%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO877^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:50:29 AM UTC 2026
% Result : Theorem 0.07s 0.20s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 35 unt; 0 typ; 2 def)
% Number of atoms : 234 ( 66 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 4735 ( 18 ~; 12 |; 0 &;4548 @)
% ( 2 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 173 ( 173 >; 0 *; 0 +; 0 <<)
% Number of symbols : 155 ( 151 usr; 9 con; 0-14 aty)
% ( 83 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 213 ( 7 sgn 105 !; 2 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c_Eps_i: ( $i > $o ) > $i ).
thf(func_def_1,type,
c_False: $o ).
thf(func_def_2,type,
c_True: $o ).
thf(func_def_3,type,
c_not: $o > $o ).
thf(func_def_4,type,
c_and: $o > $o > $o ).
thf(func_def_5,type,
c_or: $o > $o > $o ).
thf(func_def_6,type,
c_iff: $o > $o > $o ).
thf(func_def_7,type,
c_In: $i > $i > $o ).
thf(func_def_8,type,
c_Subq: $i > $i > $o ).
thf(func_def_10,type,
c_Union: $i > $i ).
thf(func_def_11,type,
c_Power: $i > $i ).
thf(func_def_12,type,
c_Repl: $i > ( $i > $i ) > $i ).
thf(func_def_13,type,
c_TransSet: $i > $o ).
thf(func_def_14,type,
c_atleast2: $i > $o ).
thf(func_def_15,type,
c_atleast3: $i > $o ).
thf(func_def_16,type,
c_atleast4: $i > $o ).
thf(func_def_17,type,
c_atleast5: $i > $o ).
thf(func_def_18,type,
c_atleast6: $i > $o ).
thf(func_def_19,type,
c_exactly2: $i > $o ).
thf(func_def_20,type,
c_exactly3: $i > $o ).
thf(func_def_21,type,
c_exactly4: $i > $o ).
thf(func_def_22,type,
c_exactly5: $i > $o ).
thf(func_def_23,type,
c_exu_i: ( $i > $o ) > $o ).
thf(func_def_24,type,
c_reflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
c_irreflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
c_symmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
c_antisymmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
c_transitive_i: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
c_eqreln_i: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
c_per_i: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
c_linear_i: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
c_partialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_34,type,
c_totalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_37,type,
c_If_i: $o > $i > $i > $i ).
thf(func_def_38,type,
c_exactly1of2: $o > $o > $o ).
thf(func_def_39,type,
c_exactly1of3: $o > $o > $o > $o ).
thf(func_def_40,type,
c_nIn: $i > $i > $o ).
thf(func_def_41,type,
c_nSubq: $i > $i > $o ).
thf(func_def_42,type,
c_UPair: $i > $i > $i ).
thf(func_def_43,type,
c_Sing: $i > $i ).
thf(func_def_44,type,
c_binunion: $i > $i > $i ).
thf(func_def_45,type,
c_SetAdjoin: $i > $i > $i ).
thf(func_def_46,type,
c_famunion: $i > ( $i > $i ) > $i ).
thf(func_def_47,type,
c_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_49,type,
c_binintersect: $i > $i > $i ).
thf(func_def_50,type,
c_setminus: $i > $i > $i ).
thf(func_def_51,type,
c_inj: $i > $i > ( $i > $i ) > $o ).
thf(func_def_52,type,
c_bij: $i > $i > ( $i > $i ) > $o ).
thf(func_def_53,type,
c_atleastp: $i > $i > $o ).
thf(func_def_54,type,
c_equip: $i > $i > $o ).
thf(func_def_55,type,
c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_56,type,
c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_57,type,
c_ordsucc: $i > $i ).
thf(func_def_58,type,
c_nat_p: $i > $o ).
thf(func_def_59,type,
c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
thf(func_def_60,type,
c_add_nat: $i > $i > $i ).
thf(func_def_61,type,
c_mul_nat: $i > $i > $i ).
thf(func_def_62,type,
c_ordinal: $i > $o ).
thf(func_def_63,type,
c_V_: $i > $i ).
thf(func_def_64,type,
c_Inj1: $i > $i ).
thf(func_def_65,type,
c_Inj0: $i > $i ).
thf(func_def_66,type,
c_Unj: $i > $i ).
thf(func_def_67,type,
c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_68,type,
c_setsum: $i > $i > $i ).
thf(func_def_69,type,
c_proj0: $i > $i ).
thf(func_def_70,type,
c_proj1: $i > $i ).
thf(func_def_71,type,
c_binrep: $i > $i > $i ).
thf(func_def_72,type,
c_lam: $i > ( $i > $i ) > $i ).
thf(func_def_73,type,
c_setprod: $i > $i > $i ).
thf(func_def_74,type,
c_ap: $i > $i > $i ).
thf(func_def_75,type,
c_setsum_p: $i > $o ).
thf(func_def_76,type,
c_tuple_p: $i > $i > $o ).
thf(func_def_77,type,
c_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_78,type,
c_setexp: $i > $i > $i ).
thf(func_def_79,type,
c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
c_set_of_pairs: $i > $o ).
thf(func_def_81,type,
c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_82,type,
c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_83,type,
c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_84,type,
c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_85,type,
c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_86,type,
c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_87,type,
c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_88,type,
c_SNoElts_: $i > $i ).
thf(func_def_89,type,
c_SNo_: $i > $i > $o ).
thf(func_def_90,type,
c_PSNo: $i > ( $i > $o ) > $i ).
thf(func_def_91,type,
c_SNo: $i > $o ).
thf(func_def_92,type,
c_SNoLev: $i > $i ).
thf(func_def_93,type,
c_SNoEq_: $i > $i > $i > $o ).
thf(func_def_94,type,
c_SNoLt: $i > $i > $o ).
thf(func_def_95,type,
c_SNoLe: $i > $i > $o ).
thf(func_def_96,type,
c_binop_on: $i > ( $i > $i > $i ) > $o ).
thf(func_def_97,type,
c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
thf(func_def_98,type,
c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_99,type,
c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_100,type,
c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_101,type,
c_combinator: $i > $o ).
thf(func_def_102,type,
c_combinator_equiv: $i > $i > $o ).
thf(func_def_103,type,
c_equip_mod: $i > $i > $i > $o ).
thf(func_def_107,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_108,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_109,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_110,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_111,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_112,type,
vIMP: $o > $o > $o ).
thf(func_def_113,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_114,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_115,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_116,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_117,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_118,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
db13:
!>[X0: $tType] : X0 ).
thf(func_def_120,type,
db12:
!>[X0: $tType] : X0 ).
thf(func_def_121,type,
db11:
!>[X0: $tType] : X0 ).
thf(func_def_122,type,
db10:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
db14:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
db15:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db16:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db17:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db18:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
sP0: ( $i > $o ) > $o ).
thf(func_def_132,type,
sP1: ( $i > $o ) > $o ).
thf(func_def_133,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_134,type,
sK3: ( $i > $o ) > $i > $i ).
thf(func_def_135,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_136,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_137,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_138,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_139,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_140,type,
vNOT: $o > $o ).
thf(func_def_141,type,
sK9: $o ).
thf(func_def_142,type,
sK10: $o ).
thf(func_def_143,type,
sK11: ( $i > $i ) > $i > $i > $i ).
thf(func_def_144,type,
sK12: $i > ( $i > $i ) > $i > $i > $o ).
thf(func_def_145,type,
sK13: $i > $i > $i ).
thf(func_def_146,type,
sK14: $i > $i > $i ).
thf(func_def_147,type,
sK15: $i > $i > $i > $o ).
thf(func_def_148,type,
sK16: $i > $i > $i ).
thf(func_def_149,type,
sK17: $i > $i > $i ).
thf(func_def_150,type,
sK18: $o > $o > $o ).
thf(func_def_151,type,
sK19: $o > $o > $o ).
thf(f13,axiom,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(f14,axiom,
( c_and
= ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> ( X1
=> X2 ) )
=> X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
thf(f109,conjecture,
( c_not
@ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i] :
( c_and
@ ( X6
= ( X1 @ ( X1 @ X5 @ ( X1 @ X7 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X1 @ X5 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X4 @ X5 ) @ ( X1 @ ( X1 @ X7 @ ( X1 @ X6 @ ( X1 @ X6 @ X6 ) ) ) @ X5 ) ) ) @ ( X1 @ ( X4 @ ( X1 @ ( X1 @ ( X4 @ X7 ) @ X5 ) @ ( X1 @ X5 @ X5 ) ) ) @ ( X1 @ X6 @ ( X1 @ X6 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X4 @ X6 ) @ X7 ) ) @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) @ X6 ) @ ( X4 @ ( X1 @ ( X1 @ X7 @ ( X1 @ X5 @ ( X1 @ ( X4 @ ( X1 @ X5 @ X7 ) ) @ X5 ) ) ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X4 @ X5 ) @ X6 ) ) @ X6 ) @ ( X4 @ ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X1 @ X7 @ X5 ) @ X7 ) ) @ X6 ) ) @ X7 ) @ ( X1 @ X7 @ ( X1 @ X5 @ X5 ) ) ) @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ X5 @ X5 ) ) @ ( X4 @ ( X4 @ ( X1 @ X7 @ ( X4 @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) ) ) ) @ X5 ) @ X6 ) @ ( X1 @ X6 @ X7 ) ) ) ) @ X5 ) @ X5 ) @ ( X4 @ X6 ) ) ) ) @ ( X1 @ ( X1 @ ( X4 @ ( X1 @ ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X7 @ ( X1 @ ( X4 @ ( X4 @ ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) ) ) @ ( X4 @ ( X1 @ X5 @ X5 ) ) ) ) @ X5 ) @ ( X4 @ X5 ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ X7 ) @ ( X4 @ ( X4 @ ( X4 @ X7 ) ) ) ) @ X7 ) @ X6 ) @ X5 ) ) ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ X5 ) @ ( X4 @ X6 ) ) @ X6 ) ) ) @ X7 ) @ X6 ) ) )
@ ? [X8: $i] : ( X3 @ ( X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f110,negated_conjecture,
~ ( c_not
@ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i] :
( c_and
@ ( X6
= ( X1 @ ( X1 @ X5 @ ( X1 @ X7 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X1 @ X5 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X4 @ X5 ) @ ( X1 @ ( X1 @ X7 @ ( X1 @ X6 @ ( X1 @ X6 @ X6 ) ) ) @ X5 ) ) ) @ ( X1 @ ( X4 @ ( X1 @ ( X1 @ ( X4 @ X7 ) @ X5 ) @ ( X1 @ X5 @ X5 ) ) ) @ ( X1 @ X6 @ ( X1 @ X6 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X4 @ X6 ) @ X7 ) ) @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) @ X6 ) @ ( X4 @ ( X1 @ ( X1 @ X7 @ ( X1 @ X5 @ ( X1 @ ( X4 @ ( X1 @ X5 @ X7 ) ) @ X5 ) ) ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X4 @ X5 ) @ X6 ) ) @ X6 ) @ ( X4 @ ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X1 @ X7 @ X5 ) @ X7 ) ) @ X6 ) ) @ X7 ) @ ( X1 @ X7 @ ( X1 @ X5 @ X5 ) ) ) @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ X5 @ X5 ) ) @ ( X4 @ ( X4 @ ( X1 @ X7 @ ( X4 @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) ) ) ) @ X5 ) @ X6 ) @ ( X1 @ X6 @ X7 ) ) ) ) @ X5 ) @ X5 ) @ ( X4 @ X6 ) ) ) ) @ ( X1 @ ( X1 @ ( X4 @ ( X1 @ ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X7 @ ( X1 @ ( X4 @ ( X4 @ ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) ) ) @ ( X4 @ ( X1 @ X5 @ X5 ) ) ) ) @ X5 ) @ ( X4 @ X5 ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ X7 ) @ ( X4 @ ( X4 @ ( X4 @ X7 ) ) ) ) @ X7 ) @ X6 ) @ X5 ) ) ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ X5 ) @ ( X4 @ X6 ) ) @ X6 ) ) ) @ X7 ) @ X6 ) ) )
@ ? [X8: $i] : ( X3 @ ( X4 @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
thf(f135,plain,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
inference(rectify,[],[f13]) ).
thf(f136,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(fool_elimination,[],[f135]) ).
thf(f137,plain,
( c_and
= ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> ( X1
=> X2 ) )
=> X2 ) ) ),
inference(rectify,[],[f14]) ).
thf(f138,plain,
( c_and
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> ( Y1
=> Y2 ) )
=> Y2 ) ) ) ),
inference(fool_elimination,[],[f137]) ).
thf(f306,plain,
~ ( c_not
@ ! [X1: $i > $i > $i,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i] :
( c_and
@ ( X6
= ( X1 @ ( X1 @ X5 @ ( X1 @ X7 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X1 @ X5 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X4 @ X5 ) @ ( X1 @ ( X1 @ X7 @ ( X1 @ X6 @ ( X1 @ X6 @ X6 ) ) ) @ X5 ) ) ) @ ( X1 @ ( X4 @ ( X1 @ ( X1 @ ( X4 @ X7 ) @ X5 ) @ ( X1 @ X5 @ X5 ) ) ) @ ( X1 @ X6 @ ( X1 @ X6 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X4 @ X6 ) @ X7 ) ) @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) @ X6 ) @ ( X4 @ ( X1 @ ( X1 @ X7 @ ( X1 @ X5 @ ( X1 @ ( X4 @ ( X1 @ X5 @ X7 ) ) @ X5 ) ) ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X4 @ X5 ) @ X6 ) ) @ X6 ) @ ( X4 @ ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X6 @ ( X1 @ ( X1 @ X7 @ X5 ) @ X7 ) ) @ X6 ) ) @ X7 ) @ ( X1 @ X7 @ ( X1 @ X5 @ X5 ) ) ) @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ ( X1 @ X5 @ X5 ) ) @ ( X4 @ ( X4 @ ( X1 @ X7 @ ( X4 @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) ) ) ) @ X5 ) @ X6 ) @ ( X1 @ X6 @ X7 ) ) ) ) @ X5 ) @ X5 ) @ ( X4 @ X6 ) ) ) ) @ ( X1 @ ( X1 @ ( X4 @ ( X1 @ ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X7 @ ( X1 @ ( X4 @ ( X4 @ ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) ) ) @ ( X4 @ ( X1 @ X5 @ X5 ) ) ) ) @ X5 ) @ ( X4 @ X5 ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ X7 ) @ ( X4 @ ( X4 @ ( X4 @ X7 ) ) ) ) @ X7 ) @ X6 ) @ X5 ) ) ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ X5 ) @ ( X4 @ X6 ) ) @ X6 ) ) ) @ X7 ) @ X6 ) ) )
@ ( X3 @ ( X4 @ X5 ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f307,plain,
( $true
!= ( c_not
@ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( c_and
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y0 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y2 ) @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y3 @ Y0 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y1 ) @ Y0 ) ) @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ ( Y3 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ ( Y5 @ Y2 @ Y0 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y3 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y0 @ Y2 ) @ Y0 ) ) @ Y1 ) ) @ Y0 ) @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y0 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y3 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y0 ) ) ) @ ( Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y3 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 ) ) ) ) @ Y0 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y3 @ Y1 ) ) @ Y1 ) ) ) @ Y0 ) @ Y1 ) )
= Y1 )
@ ( Y4 @ ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f306]) ).
thf(f309,plain,
( $true
!= ( c_not
@ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( c_and
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y0 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y2 ) @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y3 @ Y0 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y1 ) @ Y0 ) ) @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ ( Y3 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ ( Y5 @ Y2 @ Y0 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y3 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y0 @ Y2 ) @ Y0 ) ) @ Y1 ) ) @ Y0 ) @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y0 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y3 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y0 ) ) ) @ ( Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y3 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 ) ) ) ) @ Y0 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y3 @ Y1 ) ) @ Y1 ) ) ) @ Y0 ) @ Y1 ) )
= Y1 )
@ ( Y4 @ ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f307]) ).
thf(f352,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(cnf_transformation,[],[f136]) ).
thf(f353,plain,
( c_and
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> ( Y1
=> Y2 ) )
=> Y2 ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f448,plain,
( $true
!= ( c_not
@ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( c_and
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y0 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y2 ) @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y3 @ Y0 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y1 ) @ Y0 ) ) @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ ( Y3 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ ( Y5 @ Y2 @ Y0 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y3 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y0 @ Y2 ) @ Y0 ) ) @ Y1 ) ) @ Y0 ) @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y0 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y3 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y0 ) ) ) @ ( Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y3 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 ) ) ) ) @ Y0 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y3 @ Y1 ) ) @ Y1 ) ) ) @ Y0 ) @ Y1 ) )
= Y1 )
@ ( Y4 @ ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f309]) ).
thf(f543,plain,
( $true
!= ( ^ [Y0: $o] :
( Y0
=> c_False )
@ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( ^ [Y6: $o,Y7: $o] :
( !! @ $o
@ ^ [Y8: $o] :
( ( Y6
=> ( Y7
=> Y8 ) )
=> Y8 ) )
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y0 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y2 ) @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y3 @ Y0 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y1 ) @ Y0 ) ) @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ ( Y3 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ ( Y5 @ Y2 @ Y0 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y3 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y0 @ Y2 ) @ Y0 ) ) @ Y1 ) ) @ Y0 ) @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y0 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y3 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y0 ) ) ) @ ( Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y3 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 ) ) ) ) @ Y0 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y3 @ Y1 ) ) @ Y1 ) ) ) @ Y0 ) @ Y1 ) )
= Y1 )
@ ( Y4 @ ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f448,f352,f353]) ).
thf(f544,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( !! @ $o
@ ^ [Y6: $o] :
( ( ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y0 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y2 ) @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y3 @ Y0 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y1 ) @ Y0 ) ) @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ ( Y3 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ ( Y5 @ Y2 @ Y0 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y3 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y0 @ Y2 ) @ Y0 ) ) @ Y1 ) ) @ Y0 ) @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y0 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y3 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y0 ) ) ) @ ( Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y3 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 ) ) ) ) @ Y0 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y3 @ Y1 ) ) @ Y1 ) ) ) @ Y0 ) @ Y1 ) )
= Y1 )
=> ( ( Y4 @ ( Y3 @ Y2 ) )
=> Y6 ) )
=> Y6 ) ) ) ) ) ) ) )
=> c_False ) ),
inference(beta-eta_normalization,[],[f543]) ).
thf(f545,plain,
c_False = $false,
inference(imp_proxy_clausification,[],[f544]) ).
thf(f546,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( !! @ $o
@ ^ [Y6: $o] :
( ( ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y0 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y2 ) @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y3 @ Y0 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y1 ) @ Y0 ) ) @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ ( Y3 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ ( Y5 @ Y2 @ Y0 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y3 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y0 @ Y2 ) @ Y0 ) ) @ Y1 ) ) @ Y0 ) @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y0 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y3 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y0 ) ) ) @ ( Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y3 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 ) ) ) ) @ Y0 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y3 @ Y1 ) ) @ Y1 ) ) ) @ Y0 ) @ Y1 ) )
= Y1 )
=> ( ( Y4 @ ( Y3 @ Y2 ) )
=> Y6 ) )
=> Y6 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f544]) ).
thf(f547,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( !! @ $o
@ ^ [Y6: $o] :
( ( ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y0 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y2 ) @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y3 @ Y0 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ Y1 ) @ Y0 ) ) @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ ( Y3 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ ( Y5 @ ( Y3 @ ( Y5 @ Y2 @ Y0 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y3 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y0 @ Y2 ) @ Y0 ) ) @ Y1 ) ) @ Y0 ) @ ( Y5 @ Y0 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ ( Y3 @ ( Y3 @ ( Y5 @ Y0 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y0 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y3 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y0 @ ( Y5 @ ( Y3 @ ( Y3 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y0 ) ) ) @ ( Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y3 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 ) ) ) ) @ Y0 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y3 @ Y1 ) ) @ Y1 ) ) ) @ Y0 ) @ Y1 ) )
= Y1 )
=> ( ( Y4 @ ( Y3 @ Y2 ) )
=> Y6 ) )
=> Y6 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f546]) ).
thf(f548,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y4: $i > $i > $i] :
( !! @ $o
@ ^ [Y5: $o] :
( ( ( ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ X1 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y2 @ Y1 ) @ ( Y4 @ ( Y4 @ X1 @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ Y0 ) ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y2 @ ( Y4 @ ( Y4 @ ( Y2 @ X1 ) @ Y1 ) @ ( Y4 @ Y1 @ Y1 ) ) ) @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y2 @ Y0 ) @ X1 ) ) @ ( Y2 @ ( Y4 @ X1 @ Y1 ) ) ) ) @ Y0 ) @ ( Y2 @ ( Y4 @ ( Y4 @ X1 @ ( Y4 @ Y1 @ ( Y4 @ ( Y2 @ ( Y4 @ Y1 @ X1 ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y2 @ Y1 ) @ Y0 ) ) @ Y0 ) @ ( Y2 @ ( Y2 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ X1 @ Y1 ) @ X1 ) ) @ Y0 ) ) @ X1 ) @ ( Y4 @ X1 @ ( Y4 @ Y1 @ Y1 ) ) ) @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ Y1 @ Y1 ) ) @ ( Y2 @ ( Y2 @ ( Y4 @ X1 @ ( Y2 @ ( Y2 @ ( Y4 @ X1 @ Y1 ) ) ) ) ) ) ) @ Y1 ) @ Y0 ) @ ( Y4 @ Y0 @ X1 ) ) ) ) @ Y1 ) @ Y1 ) @ ( Y2 @ Y0 ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y2 @ ( Y4 @ ( Y2 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ X1 @ ( Y4 @ ( Y2 @ ( Y2 @ ( Y4 @ ( Y4 @ Y1 @ Y0 ) @ X1 ) ) ) @ ( Y2 @ ( Y4 @ Y1 @ Y1 ) ) ) ) @ Y1 ) @ ( Y2 @ Y1 ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ X1 ) @ ( Y2 @ ( Y2 @ ( Y2 @ X1 ) ) ) ) @ X1 ) @ Y0 ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ Y1 ) @ ( Y2 @ Y0 ) ) @ Y0 ) ) ) @ X1 ) @ Y0 ) )
= Y0 )
=> ( ( Y3 @ ( Y2 @ Y1 ) )
=> Y5 ) )
=> Y5 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f547]) ).
thf(f549,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y4: $i > $i > $i] :
( !! @ $o
@ ^ [Y5: $o] :
( ( ( ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ X1 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y2 @ Y1 ) @ ( Y4 @ ( Y4 @ X1 @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ Y0 ) ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y2 @ ( Y4 @ ( Y4 @ ( Y2 @ X1 ) @ Y1 ) @ ( Y4 @ Y1 @ Y1 ) ) ) @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y2 @ Y0 ) @ X1 ) ) @ ( Y2 @ ( Y4 @ X1 @ Y1 ) ) ) ) @ Y0 ) @ ( Y2 @ ( Y4 @ ( Y4 @ X1 @ ( Y4 @ Y1 @ ( Y4 @ ( Y2 @ ( Y4 @ Y1 @ X1 ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y2 @ Y1 ) @ Y0 ) ) @ Y0 ) @ ( Y2 @ ( Y2 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ X1 @ Y1 ) @ X1 ) ) @ Y0 ) ) @ X1 ) @ ( Y4 @ X1 @ ( Y4 @ Y1 @ Y1 ) ) ) @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ Y1 @ Y1 ) ) @ ( Y2 @ ( Y2 @ ( Y4 @ X1 @ ( Y2 @ ( Y2 @ ( Y4 @ X1 @ Y1 ) ) ) ) ) ) ) @ Y1 ) @ Y0 ) @ ( Y4 @ Y0 @ X1 ) ) ) ) @ Y1 ) @ Y1 ) @ ( Y2 @ Y0 ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y2 @ ( Y4 @ ( Y2 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ X1 @ ( Y4 @ ( Y2 @ ( Y2 @ ( Y4 @ ( Y4 @ Y1 @ Y0 ) @ X1 ) ) ) @ ( Y2 @ ( Y4 @ Y1 @ Y1 ) ) ) ) @ Y1 ) @ ( Y2 @ Y1 ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ X1 ) @ ( Y2 @ ( Y2 @ ( Y2 @ X1 ) ) ) ) @ X1 ) @ Y0 ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ Y1 ) @ ( Y2 @ Y0 ) ) @ Y0 ) ) ) @ X1 ) @ Y0 ) )
= Y0 )
=> ( ( Y3 @ ( Y2 @ Y1 ) )
=> Y5 ) )
=> Y5 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f548]) ).
thf(f550,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y3: $i > $i > $i] :
( !! @ $o
@ ^ [Y4: $o] :
( ( ( ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ X1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y1 @ Y0 ) @ ( Y3 @ ( Y3 @ X1 @ ( Y3 @ X2 @ ( Y3 @ X2 @ X2 ) ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y1 @ ( Y3 @ ( Y3 @ ( Y1 @ X1 ) @ Y0 ) @ ( Y3 @ Y0 @ Y0 ) ) ) @ ( Y3 @ X2 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y1 @ X2 ) @ X1 ) ) @ ( Y1 @ ( Y3 @ X1 @ Y0 ) ) ) ) @ X2 ) @ ( Y1 @ ( Y3 @ ( Y3 @ X1 @ ( Y3 @ Y0 @ ( Y3 @ ( Y1 @ ( Y3 @ Y0 @ X1 ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y1 @ Y0 ) @ X2 ) ) @ X2 ) @ ( Y1 @ ( Y1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ X1 @ Y0 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y3 @ X1 @ ( Y3 @ Y0 @ Y0 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ Y0 @ Y0 ) ) @ ( Y1 @ ( Y1 @ ( Y3 @ X1 @ ( Y1 @ ( Y1 @ ( Y3 @ X1 @ Y0 ) ) ) ) ) ) ) @ Y0 ) @ X2 ) @ ( Y3 @ X2 @ X1 ) ) ) ) @ Y0 ) @ Y0 ) @ ( Y1 @ X2 ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y1 @ ( Y3 @ ( Y1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X1 @ ( Y3 @ ( Y1 @ ( Y1 @ ( Y3 @ ( Y3 @ Y0 @ X2 ) @ X1 ) ) ) @ ( Y1 @ ( Y3 @ Y0 @ Y0 ) ) ) ) @ Y0 ) @ ( Y1 @ Y0 ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ X1 ) @ ( Y1 @ ( Y1 @ ( Y1 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ Y0 ) @ ( Y1 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( Y2 @ ( Y1 @ Y0 ) )
=> Y4 ) )
=> Y4 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f549]) ).
thf(f551,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y3: $i > $i > $i] :
( !! @ $o
@ ^ [Y4: $o] :
( ( ( ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ X1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y1 @ Y0 ) @ ( Y3 @ ( Y3 @ X1 @ ( Y3 @ X2 @ ( Y3 @ X2 @ X2 ) ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y1 @ ( Y3 @ ( Y3 @ ( Y1 @ X1 ) @ Y0 ) @ ( Y3 @ Y0 @ Y0 ) ) ) @ ( Y3 @ X2 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y1 @ X2 ) @ X1 ) ) @ ( Y1 @ ( Y3 @ X1 @ Y0 ) ) ) ) @ X2 ) @ ( Y1 @ ( Y3 @ ( Y3 @ X1 @ ( Y3 @ Y0 @ ( Y3 @ ( Y1 @ ( Y3 @ Y0 @ X1 ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y1 @ Y0 ) @ X2 ) ) @ X2 ) @ ( Y1 @ ( Y1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ X1 @ Y0 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y3 @ X1 @ ( Y3 @ Y0 @ Y0 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ Y0 @ Y0 ) ) @ ( Y1 @ ( Y1 @ ( Y3 @ X1 @ ( Y1 @ ( Y1 @ ( Y3 @ X1 @ Y0 ) ) ) ) ) ) ) @ Y0 ) @ X2 ) @ ( Y3 @ X2 @ X1 ) ) ) ) @ Y0 ) @ Y0 ) @ ( Y1 @ X2 ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y1 @ ( Y3 @ ( Y1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X1 @ ( Y3 @ ( Y1 @ ( Y1 @ ( Y3 @ ( Y3 @ Y0 @ X2 ) @ X1 ) ) ) @ ( Y1 @ ( Y3 @ Y0 @ Y0 ) ) ) ) @ Y0 ) @ ( Y1 @ Y0 ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ X1 ) @ ( Y1 @ ( Y1 @ ( Y1 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ Y0 ) @ ( Y1 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( Y2 @ ( Y1 @ Y0 ) )
=> Y4 ) )
=> Y4 ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f550]) ).
thf(f552,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( ( ( Y2 @ ( Y2 @ X3 @ ( Y2 @ X1 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y0 @ X3 ) @ ( Y2 @ ( Y2 @ X1 @ ( Y2 @ X2 @ ( Y2 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y2 @ ( Y0 @ ( Y2 @ ( Y2 @ ( Y0 @ X1 ) @ X3 ) @ ( Y2 @ X3 @ X3 ) ) ) @ ( Y2 @ X2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y0 @ X2 ) @ X1 ) ) @ ( Y0 @ ( Y2 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( Y0 @ ( Y2 @ ( Y2 @ X1 @ ( Y2 @ X3 @ ( Y2 @ ( Y0 @ ( Y2 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y0 @ X3 ) @ X2 ) ) @ X2 ) @ ( Y0 @ ( Y0 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y2 @ X1 @ ( Y2 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ X3 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y2 @ X1 @ ( Y0 @ ( Y0 @ ( Y2 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y2 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( Y0 @ X2 ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y0 @ ( Y2 @ ( Y0 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X1 @ ( Y2 @ ( Y0 @ ( Y0 @ ( Y2 @ ( Y2 @ X3 @ X2 ) @ X1 ) ) ) @ ( Y0 @ ( Y2 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( Y0 @ X3 ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ X1 ) @ ( Y0 @ ( Y0 @ ( Y0 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ X3 ) @ ( Y0 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( Y1 @ ( Y0 @ X3 ) )
=> Y3 ) )
=> Y3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f551]) ).
thf(f553,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i] :
( $true
= ( ^ [Y0: $i > $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( ( ( Y2 @ ( Y2 @ X3 @ ( Y2 @ X1 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y0 @ X3 ) @ ( Y2 @ ( Y2 @ X1 @ ( Y2 @ X2 @ ( Y2 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y2 @ ( Y0 @ ( Y2 @ ( Y2 @ ( Y0 @ X1 ) @ X3 ) @ ( Y2 @ X3 @ X3 ) ) ) @ ( Y2 @ X2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y0 @ X2 ) @ X1 ) ) @ ( Y0 @ ( Y2 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( Y0 @ ( Y2 @ ( Y2 @ X1 @ ( Y2 @ X3 @ ( Y2 @ ( Y0 @ ( Y2 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y0 @ X3 ) @ X2 ) ) @ X2 ) @ ( Y0 @ ( Y0 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y2 @ X1 @ ( Y2 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ X3 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y2 @ X1 @ ( Y0 @ ( Y0 @ ( Y2 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y2 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( Y0 @ X2 ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y0 @ ( Y2 @ ( Y0 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X1 @ ( Y2 @ ( Y0 @ ( Y0 @ ( Y2 @ ( Y2 @ X3 @ X2 ) @ X1 ) ) ) @ ( Y0 @ ( Y2 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( Y0 @ X3 ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ X1 ) @ ( Y0 @ ( Y0 @ ( Y0 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ X3 ) @ ( Y0 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( Y1 @ ( Y0 @ X3 ) )
=> Y3 ) )
=> Y3 ) ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f552]) ).
thf(f554,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( ( ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( X4 @ X3 ) @ ( Y1 @ ( Y1 @ X1 @ ( Y1 @ X2 @ ( Y1 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y1 @ ( X4 @ ( Y1 @ ( Y1 @ ( X4 @ X1 ) @ X3 ) @ ( Y1 @ X3 @ X3 ) ) ) @ ( Y1 @ X2 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( Y1 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( Y1 @ ( Y1 @ X1 @ ( Y1 @ X3 @ ( Y1 @ ( X4 @ ( Y1 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y1 @ X1 @ ( Y1 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( Y1 @ X1 @ ( X4 @ ( X4 @ ( Y1 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y1 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( Y1 @ ( Y1 @ ( X4 @ ( Y1 @ ( X4 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X1 @ ( Y1 @ ( X4 @ ( X4 @ ( Y1 @ ( Y1 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( Y1 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( Y0 @ ( X4 @ X3 ) )
=> Y2 ) )
=> Y2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f553]) ).
thf(f555,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i,X5: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( ( ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( X4 @ X3 ) @ ( Y1 @ ( Y1 @ X1 @ ( Y1 @ X2 @ ( Y1 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y1 @ ( X4 @ ( Y1 @ ( Y1 @ ( X4 @ X1 ) @ X3 ) @ ( Y1 @ X3 @ X3 ) ) ) @ ( Y1 @ X2 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( Y1 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( Y1 @ ( Y1 @ X1 @ ( Y1 @ X3 @ ( Y1 @ ( X4 @ ( Y1 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y1 @ X1 @ ( Y1 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( Y1 @ X1 @ ( X4 @ ( X4 @ ( Y1 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y1 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( Y1 @ ( Y1 @ ( X4 @ ( Y1 @ ( X4 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X1 @ ( Y1 @ ( X4 @ ( X4 @ ( Y1 @ ( Y1 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( Y1 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( Y0 @ ( X4 @ X3 ) )
=> Y2 ) )
=> Y2 ) ) )
@ X5 ) ),
inference(pi_proxy_clausification,[],[f554]) ).
thf(f556,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i,X5: $i > $o] :
( $true
= ( !! @ ( $i > $i > $i )
@ ^ [Y0: $i > $i > $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( ( ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X1 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X4 @ X3 ) @ ( Y0 @ ( Y0 @ X1 @ ( Y0 @ X2 @ ( Y0 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y0 @ ( X4 @ ( Y0 @ ( Y0 @ ( X4 @ X1 ) @ X3 ) @ ( Y0 @ X3 @ X3 ) ) ) @ ( Y0 @ X2 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( Y0 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( Y0 @ ( Y0 @ X1 @ ( Y0 @ X3 @ ( Y0 @ ( X4 @ ( Y0 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y0 @ X1 @ ( Y0 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( Y0 @ X1 @ ( X4 @ ( X4 @ ( Y0 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y0 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( Y0 @ ( Y0 @ ( X4 @ ( Y0 @ ( X4 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X1 @ ( Y0 @ ( X4 @ ( X4 @ ( Y0 @ ( Y0 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( Y0 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( X5 @ ( X4 @ X3 ) )
=> Y1 ) )
=> Y1 ) ) ) ),
inference(beta-eta_normalization,[],[f555]) ).
thf(f557,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i > $i > $i,X4: $i > $i,X5: $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( ( ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X1 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X4 @ X3 ) @ ( Y0 @ ( Y0 @ X1 @ ( Y0 @ X2 @ ( Y0 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y0 @ ( X4 @ ( Y0 @ ( Y0 @ ( X4 @ X1 ) @ X3 ) @ ( Y0 @ X3 @ X3 ) ) ) @ ( Y0 @ X2 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( Y0 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( Y0 @ ( Y0 @ X1 @ ( Y0 @ X3 @ ( Y0 @ ( X4 @ ( Y0 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( Y0 @ X1 @ ( Y0 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( Y0 @ X1 @ ( X4 @ ( X4 @ ( Y0 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y0 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( Y0 @ ( Y0 @ ( X4 @ ( Y0 @ ( X4 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X1 @ ( Y0 @ ( X4 @ ( X4 @ ( Y0 @ ( Y0 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( Y0 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( X5 @ ( X4 @ X3 ) )
=> Y1 ) )
=> Y1 ) )
@ X6 ) ),
inference(pi_proxy_clausification,[],[f556]) ).
thf(f558,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i > $i > $i,X4: $i > $i,X5: $i > $o] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X1 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X3 ) @ ( X6 @ ( X6 @ X1 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X4 @ X1 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( X6 @ ( X6 @ X1 @ ( X6 @ X3 @ ( X6 @ ( X4 @ ( X6 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( X6 @ X1 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( X6 @ X1 @ ( X4 @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X4 @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X1 @ ( X6 @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( X5 @ ( X4 @ X3 ) )
=> Y0 ) )
=> Y0 ) ) ),
inference(beta-eta_normalization,[],[f557]) ).
thf(f559,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i > $i > $i,X7: $o,X4: $i > $i,X5: $i > $o] :
( $true
= ( ^ [Y0: $o] :
( ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X1 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X3 ) @ ( X6 @ ( X6 @ X1 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X4 @ X1 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( X6 @ ( X6 @ X1 @ ( X6 @ X3 @ ( X6 @ ( X4 @ ( X6 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( X6 @ X1 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( X6 @ X1 @ ( X4 @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X4 @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X1 @ ( X6 @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( X5 @ ( X4 @ X3 ) )
=> Y0 ) )
=> Y0 )
@ X7 ) ),
inference(pi_proxy_clausification,[],[f558]) ).
thf(f560,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i > $i > $i,X7: $o,X4: $i > $i,X5: $i > $o] :
( $true
= ( ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X1 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X3 ) @ ( X6 @ ( X6 @ X1 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X4 @ X1 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( X6 @ ( X6 @ X1 @ ( X6 @ X3 @ ( X6 @ ( X4 @ ( X6 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( X6 @ X1 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( X6 @ X1 @ ( X4 @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X4 @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X1 @ ( X6 @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( X5 @ ( X4 @ X3 ) )
=> X7 ) )
=> X7 ) ),
inference(beta-eta_normalization,[],[f559]) ).
thf(f561,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i > $i > $i,X7: $o,X4: $i > $i,X5: $i > $o] :
( ( $false
= ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X1 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X3 ) @ ( X6 @ ( X6 @ X1 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X4 @ X1 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X4 @ X2 ) @ X1 ) ) @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) @ X2 ) @ ( X4 @ ( X6 @ ( X6 @ X1 @ ( X6 @ X3 @ ( X6 @ ( X4 @ ( X6 @ X3 @ X1 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X4 @ X3 ) @ X2 ) ) @ X2 ) @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X1 @ X3 ) @ X1 ) ) @ X2 ) ) @ X1 ) @ ( X6 @ X1 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X4 @ ( X4 @ ( X6 @ X1 @ ( X4 @ ( X4 @ ( X6 @ X1 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X1 ) ) ) ) @ X3 ) @ X3 ) @ ( X4 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X4 @ ( X6 @ ( X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X1 @ ( X6 @ ( X4 @ ( X4 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X1 ) ) ) @ ( X4 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X4 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X1 ) @ ( X4 @ ( X4 @ ( X4 @ X1 ) ) ) ) @ X1 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X4 @ X2 ) ) @ X2 ) ) ) @ X1 ) @ X2 ) )
= X2 )
=> ( ( X5 @ ( X4 @ X3 ) )
=> X7 ) ) )
| ( $true = X7 ) ),
inference(imp_proxy_clausification,[],[f560]) ).
thf(f562,plain,
! [X3: $i,X7: $o,X4: $i > $i,X5: $i > $o] :
( ( $false
= ( ( X5 @ ( X4 @ X3 ) )
=> X7 ) )
| ( $true = X7 ) ),
inference(imp_proxy_clausification,[],[f561]) ).
thf(f566,plain,
! [X3: $i,X7: $o,X4: $i > $i,X5: $i > $o] :
( ( $true
= ( X5 @ ( X4 @ X3 ) ) )
| ( $true = X7 ) ),
inference(imp_proxy_clausification,[],[f562]) ).
thf(f713,definition,
( spl20_1
<=> ! [X7: $o] : ( $true = X7 ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f714,plain,
( ! [X7: $o] : ( $true = X7 )
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f713]) ).
thf(f720,definition,
( spl20_3
<=> ! [X4: $i > $i,X5: $i > $o,X3: $i] :
( $true
= ( X5 @ ( X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
thf(f721,plain,
( ! [X3: $i,X4: $i > $i,X5: $i > $o] :
( $true
= ( X5 @ ( X4 @ X3 ) ) )
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f720]) ).
thf(f722,plain,
( spl20_1
| spl20_3 ),
inference(avatar_split_clause,[],[f566,f720,f713]) ).
thf(f804,plain,
( ! [X3: $i,X4: $i > $i] :
( $true
= ( ^ [Y0: $i] : $false
@ ( X4 @ X3 ) ) )
| ~ spl20_3 ),
inference(primitive_instantiation,[],[f721]) ).
thf(f815,plain,
( ( $true = $false )
| ~ spl20_3 ),
inference(beta-eta_normalization,[],[f804]) ).
thf(f816,plain,
( $false
| ~ spl20_3 ),
inference(trivial_inequality_removal,[],[f815]) ).
thf(f817,plain,
~ spl20_3,
inference(avatar_contradiction_clause,[],[f816]) ).
thf(f821,plain,
( ( $true = $false )
| ~ spl20_1 ),
inference(constrained_superposition,[],[f545,f714]) ).
thf(f822,plain,
( $false
| ~ spl20_1 ),
inference(trivial_inequality_removal,[],[f821]) ).
thf(f823,plain,
~ spl20_1,
inference(avatar_contradiction_clause,[],[f822]) ).
cnf(s2,plain,
( spl20_1
| spl20_3 ),
inference(sat_conversion,[],[f722]) ).
cnf(s24,plain,
~ spl20_3,
inference(sat_conversion,[],[f817]) ).
cnf(s25,plain,
~ spl20_1,
inference(sat_conversion,[],[f823]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s2,s24,s25]) ).
thf(f826,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO877^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.12 % Computer : n012.cluster.edu
% 0.07/0.12 % Model : x86_64 x86_64
% 0.07/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.12 % Memory : 8046.5625MB
% 0.07/0.12 % OS : Linux 6.8.0-71-generic
% 0.07/0.12 % CPULimit : 300
% 0.07/0.12 % WCLimit : 300
% 0.07/0.12 % DateTime : Tue Sep 29 17:23:04 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.14 Running first-order model finding
% 0.07/0.14 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % (416568)Will run a generic schedule for satisfiability detection.
% 0.07/0.20 % (416574)% WARNING: option uhcvi not known.
% 0.07/0.20 % (416574)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3081736819:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.20 % (416577)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3379195890:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.20 % (416573)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1399524317_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.20 % (416575)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2275613026:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.20 % (416576)dis+10_1_sil=32000:sp=arity:random_seed=1201286989:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.20 % (416579)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1501797219:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.20 % (416578)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3995649280:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.20 % (416574)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.20 % (416577)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.20 % (416574)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.20 % Exception at run slice level
% 0.07/0.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.20 % (416579) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-416568-416579"...
% 0.07/0.20 % (416576) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-416568-416576"...
% 0.07/0.20 % (416575) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-416568-416575"...
% 0.07/0.20 % (416574) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-416568-416574"...
% 0.07/0.20 % (416579)...printing done.
% 0.07/0.20 % (416579)Refutation found. Thanks to Tanya!
% 0.07/0.20 % SZS status Theorem for theBenchmark
% 0.07/0.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.20 % (416579)------------------------------
% 0.07/0.20 % (416579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.20 % (416579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.20 % (416579)CaDiCaL version: 2.1.3
% 0.07/0.20 % (416579)Termination reason: Refutation
% 0.07/0.20 % (416579)Time elapsed: 0.026 s
% 0.07/0.20 % (416579)Peak memory usage: 14 MB
% 0.07/0.20 % (416579)Instructions burned: 114 (million)
% 0.07/0.20 % (416568)Success in time 0.056 s
% 0.07/0.20 % Vampire exiting
%------------------------------------------------------------------------------