.13 % (961449)Instructions burned: 125 (million)
% 19.71/3.13 % (961449)------------------------------
% 19.71/3.13 % (961449)------------------------------
% 19.71/3.13 % (961451)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=128943587:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2976 on theBenchmark for (2976ds/160Mi)
% 19.71/3.13 % (961447)Instruction limit reached!
% 19.71/3.13 % (961447)------------------------------
% 19.71/3.13 % (961447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.71/3.13 % (961447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.71/3.13 % (961447)CaDiCaL version: 2.1.3
% 19.71/3.13 % (961447)Termination reason: Instruction limit
% 19.71/3.13 % (961447)Termination phase: Saturation
% 19.71/3.13 % (961447)Time elapsed: 0.099 s
% 19.71/3.13 % (961447)Peak memory usage: 12 MB
% 19.71/3.13 % (961447)Instructions burned: 254 (million)
% 19.71/3.13 % (961454)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 19.71/3.13 % (961452)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=2284377335:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2976 on theBenchmark for (2976ds/763Mi)
% 19.71/3.13 % (961454)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1492139866:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2976 on theBenchmark for (2976ds/237Mi)
% 19.71/3.13 % (961451)Instruction limit reached!
% 19.71/3.13 % (961451)------------------------------
% 19.71/3.13 % (961451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.71/3.13 % (961451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.71/3.13 % (961451)CaDiCaL version: 2.1.3
% 19.71/3.13 % (961451)Termination reason: Instruction limit
% 19.71/3.13 % (961451)Termination phase: Twee Goal Transformation
% 19.71/3.13 % (961451)Time elapsed: 0.064 s
% 19.71/3.13 % (961451)Peak memory usage: 11 MB
% 19.71/3.13 % (961451)Instructions burned: 162 (million)
% 19.71/3.13 % (961457)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=877562685:s2a=on:i=386:rtra=on:ntd=on_2975 on theBenchmark for (2975ds/386Mi)
% 19.71/3.13 % (961431)Instruction limit reached!
% 19.71/3.13 % (961431)------------------------------
% 19.71/3.13 % (961431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.71/3.13 % (961431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.71/3.13 % (961431)CaDiCaL version: 2.1.3
% 19.71/3.13 % (961431)Termination reason: Instruction limit
% 19.71/3.13 % (961431)Termination phase: Saturation
% 19.71/3.13 % (961431)Time elapsed: 0.518 s
% 19.71/3.13 % (961431)Peak memory usage: 31 MB
% 19.71/3.13 % (961431)Instructions burned: 2474 (million)
% 19.71/3.13 % (961454)Instruction limit reached!
% 19.71/3.13 % (961454)------------------------------
% 19.71/3.13 % (961454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.71/3.13 % (961454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.71/3.13 % (961454)CaDiCaL version: 2.1.3
% 19.71/3.13 % (961454)Termination reason: Instruction limit
% 19.71/3.13 % (961454)Termination phase: Saturation
% 19.71/3.13 % (961454)Time elapsed: 0.097 s
% 19.71/3.13 % (961454)Peak memory usage: 13 MB
% 19.71/3.13 % (961454)Instructions burned: 244 (million)
% 19.71/3.13 % (961459)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=121085334:i=300:piset=and:nm=32:rtra=on_2975 on theBenchmark for (2975ds/300Mi)
% 19.71/3.13 % (961460)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=3012908519:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2975 on theBenchmark for (2975ds/567Mi)
% 19.71/3.13 % (961457)Instruction limit reached!
% 19.71/3.13 % (961457)------------------------------
% 19.71/3.13 % (961457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.71/3.13 % (961457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.71/3.13 % (961457)CaDiCaL version: 2.1.3
% 19.71/3.13 % (961457)Termination reason: Instruction limit
% 19.71/3.13 % (961457)Termination phase: Saturation
% 19.71/3.13 % (961457)Time elapsed: 0.154 s
% 19.71/3.13 % (961457)Peak memory usage: 12 MB
% 20.51/3.23 % (961457)Instructions burned: 388 (million)
% 20.51/3.23 % (961463)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=625667783:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2974 on theBenchmark for (2974ds/379Mi)
% 20.51/3.23 % (961459)Instruction limit reached!
% 20.51/3.23 % (961459)------------------------------
% 20.51/3.23 % (961459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.51/3.23 % (961459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.51/3.23 % (961459)CaDiCaL version: 2.1.3
% 20.51/3.23 % (961459)Termination reason: Instruction limit
% 20.51/3.23 % (961459)Termination phase: Saturation
% 20.51/3.23 % (961459)Time elapsed: 0.139 s
% 20.51/3.23 % (961459)Peak memory usage: 12 MB
% 20.51/3.23 % (961459)Instructions burned: 301 (million)
% 20.51/3.23 % (961465)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=1759239593:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2973 on theBenchmark for (2973ds/429Mi)
% 20.51/3.23 % (961452)Instruction limit reached!
% 20.51/3.23 % (961452)------------------------------
% 20.51/3.23 % (961452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.51/3.23 % (961452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.51/3.23 % (961452)CaDiCaL version: 2.1.3
% 20.51/3.23 % (961452)Termination reason: Instruction limit
% 20.51/3.23 % (961452)Termination phase: Saturation
% 20.51/3.23 % (961452)Time elapsed: 0.303 s
% 20.51/3.23 % (961452)Peak memory usage: 12 MB
% 20.51/3.23 % (961452)Instructions burned: 763 (million)
% 20.51/3.23 % (961415)Instruction limit reached!
% 20.51/3.23 % (961415)------------------------------
% 20.51/3.23 % (961415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.51/3.23 % (961415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.51/3.23 % (961415)CaDiCaL version: 2.1.3
% 20.51/3.23 % (961415)Termination reason: Instruction limit
% 20.51/3.23 % (961415)Termination phase: Saturation
% 20.51/3.23 % (961415)Time elapsed: 0.984 s
% 20.51/3.23 % (961415)Peak memory usage: 33 MB
% 20.51/3.23 % (961415)Instructions burned: 2187 (million)
% 20.51/3.23 % (961468)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3001719826:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2973 on theBenchmark for (2973ds/445Mi)
% 20.51/3.23 % (961467)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=1691436201:i=478:bd=all:rtra=on_2973 on theBenchmark for (2973ds/478Mi)
% 20.51/3.23 % (961460)Instruction limit reached!
% 20.51/3.23 % (961460)------------------------------
% 20.51/3.23 % (961460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.51/3.23 % (961460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.51/3.23 % (961460)CaDiCaL version: 2.1.3
% 20.51/3.23 % (961460)Termination reason: Instruction limit
% 20.51/3.23 % (961460)Termination phase: Saturation
% 20.51/3.23 % (961460)Time elapsed: 0.240 s
% 20.51/3.23 % (961460)Peak memory usage: 12 MB
% 20.51/3.23 % (961460)Instructions burned: 569 (million)
% 20.51/3.23 % (961471)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=1178702002:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2972 on theBenchmark for (2972ds/71Mi)
% 20.51/3.23 % (961463)Instruction limit reached!
% 20.51/3.23 % (961463)------------------------------
% 20.51/3.23 % (961463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.51/3.23 % (961463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.51/3.23 % (961463)CaDiCaL version: 2.1.3
% 20.51/3.23 % (961463)Termination reason: Instruction limit
% 20.51/3.23 % (961463)Termination phase: Saturation
% 20.51/3.23 % (961463)Time elapsed: 0.155 s
% 20.51/3.23 % (961463)Peak memory usage: 12 MB
% 20.51/3.23 % (961463)Instructions burned: 379 (million)
% 20.51/3.23 % (961471)Instruction limit reached!
% 20.51/3.23 % (961471)------------------------------
% 20.51/3.23 % (961471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.51/3.23 % (961471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.51/3.23 % (961471)CaDiCaL version: 2.1.3
% 20.51/3.23 % (961471)Termination reason: Instruction limit
% 20.51/3.23 % (961471)Termination phase: Function definition elimination
% 20.51/3.23 % (961471)Time elapsed: 0.030 s
% 20.51/3.23 % (961471)Peak memory usage: 10 MB
% 20.51/3.23 % (961471)Instructions burned: 73 (million)
% 20.51/3.23 % (961473)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1336701432:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2972 on theBenchmark for (2972ds/302Mi)
% 21.51/3.44 % (961468)Instruction limit reached!
% 21.51/3.44 % (961468)------------------------------
% 21.51/3.44 % (961468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.51/3.44 % (961468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.51/3.44 % (961468)CaDiCaL version: 2.1.3
% 21.51/3.44 % (961468)Termination reason: Instruction limit
% 21.51/3.44 % (961468)Termination phase: Saturation
% 21.51/3.44 % (961468)Time elapsed: 0.093 s
% 21.51/3.44 % (961468)Peak memory usage: 12 MB
% 21.51/3.44 % (961468)Instructions burned: 448 (million)
% 21.51/3.44 % (961476)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 21.51/3.44 % (961476)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 21.51/3.44 % (961476)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3731813855:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2972 on theBenchmark for (2972ds/100Mi)
% 21.51/3.44 % (961474)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=249472660:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2972 on theBenchmark for (2972ds/4980Mi)
% 21.51/3.44 % (961476)Instruction limit reached!
% 21.51/3.44 % (961476)------------------------------
% 21.51/3.44 % (961476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.51/3.44 % (961476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.51/3.44 % (961476)CaDiCaL version: 2.1.3
% 21.51/3.44 % (961476)Termination reason: Instruction limit
% 21.51/3.44 % (961476)Termination phase: Twee Goal Transformation
% 21.51/3.44 % (961476)Time elapsed: 0.021 s
% 21.51/3.44 % (961476)Peak memory usage: 11 MB
% 21.51/3.44 % (961476)Instructions burned: 101 (million)
% 21.51/3.44 % (961474)Refutation not found, incomplete strategy
% 21.51/3.44 % (961474)------------------------------
% 21.51/3.44 % (961474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.51/3.44 % (961474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.51/3.44 % (961474)CaDiCaL version: 2.1.3
% 21.51/3.44 % (961474)Termination reason: Refutation not found, incomplete strategy
% 21.51/3.44 % (961474)Time elapsed: 0.022 s
% 21.51/3.44 % (961474)Peak memory usage: 13 MB
% 21.51/3.44 % (961474)Instructions burned: 46 (million)
% 21.51/3.44 % (961474)------------------------------
% 21.51/3.44 % (961474)------------------------------
% 21.51/3.44 % (961479)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1002074749:i=76:piset=equals:rtra=on:ntd=on_2971 on theBenchmark for (2971ds/76Mi)
% 21.51/3.44 % (961480)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=3415923992:i=289:rtra=on_2971 on theBenchmark for (2971ds/289Mi)
% 21.51/3.44 % (961479)Instruction limit reached!
% 21.51/3.44 % (961479)------------------------------
% 21.51/3.44 % (961479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.51/3.44 % (961479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.51/3.44 % (961479)CaDiCaL version: 2.1.3
% 21.51/3.44 % (961479)Termination reason: Instruction limit
% 21.51/3.44 % (961479)Termination phase: Function definition elimination
% 21.51/3.44 % (961479)Time elapsed: 0.017 s
% 21.51/3.44 % (961479)Peak memory usage: 10 MB
% 21.51/3.44 % (961479)Instructions burned: 78 (million)
% 21.51/3.44 % (961483)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=347422594:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2971 on theBenchmark for (2971ds/493Mi)
% 21.51/3.44 % (961465)Instruction limit reached!
% 21.51/3.44 % (961465)------------------------------
% 21.51/3.44 % (961465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.51/3.44 % (961465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.51/3.44 % (961465)CaDiCaL version: 2.1.3
% 21.51/3.44 % (961465)Termination reason: Instruction limit
% 21.51/3.44 % (961465)Termination phase: Saturation
% 21.51/3.44 % (961465)Time elapsed: 0.225 s
% 23.05/3.65 % (961465)Peak memory usage: 12 MB
% 23.05/3.65 % (961465)Instructions burned: 430 (million)
% 23.05/3.65 % (961467)Instruction limit reached!
% 23.05/3.65 % (961467)------------------------------
% 23.05/3.65 % (961467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.05/3.65 % (961467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.05/3.65 % (961467)CaDiCaL version: 2.1.3
% 23.05/3.65 % (961467)Termination reason: Instruction limit
% 23.05/3.65 % (961467)Termination phase: Saturation
% 23.05/3.65 % (961467)Time elapsed: 0.194 s
% 23.05/3.65 % (961467)Peak memory usage: 13 MB
% 23.05/3.65 % (961467)Instructions burned: 480 (million)
% 23.05/3.65 % (961485)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=955638485:cond=on:i=34:hud=10:nm=10:rtra=on_2971 on theBenchmark for (2971ds/34Mi)
% 23.05/3.65 % (961486)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 23.05/3.65 % (961473)Instruction limit reached!
% 23.05/3.65 % (961473)------------------------------
% 23.05/3.65 % (961473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.05/3.66 % (961473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.05/3.66 % (961473)CaDiCaL version: 2.1.3
% 23.05/3.66 % (961473)Termination reason: Instruction limit
% 23.05/3.66 % (961473)Termination phase: Saturation
% 23.05/3.66 % (961473)Time elapsed: 0.117 s
% 23.05/3.66 % (961473)Peak memory usage: 12 MB
% 23.05/3.66 % (961473)Instructions burned: 303 (million)
% 23.05/3.66 % (961486)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=1729604927:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2971 on theBenchmark for (2971ds/372Mi)
% 23.05/3.66 % (961485)Instruction limit reached!
% 23.05/3.66 % (961485)------------------------------
% 23.05/3.66 % (961485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.05/3.66 % (961485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.05/3.66 % (961485)CaDiCaL version: 2.1.3
% 23.05/3.66 % (961485)Termination reason: Instruction limit
% 23.05/3.66 % (961485)Termination phase: Property scanning
% 23.05/3.66 % (961485)Time elapsed: 0.015 s
% 23.05/3.66 % (961485)Peak memory usage: 11 MB
% 23.05/3.66 % (961485)Instructions burned: 34 (million)
% 23.05/3.66 % (961488)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=2003846709:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2970 on theBenchmark for (2970ds/670Mi)
% 23.05/3.66 % (961490)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3998314554:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2970 on theBenchmark for (2970ds/647Mi)
% 23.05/3.66 % (961480)Instruction limit reached!
% 23.05/3.66 % (961480)------------------------------
% 23.05/3.66 % (961480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.05/3.66 % (961480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.05/3.66 % (961480)CaDiCaL version: 2.1.3
% 23.05/3.66 % (961480)Termination reason: Instruction limit
% 23.05/3.66 % (961480)Termination phase: Saturation
% 23.05/3.66 % (961480)Time elapsed: 0.115 s
% 23.05/3.66 % (961480)Peak memory usage: 12 MB
% 23.05/3.66 % (961480)Instructions burned: 289 (million)
% 23.05/3.66 % (961483)Instruction limit reached!
% 23.05/3.66 % (961483)------------------------------
% 23.05/3.66 % (961483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.05/3.66 % (961483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.05/3.66 % (961483)CaDiCaL version: 2.1.3
% 23.05/3.66 % (961483)Termination reason: Instruction limit
% 23.05/3.66 % (961483)Termination phase: Saturation
% 23.05/3.66 % (961483)Time elapsed: 0.103 s
% 23.05/3.66 % (961483)Peak memory usage: 12 MB
% 23.05/3.66 % (961483)Instructions burned: 495 (million)
% 23.05/3.66 % (961494)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=3805915284:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2970 on theBenchmark for (2970ds/693Mi)
% 23.05/3.66 % (961493)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=1073153798:i=857:add=off:kws=frequency:rtra=on:ntd=on_2970 on theBenchmark for (2970ds/857Mi)
% 23.83/3.92 % (961486)Instruction limit reached!
% 23.83/3.92 % (961486)------------------------------
% 23.83/3.92 % (961486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/3.92 % (961486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/3.92 % (961486)CaDiCaL version: 2.1.3
% 23.83/3.92 % (961486)Termination reason: Instruction limit
% 23.83/3.92 % (961486)Termination phase: Saturation
% 23.83/3.92 % (961486)Time elapsed: 0.148 s
% 23.83/3.92 % (961486)Peak memory usage: 12 MB
% 23.83/3.92 % (961486)Instructions burned: 374 (million)
% 23.83/3.92 % (961497)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=1060304931:i=285:hud=10:bd=all:rtra=on:ss=axioms_2969 on theBenchmark for (2969ds/285Mi)
% 23.83/3.92 % (961494)Instruction limit reached!
% 23.83/3.92 % (961494)------------------------------
% 23.83/3.92 % (961494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/3.92 % (961494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/3.92 % (961494)CaDiCaL version: 2.1.3
% 23.83/3.92 % (961494)Termination reason: Instruction limit
% 23.83/3.92 % (961494)Termination phase: Saturation
% 23.83/3.92 % (961494)Time elapsed: 0.155 s
% 23.83/3.92 % (961494)Peak memory usage: 13 MB
% 23.83/3.92 % (961494)Instructions burned: 698 (million)
% 23.83/3.92 % (961499)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 23.83/3.92 % (961499)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=813724375:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2968 on theBenchmark for (2968ds/52Mi)
% 23.83/3.92 % (961493)Refutation not found, incomplete strategy
% 23.83/3.92 % (961493)------------------------------
% 23.83/3.92 % (961493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/3.92 % (961493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/3.92 % (961493)CaDiCaL version: 2.1.3
% 23.83/3.92 % (961493)Termination reason: Refutation not found, incomplete strategy
% 23.83/3.92 % (961493)Time elapsed: 0.190 s
% 23.83/3.92 % (961493)Peak memory usage: 16 MB
% 23.83/3.93 % (961493)Instructions burned: 460 (million)
% 23.83/3.93 % (961497)Instruction limit reached!
% 23.83/3.93 % (961497)------------------------------
% 23.83/3.93 % (961497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/3.93 % (961497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/3.93 % (961497)CaDiCaL version: 2.1.3
% 23.83/3.93 % (961497)Termination reason: Instruction limit
% 23.83/3.93 % (961497)Termination phase: Saturation
% 23.83/3.93 % (961497)Time elapsed: 0.092 s
% 23.83/3.93 % (961497)Peak memory usage: 15 MB
% 23.83/3.93 % (961497)Instructions burned: 288 (million)
% 23.83/3.93 % (961493)------------------------------
% 23.83/3.93 % (961493)------------------------------
% 23.83/3.93 % (961499)Instruction limit reached!
% 23.83/3.93 % (961499)------------------------------
% 23.83/3.93 % (961499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/3.93 % (961499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/3.93 % (961499)CaDiCaL version: 2.1.3
% 23.83/3.93 % (961499)Termination reason: Instruction limit
% 23.83/3.93 % (961499)Termination phase: Function definition elimination
% 23.83/3.93 % (961499)Time elapsed: 0.022 s
% 23.83/3.93 % (961499)Peak memory usage: 11 MB
% 23.83/3.93 % (961499)Instructions burned: 53 (million)
% 23.83/3.93 % (961501)dis+10_1_si=on:random_seed=3764920449:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2968 on theBenchmark for (2968ds/407Mi)
% 23.83/3.93 % (961502)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=283779264:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2968 on theBenchmark for (2968ds/2240Mi)
% 23.83/3.93 % (961488)Instruction limit reached!
% 23.83/3.93 % (961488)------------------------------
% 23.83/3.93 % (961488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.83/3.93 % (961488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.83/3.93 % (961488)CaDiCaL version: 2.1.3
% 23.83/3.93 % (961488)Termination reason: Instruction limit
% 23.83/3.93 % (961488)Termination phase: Saturation
% 23.83/3.93 % (961488)Time elapsed: 0.266 s
% 23.83/3.93 % (961488)Peak memory usage: 13 MB
% 23.83/3.93 % (961488)Instructions burned: 672 (million)
% 26.79/4.11 % (961503)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=4165402323:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2968 on theBenchmark for (2968ds/336Mi)
% 26.79/4.11 % (961507)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=3459503643:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2968 on theBenchmark for (2968ds/1142Mi)
% 26.79/4.11 % (961490)Instruction limit reached!
% 26.79/4.11 % (961490)------------------------------
% 26.79/4.11 % (961490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.79/4.11 % (961490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.79/4.11 % (961490)CaDiCaL version: 2.1.3
% 26.79/4.11 % (961490)Termination reason: Instruction limit
% 26.79/4.11 % (961490)Termination phase: Saturation
% 26.79/4.11 % (961490)Time elapsed: 0.281 s
% 26.79/4.11 % (961490)Peak memory usage: 14 MB
% 26.79/4.11 % (961490)Instructions burned: 648 (million)
% 26.79/4.11 % (961509)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=3671208141:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2967 on theBenchmark for (2967ds/376Mi)
% 26.79/4.11 % (961501)Instruction limit reached!
% 26.79/4.11 % (961501)------------------------------
% 26.79/4.11 % (961501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.79/4.11 % (961501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.79/4.11 % (961501)CaDiCaL version: 2.1.3
% 26.79/4.11 % (961501)Termination reason: Instruction limit
% 26.79/4.11 % (961501)Termination phase: Saturation
% 26.79/4.11 % (961501)Time elapsed: 0.085 s
% 26.79/4.11 % (961501)Peak memory usage: 12 MB
% 26.79/4.11 % (961501)Instructions burned: 409 (million)
% 26.79/4.11 % (961332)Instruction limit reached!
% 26.79/4.11 % (961332)------------------------------
% 26.79/4.11 % (961332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.79/4.11 % (961332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.79/4.11 % (961332)CaDiCaL version: 2.1.3
% 26.79/4.11 % (961332)Termination reason: Instruction limit
% 26.79/4.11 % (961332)Termination phase: Saturation
% 26.79/4.11 % (961332)Time elapsed: 2.562 s
% 26.79/4.11 % (961332)Peak memory usage: 21 MB
% 26.79/4.11 % (961332)Instructions burned: 5756 (million)
% 26.79/4.11 % (961511)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=303369447:i=766:bd=all:rtra=on_2967 on theBenchmark for (2967ds/766Mi)
% 26.79/4.11 % (961512)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 26.79/4.11 % (961512)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=3751186278:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2967 on theBenchmark for (2967ds/959Mi)
% 26.79/4.11 % (961503)Instruction limit reached!
% 26.79/4.11 % (961503)------------------------------
% 26.79/4.11 % (961503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.79/4.11 % (961503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.79/4.11 % (961503)CaDiCaL version: 2.1.3
% 26.79/4.11 % (961503)Termination reason: Instruction limit
% 26.79/4.11 % (961503)Termination phase: Saturation
% 26.79/4.11 % (961503)Time elapsed: 0.124 s
% 26.79/4.11 % (961503)Peak memory usage: 12 MB
% 26.79/4.11 % (961503)Instructions burned: 337 (million)
% 26.79/4.11 % (961515)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=1071138139:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2966 on theBenchmark for (2966ds/6359Mi)
% 26.79/4.11 % (961509)Instruction limit reached!
% 26.79/4.11 % (961509)------------------------------
% 26.79/4.11 % (961509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.79/4.11 % (961509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.79/4.11 % (961509)CaDiCaL version: 2.1.3
% 26.79/4.11 % (961509)Termination reason: Instruction limit
% 26.79/4.11 % (961509)Termination phase: Saturation
% 26.79/4.11 % (961509)Time elapsed: 0.153 s
% 26.79/4.11 % (961509)Peak memory usage: 12 MB
% 26.79/4.11 % (961509)Instructions burned: 377 (million)
% 26.79/4.11 % (961517)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1240709207:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2966 on theBenchmark for (2966ds/35Mi)
% 27.77/4.26 % (961517)Instruction limit reached!
% 27.77/4.26 % (961517)------------------------------
% 27.77/4.26 % (961517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.77/4.26 % (961517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.77/4.26 % (961517)CaDiCaL version: 2.1.3
% 27.77/4.26 % (961517)Termination reason: Instruction limit
% 27.77/4.26 % (961517)Termination phase: Property scanning
% 27.77/4.26 % (961517)Time elapsed: 0.016 s
% 27.77/4.26 % (961517)Peak memory usage: 11 MB
% 27.77/4.26 % (961517)Instructions burned: 35 (million)
% 27.77/4.26 % (961511)Instruction limit reached!
% 27.77/4.26 % (961511)------------------------------
% 27.77/4.26 % (961511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.77/4.26 % (961511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.77/4.26 % (961511)CaDiCaL version: 2.1.3
% 27.77/4.26 % (961511)Termination reason: Instruction limit
% 27.77/4.26 % (961511)Termination phase: Saturation
% 27.77/4.26 % (961511)Time elapsed: 0.160 s
% 27.77/4.26 % (961511)Peak memory usage: 13 MB
% 27.77/4.26 % (961511)Instructions burned: 769 (million)
% 27.77/4.26 % (961519)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=2659173691:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2965 on theBenchmark for (2965ds/53Mi)
% 27.77/4.26 % (961520)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=4051139663:s2a=on:i=876:s2at=6:nm=2:rtra=on_2965 on theBenchmark for (2965ds/876Mi)
% 27.77/4.26 % (961519)Instruction limit reached!
% 27.77/4.26 % (961519)------------------------------
% 27.77/4.26 % (961519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.77/4.26 % (961519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.77/4.26 % (961519)CaDiCaL version: 2.1.3
% 27.77/4.26 % (961519)Termination reason: Instruction limit
% 27.77/4.26 % (961519)Termination phase: Function definition elimination
% 27.77/4.26 % (961519)Time elapsed: 0.024 s
% 27.77/4.26 % (961519)Peak memory usage: 10 MB
% 27.77/4.26 % (961519)Instructions burned: 55 (million)
% 27.77/4.26 % (961523)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=893175030:i=57:ep=R:rtra=on:ntd=on_2965 on theBenchmark for (2965ds/57Mi)
% 27.77/4.26 % (961523)Instruction limit reached!
% 27.77/4.26 % (961523)------------------------------
% 27.77/4.26 % (961523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.77/4.26 % (961523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.77/4.26 % (961523)CaDiCaL version: 2.1.3
% 27.77/4.26 % (961523)Termination reason: Instruction limit
% 27.77/4.26 % (961523)Termination phase: Function definition elimination
% 27.77/4.26 % (961523)Time elapsed: 0.024 s
% 27.77/4.26 % (961523)Peak memory usage: 10 MB
% 27.77/4.26 % (961523)Instructions burned: 58 (million)
% 27.77/4.26 % (961525)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 27.77/4.26 % (961525)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3733045275:i=306:bd=all:rtra=on_2964 on theBenchmark for (2964ds/306Mi)
% 27.77/4.26 % (961520)Instruction limit reached!
% 27.77/4.26 % (961520)------------------------------
% 27.77/4.26 % (961520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.77/4.26 % (961520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.77/4.26 % (961520)CaDiCaL version: 2.1.3
% 27.77/4.26 % (961520)Termination reason: Instruction limit
% 27.77/4.26 % (961520)Termination phase: Saturation
% 27.77/4.26 % (961520)Time elapsed: 0.198 s
% 27.77/4.26 % (961520)Peak memory usage: 17 MB
% 27.77/4.26 % (961520)Instructions burned: 877 (million)
% 27.77/4.26 % (961527)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=4113268060:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2963 on theBenchmark for (2963ds/262Mi)
% 27.77/4.26 % (961512)Instruction limit reached!
% 27.77/4.26 % (961512)------------------------------
% 27.77/4.26 % (961512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.77/4.26 % (961512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.77/4.26 % (961512)CaDiCaL version: 2.1.3
% 27.77/4.26 % (961512)Termination reason: Instruction limit
% 27.77/4.26 % (961512)Termination phase: Saturation
% 27.77/4.26 % (961512)Time elapsed: 0.380 s
% 29.08/4.41 % (961512)Peak memory usage: 13 MB
% 29.08/4.41 % (961512)Instructions burned: 960 (million)
% 29.08/4.41 % (961525)Instruction limit reached!
% 29.08/4.41 % (961525)------------------------------
% 29.08/4.41 % (961525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.08/4.41 % (961525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.08/4.41 % (961525)CaDiCaL version: 2.1.3
% 29.08/4.41 % (961525)Termination reason: Instruction limit
% 29.08/4.41 % (961525)Termination phase: Saturation
% 29.08/4.41 % (961525)Time elapsed: 0.151 s
% 29.08/4.41 % (961525)Peak memory usage: 13 MB
% 29.08/4.41 % (961525)Instructions burned: 306 (million)
% 29.08/4.41 % (961529)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 29.08/4.41 % (961529)ott+1002_16_sil=128000:si=on:random_seed=2705256698:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2963 on theBenchmark for (2963ds/409Mi)
% 29.08/4.41 % (961530)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=2587133620:s2a=on:i=381:rtra=on_2963 on theBenchmark for (2963ds/381Mi)
% 29.08/4.41 % (961527)Instruction limit reached!
% 29.08/4.41 % (961527)------------------------------
% 29.08/4.41 % (961527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.08/4.41 % (961527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.08/4.41 % (961527)CaDiCaL version: 2.1.3
% 29.08/4.41 % (961527)Termination reason: Instruction limit
% 29.08/4.41 % (961527)Termination phase: Saturation
% 29.08/4.41 % (961527)Time elapsed: 0.055 s
% 29.08/4.41 % (961527)Peak memory usage: 12 MB
% 29.08/4.41 % (961527)Instructions burned: 265 (million)
% 29.08/4.41 % (961533)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=702075349:cond=on:i=324:rtra=on:ntd=on_2962 on theBenchmark for (2962ds/324Mi)
% 29.08/4.41 % (961507)Instruction limit reached!
% 29.08/4.41 % (961507)------------------------------
% 29.08/4.41 % (961507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.08/4.41 % (961507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.08/4.41 % (961507)CaDiCaL version: 2.1.3
% 29.08/4.41 % (961507)Termination reason: Instruction limit
% 29.08/4.41 % (961507)Termination phase: Saturation
% 29.08/4.41 % (961507)Time elapsed: 0.548 s
% 29.08/4.41 % (961507)Peak memory usage: 20 MB
% 29.08/4.41 % (961507)Instructions burned: 1142 (million)
% 29.08/4.41 % (961535)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=1550371797:i=240:kws=inv_precedence:rtra=on_2962 on theBenchmark for (2962ds/240Mi)
% 29.08/4.41 % (961533)Instruction limit reached!
% 29.08/4.41 % (961533)------------------------------
% 29.08/4.41 % (961533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.08/4.41 % (961533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.08/4.41 % (961533)CaDiCaL version: 2.1.3
% 29.08/4.41 % (961533)Termination reason: Instruction limit
% 29.08/4.41 % (961533)Termination phase: Saturation
% 29.08/4.41 % (961533)Time elapsed: 0.072 s
% 29.08/4.41 % (961533)Peak memory usage: 13 MB
% 29.08/4.41 % (961533)Instructions burned: 328 (million)
% 29.08/4.41 % (961537)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 29.08/4.41 % (961537)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=796365761:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2961 on theBenchmark for (2961ds/124Mi)
% 29.08/4.41 % (961537)Instruction limit reached!
% 29.08/4.41 % (961537)------------------------------
% 29.08/4.41 % (961537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.08/4.41 % (961537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.08/4.41 % (961537)CaDiCaL version: 2.1.3
% 29.08/4.41 % (961537)Termination reason: Instruction limit
% 29.08/4.41 % (961537)Termination phase: Property scanning
% 29.08/4.41 % (961537)Time elapsed: 0.027 s
% 29.08/4.41 % (961537)Peak memory usage: 11 MB
% 29.08/4.41 % (961537)Instructions burned: 127 (million)
% 29.08/4.41 % (961539)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=2723625993:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2961 on theBenchmark for (2961ds/223Mi)
% 29.08/4.41 % (961529)Instruction limit reached!
% 29.08/4.41 % (961529)------------------------------
% 29.08/4.41 % (961529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.08/4.41 % (961529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.36/4.77 % (961529)CaDiCaL version: 2.1.3
% 30.36/4.77 % (961529)Termination reason: Instruction limit
% 30.36/4.77 % (961529)Termination phase: Saturation
% 30.36/4.77 % (961529)Time elapsed: 0.163 s
% 30.36/4.77 % (961529)Peak memory usage: 12 MB
% 30.36/4.77 % (961529)Instructions burned: 409 (million)
% 30.36/4.77 % (961541)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3757981891:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2961 on theBenchmark for (2961ds/282Mi)
% 30.36/4.77 % (961535)Instruction limit reached!
% 30.36/4.77 % (961535)------------------------------
% 30.36/4.77 % (961535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.36/4.77 % (961535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.36/4.77 % (961535)CaDiCaL version: 2.1.3
% 30.36/4.77 % (961535)Termination reason: Instruction limit
% 30.36/4.77 % (961535)Termination phase: Saturation
% 30.36/4.77 % (961535)Time elapsed: 0.103 s
% 30.36/4.77 % (961535)Peak memory usage: 14 MB
% 30.36/4.77 % (961535)Instructions burned: 241 (million)
% 30.36/4.77 % (961539)Instruction limit reached!
% 30.36/4.77 % (961539)------------------------------
% 30.36/4.77 % (961539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.36/4.77 % (961539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.36/4.77 % (961539)CaDiCaL version: 2.1.3
% 30.36/4.77 % (961539)Termination reason: Instruction limit
% 30.36/4.77 % (961539)Termination phase: Saturation
% 30.36/4.77 % (961539)Time elapsed: 0.047 s
% 30.36/4.77 % (961539)Peak memory usage: 12 MB
% 30.36/4.77 % (961539)Instructions burned: 224 (million)
% 30.36/4.77 % (961543)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=39330746:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2961 on theBenchmark for (2961ds/464Mi)
% 30.36/4.77 % (961544)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3412010993:i=88:s2at=3:nm=2:rtra=on:rawr=on_2960 on theBenchmark for (2960ds/88Mi)
% 30.36/4.77 % (961544)Instruction limit reached!
% 30.36/4.77 % (961544)------------------------------
% 30.36/4.77 % (961544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.36/4.77 % (961544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.36/4.77 % (961544)CaDiCaL version: 2.1.3
% 30.36/4.77 % (961544)Termination reason: Instruction limit
% 30.36/4.77 % (961544)Termination phase: Function definition elimination
% 30.36/4.77 % (961544)Time elapsed: 0.019 s
% 30.36/4.77 % (961544)Peak memory usage: 11 MB
% 30.36/4.77 % (961544)Instructions burned: 90 (million)
% 30.36/4.77 % (961530)Instruction limit reached!
% 30.36/4.77 % (961530)------------------------------
% 30.36/4.77 % (961530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.36/4.77 % (961530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.36/4.77 % (961530)CaDiCaL version: 2.1.3
% 30.36/4.77 % (961530)Termination reason: Instruction limit
% 30.36/4.77 % (961530)Termination phase: Saturation
% 30.36/4.77 % (961530)Time elapsed: 0.238 s
% 30.36/4.77 % (961530)Peak memory usage: 12 MB
% 30.36/4.77 % (961530)Instructions burned: 381 (million)
% 30.36/4.77 % (961547)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=627167675:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2960 on theBenchmark for (2960ds/280Mi)
% 30.36/4.77 % (961549)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 30.36/4.77 % (961549)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=98476202:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2960 on theBenchmark for (2960ds/4386Mi)
% 30.36/4.77 % (961547)Instruction limit reached!
% 30.36/4.77 % (961547)------------------------------
% 30.36/4.77 % (961547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.36/4.77 % (961547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.36/4.77 % (961547)CaDiCaL version: 2.1.3
% 30.36/4.77 % (961547)Termination reason: Instruction limit
% 30.36/4.77 % (961547)Termination phase: Saturation
% 30.36/4.77 % (961547)Time elapsed: 0.058 s
% 30.36/4.77 % (961547)Peak memory usage: 12 MB
% 30.36/4.77 % (961547)Instructions burned: 283 (million)
% 30.36/4.77 % (961551)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 33.91/5.14 % (961551)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 33.91/5.14 % (961551)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=2304510390:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2959 on theBenchmark for (2959ds/483Mi)
% 33.91/5.14 % (961541)Instruction limit reached!
% 33.91/5.14 % (961541)------------------------------
% 33.91/5.14 % (961541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.91/5.14 % (961541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.91/5.14 % (961541)CaDiCaL version: 2.1.3
% 33.91/5.14 % (961541)Termination reason: Instruction limit
% 33.91/5.14 % (961541)Termination phase: Saturation
% 33.91/5.14 % (961541)Time elapsed: 0.147 s
% 33.91/5.14 % (961541)Peak memory usage: 15 MB
% 33.91/5.14 % (961541)Instructions burned: 283 (million)
% 33.91/5.14 % (961553)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1626646003:i=73:rtra=on_2959 on theBenchmark for (2959ds/73Mi)
% 33.91/5.14 % (961553)Instruction limit reached!
% 33.91/5.14 % (961553)------------------------------
% 33.91/5.14 % (961553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.91/5.14 % (961553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.91/5.14 % (961553)CaDiCaL version: 2.1.3
% 33.91/5.14 % (961553)Termination reason: Instruction limit
% 33.91/5.14 % (961553)Termination phase: Function definition elimination
% 33.91/5.14 % (961553)Time elapsed: 0.031 s
% 33.91/5.14 % (961553)Peak memory usage: 11 MB
% 33.91/5.14 % (961553)Instructions burned: 73 (million)
% 33.91/5.14 % (961555)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=504209154:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2959 on theBenchmark for (2959ds/176Mi)
% 33.91/5.14 % (961543)Instruction limit reached!
% 33.91/5.14 % (961543)------------------------------
% 33.91/5.14 % (961543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.91/5.14 % (961543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.91/5.14 % (961543)CaDiCaL version: 2.1.3
% 33.91/5.14 % (961543)Termination reason: Instruction limit
% 33.91/5.14 % (961543)Termination phase: Saturation
% 33.91/5.14 % (961543)Time elapsed: 0.204 s
% 33.91/5.14 % (961543)Peak memory usage: 13 MB
% 33.91/5.14 % (961543)Instructions burned: 466 (million)
% 33.91/5.14 % (961557)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 33.91/5.14 % (961557)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=2364463383:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2958 on theBenchmark for (2958ds/39Mi)
% 33.91/5.14 % (961557)Instruction limit reached!
% 33.91/5.14 % (961557)------------------------------
% 33.91/5.14 % (961557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.91/5.14 % (961557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.91/5.14 % (961557)CaDiCaL version: 2.1.3
% 33.91/5.14 % (961557)Termination reason: Instruction limit
% 33.91/5.14 % (961557)Termination phase: Function definition elimination
% 33.91/5.14 % (961557)Time elapsed: 0.017 s
% 33.91/5.14 % (961557)Peak memory usage: 10 MB
% 33.91/5.14 % (961557)Instructions burned: 40 (million)
% 33.91/5.14 % (961551)Instruction limit reached!
% 33.91/5.14 % (961551)------------------------------
% 33.91/5.14 % (961551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.91/5.14 % (961551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.91/5.14 % (961551)CaDiCaL version: 2.1.3
% 33.91/5.14 % (961551)Termination reason: Instruction limit
% 33.91/5.14 % (961551)Termination phase: Saturation
% 33.91/5.14 % (961551)Time elapsed: 0.137 s
% 33.91/5.14 % (961551)Peak memory usage: 16 MB
% 33.91/5.14 % (961551)Instructions burned: 483 (million)
% 33.91/5.14 % (961560)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 33.91/5.14 % (961560)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3117872679:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2958 on theBenchmark for (2958ds/252Mi)
% 36.36/5.53 % (961559)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3746527729:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2958 on theBenchmark for (2958ds/708Mi)
% 36.36/5.53 % (961555)Instruction limit reached!
% 36.36/5.53 % (961555)------------------------------
% 36.36/5.53 % (961555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.53 % (961555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.53 % (961555)CaDiCaL version: 2.1.3
% 36.36/5.53 % (961555)Termination reason: Instruction limit
% 36.36/5.53 % (961555)Termination phase: Property scanning
% 36.36/5.53 % (961555)Time elapsed: 0.069 s
% 36.36/5.53 % (961555)Peak memory usage: 10 MB
% 36.36/5.53 % (961555)Instructions burned: 177 (million)
% 36.36/5.53 % (961563)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=1693023034:i=823:fsr=off:rtra=on_2958 on theBenchmark for (2958ds/823Mi)
% 36.36/5.53 % (961560)Instruction limit reached!
% 36.36/5.53 % (961560)------------------------------
% 36.36/5.53 % (961560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.53 % (961560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.53 % (961560)CaDiCaL version: 2.1.3
% 36.36/5.53 % (961560)Termination reason: Instruction limit
% 36.36/5.53 % (961560)Termination phase: Saturation
% 36.36/5.53 % (961560)Time elapsed: 0.053 s
% 36.36/5.53 % (961560)Peak memory usage: 12 MB
% 36.36/5.53 % (961560)Instructions burned: 255 (million)
% 36.36/5.53 % (961565)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 36.36/5.53 % (961565)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=2895592444:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2957 on theBenchmark for (2957ds/16202Mi)
% 36.36/5.53 % (961502)Instruction limit reached!
% 36.36/5.53 % (961502)------------------------------
% 36.36/5.53 % (961502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.53 % (961502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.53 % (961502)CaDiCaL version: 2.1.3
% 36.36/5.53 % (961502)Termination reason: Instruction limit
% 36.36/5.53 % (961502)Termination phase: Saturation
% 36.36/5.53 % (961502)Time elapsed: 1.141 s
% 36.36/5.53 % (961502)Peak memory usage: 31 MB
% 36.36/5.53 % (961502)Instructions burned: 2242 (million)
% 36.36/5.53 % (961567)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=2976130852:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2956 on theBenchmark for (2956ds/300Mi)
% 36.36/5.53 % (961559)Instruction limit reached!
% 36.36/5.53 % (961559)------------------------------
% 36.36/5.53 % (961559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.53 % (961559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.53 % (961559)CaDiCaL version: 2.1.3
% 36.36/5.53 % (961559)Termination reason: Instruction limit
% 36.36/5.53 % (961559)Termination phase: Saturation
% 36.36/5.53 % (961559)Time elapsed: 0.282 s
% 36.36/5.53 % (961559)Peak memory usage: 13 MB
% 36.36/5.53 % (961559)Instructions burned: 709 (million)
% 36.36/5.53 % (961569)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 36.36/5.53 % (961569)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 36.36/5.53 % (961569)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=1450047353:i=177:add=on:bd=preordered:rtra=on:rawr=on_2955 on theBenchmark for (2955ds/177Mi)
% 36.36/5.53 % (961567)Instruction limit reached!
% 36.36/5.53 % (961567)------------------------------
% 36.36/5.53 % (961567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.53 % (961567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.53 % (961567)CaDiCaL version: 2.1.3
% 36.36/5.53 % (961567)Termination reason: Instruction limit
% 36.36/5.53 % (961567)Termination phase: Saturation
% 36.36/5.53 % (961567)Time elapsed: 0.120 s
% 36.36/5.53 % (961567)Peak memory usage: 12 MB
% 36.36/5.53 % (961567)Instructions burned: 302 (million)
% 36.36/5.53 % (961571)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=3247681857:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2955 on theBenchmark for (2955ds/715Mi)
% 36.36/5.53 % (961563)Instruction limit reached!
% 40.96/6.13 % (961563)------------------------------
% 40.96/6.13 % (961563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.96/6.13 % (961563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.96/6.13 % (961563)CaDiCaL version: 2.1.3
% 40.96/6.13 % (961563)Termination reason: Instruction limit
% 40.96/6.13 % (961563)Termination phase: Saturation
% 40.96/6.13 % (961563)Time elapsed: 0.330 s
% 40.96/6.13 % (961563)Peak memory usage: 13 MB
% 40.96/6.13 % (961563)Instructions burned: 825 (million)
% 40.96/6.13 % (961573)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 40.96/6.13 % (961573)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 40.96/6.13 % (961573)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=2095068056:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2954 on theBenchmark for (2954ds/230Mi)
% 40.96/6.13 % (961569)Instruction limit reached!
% 40.96/6.13 % (961569)------------------------------
% 40.96/6.13 % (961569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.96/6.13 % (961569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.96/6.13 % (961569)CaDiCaL version: 2.1.3
% 40.96/6.13 % (961569)Termination reason: Instruction limit
% 40.96/6.13 % (961569)Termination phase: Property scanning
% 40.96/6.13 % (961569)Time elapsed: 0.070 s
% 40.96/6.13 % (961569)Peak memory usage: 11 MB
% 40.96/6.13 % (961569)Instructions burned: 179 (million)
% 40.96/6.13 % (961575)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=1952519344:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2954 on theBenchmark for (2954ds/606Mi)
% 40.96/6.13 % (961573)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 40.96/6.13 % (961573)Instruction limit reached!
% 40.96/6.13 % (961573)------------------------------
% 40.96/6.13 % (961573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.96/6.13 % (961573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.96/6.13 % (961573)CaDiCaL version: 2.1.3
% 40.96/6.13 % (961573)Termination reason: Instruction limit
% 40.96/6.13 % (961573)Termination phase: Saturation
% 40.96/6.13 % (961573)Time elapsed: 0.091 s
% 40.96/6.13 % (961573)Peak memory usage: 12 MB
% 40.96/6.13 % (961573)Instructions burned: 233 (million)
% 40.96/6.13 % (961577)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 40.96/6.13 % (961577)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=2857129434:lrd=on:i=841:nm=0:rtra=on_2953 on theBenchmark for (2953ds/841Mi)
% 40.96/6.13 % (961575)Instruction limit reached!
% 40.96/6.13 % (961575)------------------------------
% 40.96/6.13 % (961575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.96/6.13 % (961575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.96/6.13 % (961575)CaDiCaL version: 2.1.3
% 40.96/6.13 % (961575)Termination reason: Instruction limit
% 40.96/6.13 % (961575)Termination phase: Saturation
% 40.96/6.13 % (961575)Time elapsed: 0.243 s
% 40.96/6.13 % (961575)Peak memory usage: 12 MB
% 40.96/6.13 % (961575)Instructions burned: 606 (million)
% 40.96/6.13 % (961579)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2209877650:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2951 on theBenchmark for (2951ds/445Mi)
% 40.96/6.13 % (961571)Instruction limit reached!
% 40.96/6.13 % (961571)------------------------------
% 40.96/6.13 % (961571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.96/6.13 % (961571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.96/6.13 % (961571)CaDiCaL version: 2.1.3
% 40.96/6.13 % (961571)Termination reason: Instruction limit
% 40.96/6.13 % (961571)Termination phase: Saturation
% 40.96/6.13 % (961571)Time elapsed: 0.373 s
% 40.96/6.13 % (961571)Peak memory usage: 14 MB
% 40.96/6.13 % (961571)Instructions burned: 717 (million)
% 40.96/6.13 % (961581)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=1367643730:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2951 on theBenchmark for (2951ds/71Mi)
% 42.15/6.33 % (961581)Instruction limit reached!
% 42.15/6.33 % (961581)------------------------------
% 42.15/6.33 % (961581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.15/6.33 % (961581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.15/6.33 % (961581)CaDiCaL version: 2.1.3
% 42.15/6.33 % (961581)Termination reason: Instruction limit
% 42.15/6.33 % (961581)Termination phase: Function definition elimination
% 42.15/6.33 % (961581)Time elapsed: 0.030 s
% 42.15/6.33 % (961581)Peak memory usage: 10 MB
% 42.15/6.33 % (961581)Instructions burned: 72 (million)
% 42.15/6.33 % (961583)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 42.15/6.33 % (961583)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 42.15/6.33 % (961583)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2267444638:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2950 on theBenchmark for (2950ds/100Mi)
% 42.15/6.33 % (961583)Instruction limit reached!
% 42.15/6.33 % (961583)------------------------------
% 42.15/6.33 % (961583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.15/6.33 % (961583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.15/6.33 % (961583)CaDiCaL version: 2.1.3
% 42.15/6.33 % (961583)Termination reason: Instruction limit
% 42.15/6.33 % (961583)Termination phase: Twee Goal Transformation
% 42.15/6.33 % (961583)Time elapsed: 0.041 s
% 42.15/6.33 % (961583)Peak memory usage: 11 MB
% 42.15/6.33 % (961583)Instructions burned: 102 (million)
% 42.15/6.33 % (961577)Instruction limit reached!
% 42.15/6.33 % (961577)------------------------------
% 42.15/6.33 % (961577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.15/6.33 % (961577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.15/6.33 % (961577)CaDiCaL version: 2.1.3
% 42.15/6.33 % (961577)Termination reason: Instruction limit
% 42.15/6.33 % (961577)Termination phase: Saturation
% 42.15/6.33 % (961577)Time elapsed: 0.333 s
% 42.15/6.33 % (961577)Peak memory usage: 13 MB
% 42.15/6.33 % (961577)Instructions burned: 841 (million)
% 42.15/6.33 % (961585)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 42.15/6.33 % (961585)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=2629067516:i=1352:add=on:aac=none:rtra=on_2950 on theBenchmark for (2950ds/1352Mi)
% 42.15/6.33 % (961586)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=3208393108:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2950 on theBenchmark for (2950ds/646Mi)
% 42.15/6.33 % (961579)Instruction limit reached!
% 42.15/6.33 % (961579)------------------------------
% 42.15/6.33 % (961579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.15/6.33 % (961579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.15/6.33 % (961579)CaDiCaL version: 2.1.3
% 42.15/6.33 % (961579)Termination reason: Instruction limit
% 42.15/6.33 % (961579)Termination phase: Saturation
% 42.15/6.33 % (961579)Time elapsed: 0.181 s
% 42.15/6.33 % (961579)Peak memory usage: 12 MB
% 42.15/6.33 % (961579)Instructions burned: 446 (million)
% 42.15/6.33 % (961589)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=2338813171:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2949 on theBenchmark for (2949ds/1924Mi)
% 42.15/6.33 % (961586)Instruction limit reached!
% 42.15/6.33 % (961586)------------------------------
% 42.15/6.33 % (961586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.15/6.33 % (961586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.15/6.33 % (961586)CaDiCaL version: 2.1.3
% 42.15/6.33 % (961586)Termination reason: Instruction limit
% 42.15/6.33 % (961586)Termination phase: Saturation
% 42.15/6.33 % (961586)Time elapsed: 0.259 s
% 42.15/6.33 % (961586)Peak memory usage: 13 MB
% 42.15/6.33 % (961586)Instructions burned: 648 (million)
% 42.15/6.33 % (961591)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=141161458:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2947 on theBenchmark for (2947ds/984Mi)
% 42.84/6.51 % (961585)Instruction limit reached!
% 42.84/6.51 % (961585)------------------------------
% 42.84/6.51 % (961585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961585)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961585)Termination reason: Instruction limit
% 42.84/6.51 % (961585)Termination phase: Saturation
% 42.84/6.51 % (961585)Time elapsed: 0.544 s
% 42.84/6.51 % (961585)Peak memory usage: 22 MB
% 42.84/6.51 % (961585)Instructions burned: 1353 (million)
% 42.84/6.51 % (961593)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=1501491922:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2944 on theBenchmark for (2944ds/592Mi)
% 42.84/6.51 % (961591)Instruction limit reached!
% 42.84/6.51 % (961591)------------------------------
% 42.84/6.51 % (961591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961591)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961591)Termination reason: Instruction limit
% 42.84/6.51 % (961591)Termination phase: Saturation
% 42.84/6.51 % (961591)Time elapsed: 0.389 s
% 42.84/6.51 % (961591)Peak memory usage: 13 MB
% 42.84/6.51 % (961591)Instructions burned: 984 (million)
% 42.84/6.51 % (961595)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=1685565164:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2943 on theBenchmark for (2943ds/872Mi)
% 42.84/6.51 % (961515)Instruction limit reached!
% 42.84/6.51 % (961515)------------------------------
% 42.84/6.51 % (961515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961515)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961515)Termination reason: Instruction limit
% 42.84/6.51 % (961515)Termination phase: Saturation
% 42.84/6.51 % (961515)Time elapsed: 2.460 s
% 42.84/6.51 % (961515)Peak memory usage: 13 MB
% 42.84/6.51 % (961515)Instructions burned: 6362 (million)
% 42.84/6.51 % (961597)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 42.84/6.51 % (961597)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=63447525:i=999:add=on:rtra=on_2941 on theBenchmark for (2941ds/999Mi)
% 42.84/6.51 % (961589)Instruction limit reached!
% 42.84/6.51 % (961589)------------------------------
% 42.84/6.51 % (961589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961589)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961589)Termination reason: Instruction limit
% 42.84/6.51 % (961589)Termination phase: Saturation
% 42.84/6.51 % (961589)Time elapsed: 0.834 s
% 42.84/6.51 % (961589)Peak memory usage: 13 MB
% 42.84/6.51 % (961589)Instructions burned: 1924 (million)
% 42.84/6.51 % (961593)Instruction limit reached!
% 42.84/6.51 % (961593)------------------------------
% 42.84/6.51 % (961593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961593)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961593)Termination reason: Instruction limit
% 42.84/6.51 % (961593)Termination phase: Saturation
% 42.84/6.51 % (961593)Time elapsed: 0.300 s
% 42.84/6.51 % (961593)Peak memory usage: 15 MB
% 42.84/6.51 % (961593)Instructions burned: 593 (million)
% 42.84/6.51 % (961599)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 42.84/6.51 % (961599)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=2891794574:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2941 on theBenchmark for (2941ds/244Mi)
% 42.84/6.51 % (961365)Instruction limit reached!
% 42.84/6.51 % (961365)------------------------------
% 42.84/6.51 % (961365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961365)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961365)Termination reason: Instruction limit
% 42.84/6.51 % (961365)Termination phase: Saturation
% 42.84/6.51 % (961365)Time elapsed: 4.926 s
% 42.84/6.51 % (961365)Peak memory usage: 36 MB
% 42.84/6.51 % (961365)Instructions burned: 9841 (million)
% 42.84/6.51 % (961600)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=1604882395:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2941 on theBenchmark for (2941ds/113Mi)
% 42.84/6.51 % (961603)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=228861997:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2941 on theBenchmark for (2941ds/7795Mi)
% 42.84/6.51 % (961600)Instruction limit reached!
% 42.84/6.51 % (961600)------------------------------
% 42.84/6.51 % (961600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961600)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961600)Termination reason: Instruction limit
% 42.84/6.51 % (961600)Termination phase: Property scanning
% 42.84/6.51 % (961600)Time elapsed: 0.046 s
% 42.84/6.51 % (961600)Peak memory usage: 11 MB
% 42.84/6.51 % (961600)Instructions burned: 114 (million)
% 42.84/6.51 % (961605)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2151681050:st=2:i=5026:sd=1:rtra=on:ss=axioms_2940 on theBenchmark for (2940ds/5026Mi)
% 42.84/6.51 % (961549)Instruction limit reached!
% 42.84/6.51 % (961549)------------------------------
% 42.84/6.51 % (961549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961549)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961549)Termination reason: Instruction limit
% 42.84/6.51 % (961549)Termination phase: Saturation
% 42.84/6.51 % (961549)Time elapsed: 2.016 s
% 42.84/6.51 % (961549)Peak memory usage: 37 MB
% 42.84/6.51 % (961549)Instructions burned: 4388 (million)
% 42.84/6.51 % (961599)Instruction limit reached!
% 42.84/6.51 % (961599)------------------------------
% 42.84/6.51 % (961599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961599)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961599)Termination reason: Instruction limit
% 42.84/6.51 % (961599)Termination phase: Saturation
% 42.84/6.51 % (961599)Time elapsed: 0.100 s
% 42.84/6.51 % (961599)Peak memory usage: 12 MB
% 42.84/6.51 % (961599)Instructions burned: 247 (million)
% 42.84/6.51 % (961607)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 42.84/6.51 % (961607)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=1488362856:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2940 on theBenchmark for (2940ds/763Mi)
% 42.84/6.51 % (961608)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3022912717:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2940 on theBenchmark for (2940ds/1144Mi)
% 42.84/6.51 % (961595)Instruction limit reached!
% 42.84/6.51 % (961595)------------------------------
% 42.84/6.51 % (961595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961595)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961595)Termination reason: Instruction limit
% 42.84/6.51 % (961595)Termination phase: Saturation
% 42.84/6.51 % (961595)Time elapsed: 0.346 s
% 42.84/6.51 % (961595)Peak memory usage: 13 MB
% 42.84/6.51 % (961595)Instructions burned: 872 (million)
% 42.84/6.51 % (961611)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 42.84/6.51 % (961611)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=1238260098:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2939 on theBenchmark for (2939ds/52Mi)
% 42.84/6.51 % (961611)Instruction limit reached!
% 42.84/6.51 % (961611)------------------------------
% 42.84/6.51 % (961611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961611)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961611)Termination reason: Instruction limit
% 42.84/6.51 % (961611)Termination phase: Function definition elimination
% 42.84/6.51 % (961611)Time elapsed: 0.024 s
% 42.84/6.51 % (961611)Peak memory usage: 11 MB
% 42.84/6.51 % (961611)Instructions burned: 54 (million)
% 42.84/6.51 % (961613)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=1011243691:i=1724:fsr=off:rtra=on:fe=abstraction_2939 on theBenchmark for (2939ds/1724Mi)
% 42.84/6.51 % (961607) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-961194-961607"...
% 42.84/6.51 % (961597)Instruction limit reached!
% 42.84/6.51 % (961597)------------------------------
% 42.84/6.51 % (961597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.51 % (961597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.51 % (961597)CaDiCaL version: 2.1.3
% 42.84/6.51 % (961597)Termination reason: Instruction limit
% 42.84/6.51 % (961597)Termination phase: Saturation
% 42.84/6.51 % (961597)Time elapsed: 0.411 s
% 42.84/6.51 % (961597)Peak memory usage: 18 MB
% 42.84/6.51 % (961597)Instructions burned: 1000 (million)
% 42.84/6.51 % (961615)dis-1004_128_to=kbo:sil=128000:tgt=full:si=on:fdtod=off:sp=const_frequency:spb=goal:uwa=off:slsqc=3:slsq=on:random_seed=1444790064:i=439:add=on:slsql=off:rtra=on:ntd=on_2937 on theBenchmark for (2937ds/439Mi)
% 42.84/6.51 % (961607)...printing done.
% 42.84/6.51 % (961607)Refutation found. Thanks to Tanya!
% 42.84/6.51 % SZS status Theorem for theBenchmark
% 42.84/6.51 % SZS output start Proof for theBenchmark
% See solution above
% 42.84/6.52 % (961607)------------------------------
% 42.84/6.52 % (961607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.84/6.52 % (961607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.84/6.52 % (961607)CaDiCaL version: 2.1.3
% 42.84/6.52 % (961607)Termination reason: Refutation
% 42.84/6.52 % (961607)Time elapsed: 0.263 s
% 42.84/6.52 % (961607)Peak memory usage: 17 MB
% 42.84/6.52 % (961607)Instructions burned: 584 (million)
% 42.84/6.52 % (961194)Success in time 6.271 s
% 42.84/6.52 % Vampire exiting
%------------------------------------------------------------------------------