%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO877^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:58 AM UTC 2026
% Result : Theorem 2.78s 1.80s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 39 unt; 0 typ; 2 def)
% Number of atoms : 244 ( 72 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 4748 ( 15 ~; 10 |; 0 &;4559 @)
% ( 2 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 166 ( 166 >; 0 *; 0 +; 0 <<)
% Number of symbols : 129 ( 125 usr; 7 con; 0-14 aty)
% ( 89 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 220 ( 113 ^; 105 !; 2 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
c_Eps_i: ( $i > $o ) > $i ).
thf(func_def_3,type,
c_not: $o > $o ).
thf(func_def_4,type,
c_and: $o > $o > $o ).
thf(func_def_5,type,
c_or: $o > $o > $o ).
thf(func_def_6,type,
c_iff: $o > $o > $o ).
thf(func_def_7,type,
c_In: $i > $i > $o ).
thf(func_def_8,type,
c_Subq: $i > $i > $o ).
thf(func_def_10,type,
c_Union: $i > $i ).
thf(func_def_11,type,
c_Power: $i > $i ).
thf(func_def_12,type,
c_Repl: $i > ( $i > $i ) > $i ).
thf(func_def_13,type,
c_TransSet: $i > $o ).
thf(func_def_14,type,
c_atleast2: $i > $o ).
thf(func_def_15,type,
c_atleast3: $i > $o ).
thf(func_def_16,type,
c_atleast4: $i > $o ).
thf(func_def_17,type,
c_atleast5: $i > $o ).
thf(func_def_18,type,
c_atleast6: $i > $o ).
thf(func_def_19,type,
c_exactly2: $i > $o ).
thf(func_def_20,type,
c_exactly3: $i > $o ).
thf(func_def_21,type,
c_exactly4: $i > $o ).
thf(func_def_22,type,
c_exactly5: $i > $o ).
thf(func_def_23,type,
c_exu_i: ( $i > $o ) > $o ).
thf(func_def_24,type,
c_reflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
c_irreflexive_i: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
c_symmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
c_antisymmetric_i: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
c_transitive_i: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
c_eqreln_i: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
c_per_i: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
c_linear_i: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
c_partialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_34,type,
c_totalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
thf(func_def_37,type,
c_If_i: $o > $i > $i > $i ).
thf(func_def_38,type,
c_exactly1of2: $o > $o > $o ).
thf(func_def_39,type,
c_exactly1of3: $o > $o > $o > $o ).
thf(func_def_40,type,
c_nIn: $i > $i > $o ).
thf(func_def_41,type,
c_nSubq: $i > $i > $o ).
thf(func_def_42,type,
c_UPair: $i > $i > $i ).
thf(func_def_43,type,
c_Sing: $i > $i ).
thf(func_def_44,type,
c_binunion: $i > $i > $i ).
thf(func_def_45,type,
c_SetAdjoin: $i > $i > $i ).
thf(func_def_46,type,
c_famunion: $i > ( $i > $i ) > $i ).
thf(func_def_47,type,
c_Sep: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_49,type,
c_binintersect: $i > $i > $i ).
thf(func_def_50,type,
c_setminus: $i > $i > $i ).
thf(func_def_51,type,
c_inj: $i > $i > ( $i > $i ) > $o ).
thf(func_def_52,type,
c_bij: $i > $i > ( $i > $i ) > $o ).
thf(func_def_53,type,
c_atleastp: $i > $i > $o ).
thf(func_def_54,type,
c_equip: $i > $i > $o ).
thf(func_def_55,type,
c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
thf(func_def_56,type,
c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
thf(func_def_57,type,
c_ordsucc: $i > $i ).
thf(func_def_58,type,
c_nat_p: $i > $o ).
thf(func_def_59,type,
c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
thf(func_def_60,type,
c_add_nat: $i > $i > $i ).
thf(func_def_61,type,
c_mul_nat: $i > $i > $i ).
thf(func_def_62,type,
c_ordinal: $i > $o ).
thf(func_def_63,type,
c_V_: $i > $i ).
thf(func_def_64,type,
c_Inj1: $i > $i ).
thf(func_def_65,type,
c_Inj0: $i > $i ).
thf(func_def_66,type,
c_Unj: $i > $i ).
thf(func_def_67,type,
c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_68,type,
c_setsum: $i > $i > $i ).
thf(func_def_69,type,
c_proj0: $i > $i ).
thf(func_def_70,type,
c_proj1: $i > $i ).
thf(func_def_71,type,
c_binrep: $i > $i > $i ).
thf(func_def_72,type,
c_lam: $i > ( $i > $i ) > $i ).
thf(func_def_73,type,
c_setprod: $i > $i > $i ).
thf(func_def_74,type,
c_ap: $i > $i > $i ).
thf(func_def_75,type,
c_setsum_p: $i > $o ).
thf(func_def_76,type,
c_tuple_p: $i > $i > $o ).
thf(func_def_77,type,
c_Pi: $i > ( $i > $i ) > $i ).
thf(func_def_78,type,
c_setexp: $i > $i > $i ).
thf(func_def_79,type,
c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
c_set_of_pairs: $i > $o ).
thf(func_def_81,type,
c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_82,type,
c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_83,type,
c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_84,type,
c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_85,type,
c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_86,type,
c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_87,type,
c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
thf(func_def_88,type,
c_SNoElts_: $i > $i ).
thf(func_def_89,type,
c_SNo_: $i > $i > $o ).
thf(func_def_90,type,
c_PSNo: $i > ( $i > $o ) > $i ).
thf(func_def_91,type,
c_SNo: $i > $o ).
thf(func_def_92,type,
c_SNoLev: $i > $i ).
thf(func_def_93,type,
c_SNoEq_: $i > $i > $i > $o ).
thf(func_def_94,type,
c_SNoLt: $i > $i > $o ).
thf(func_def_95,type,
c_SNoLe: $i > $i > $o ).
thf(func_def_96,type,
c_binop_on: $i > ( $i > $i > $i ) > $o ).
thf(func_def_97,type,
c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
thf(func_def_98,type,
c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_99,type,
c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_100,type,
c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
thf(func_def_101,type,
c_combinator: $i > $o ).
thf(func_def_102,type,
c_combinator_equiv: $i > $i > $o ).
thf(func_def_103,type,
c_equip_mod: $i > $i > $i > $o ).
thf(func_def_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 ).
thf(func_def_135,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_136,type,
sK5: ( $i > $o ) > $i > $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_142,type,
sK11: $i > $i > $i ).
thf(func_def_143,type,
sK12: $i > $i > $i ).
thf(func_def_144,type,
sK13: $i > $i > $i ).
thf(func_def_145,type,
sK14: $i > $i > $i ).
thf(func_def_146,type,
sK15: $i > $i > $i > $o ).
thf(func_def_147,type,
sK16: $o > $o > $o ).
thf(func_def_148,type,
sK17: $o > $o > $o ).
thf(func_def_149,type,
sK18: $i > $i > $i ).
thf(func_def_150,type,
sK19: ( $i > $i ) > $i > $i > $i ).
thf(func_def_151,type,
sK20: ( $i > $i ) > $i > $i > $i > $o ).
thf(func_def_154,type,
ph22:
!>[X0: $tType] : X0 ).
thf(f848,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f764,f791,f845]) ).
thf(f845,plain,
~ spl9_18,
inference(avatar_contradiction_clause,[status(thm)],[f844]) ).
thf(f844,plain,
( $false
| ~ spl9_18 ),
inference(trivial_inequality_removal,[status(thm)],[f826]) ).
thf(f826,plain,
( ( $false = $true )
| ~ spl9_18 ),
inference(superposition,[status(thm)],[f763,f554]) ).
thf(f554,plain,
$false = sK10,
inference(beta_eta_normalization,[status(thm)],[f553]) ).
thf(f553,plain,
( $false
= ( ^ [Y0: $o] : Y0
@ sK10 ) ),
inference(sigma_clausification,[status(thm)],[f531]) ).
thf(f531,plain,
( ( !! @ $o
@ ^ [Y0: $o] : Y0 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f530]) ).
thf(f530,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( !! @ $o
@ ^ [Y6: $o] :
( ( ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y2 ) @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y4 @ Y3 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y1 ) @ Y3 ) ) @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) @ Y1 ) @ ( Y4 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ ( Y5 @ Y2 @ Y3 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y4 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y3 @ Y2 ) @ Y3 ) ) @ Y1 ) ) @ Y3 ) @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y3 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y4 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y3 ) ) ) @ ( Y4 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y4 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y3 ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y3 ) ) ) ) @ Y3 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y4 @ Y1 ) ) @ Y1 ) ) ) @ Y3 ) @ Y1 ) )
= Y1 )
=> ( ( Y0 @ ( Y4 @ Y2 ) )
=> Y6 ) )
=> Y6 ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f524]) ).
thf(f524,plain,
( ( ^ [Y0: $o] :
( Y0
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( ^ [Y6: $o,Y7: $o] :
( !! @ $o
@ ^ [Y8: $o] :
( ( Y6
=> ( Y7
=> Y8 ) )
=> Y8 ) )
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y2 ) @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y4 @ Y3 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y1 ) @ Y3 ) ) @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) @ Y1 ) @ ( Y4 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ ( Y5 @ Y2 @ Y3 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y4 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y3 @ Y2 ) @ Y3 ) ) @ Y1 ) ) @ Y3 ) @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y3 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y4 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y3 ) ) ) @ ( Y4 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y4 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y3 ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y3 ) ) ) ) @ Y3 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y4 @ Y1 ) ) @ Y1 ) ) ) @ Y3 ) @ Y1 ) )
= Y1 )
@ ( Y0 @ ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f403,f435,f382]) ).
thf(f382,plain,
( c_and
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> ( Y1
=> Y2 ) )
=> Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
thf(f228,plain,
( c_and
= ( ^ [Y0: $o,Y1: $o] :
( !! @ $o
@ ^ [Y2: $o] :
( ( Y0
=> ( Y1
=> Y2 ) )
=> Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f227]) ).
thf(f227,plain,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> ( X1
=> X2 ) )
=> X2 ) )
= c_and ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o] :
( ( X0
=> ( X1
=> X2 ) )
=> X2 ) )
= c_and ),
file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',ax14) ).
thf(f435,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f375,f409]) ).
thf(f409,plain,
( c_False
= ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
thf(f246,plain,
( c_False
= ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ),
inference(fool_elimination,[status(thm)],[f245]) ).
thf(f245,plain,
( c_False
= ( ! [X0: $o] : X0 ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( c_False
= ( ! [X0: $o] : X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',ax11) ).
thf(f375,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
thf(f193,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(fool_elimination,[status(thm)],[f192]) ).
thf(f192,plain,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( c_not
= ( ^ [X0: $o] :
( X0
=> c_False ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',ax13) ).
thf(f403,plain,
( $true
!= ( c_not
@ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( c_and
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y2 ) @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y4 @ Y3 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y1 ) @ Y3 ) ) @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) @ Y1 ) @ ( Y4 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ ( Y5 @ Y2 @ Y3 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y4 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y3 @ Y2 ) @ Y3 ) ) @ Y1 ) ) @ Y3 ) @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y3 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y4 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y3 ) ) ) @ ( Y4 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y4 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y3 ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y3 ) ) ) ) @ Y3 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y4 @ Y1 ) ) @ Y1 ) ) ) @ Y3 ) @ Y1 ) )
= Y1 )
@ ( Y0 @ ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f288]) ).
thf(f288,plain,
( $true
!= ( c_not
@ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( c_and
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y2 ) @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y4 @ Y3 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y1 ) @ Y3 ) ) @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) @ Y1 ) @ ( Y4 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ ( Y5 @ Y2 @ Y3 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y4 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y3 @ Y2 ) @ Y3 ) ) @ Y1 ) ) @ Y3 ) @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y3 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y4 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y3 ) ) ) @ ( Y4 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y4 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y3 ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y3 ) ) ) ) @ Y3 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y4 @ Y1 ) ) @ Y1 ) ) ) @ Y3 ) @ Y1 ) )
= Y1 )
@ ( Y0 @ ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f206]) ).
thf(f206,plain,
( $true
!= ( c_not
@ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( c_and
@ ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y2 ) @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y4 @ Y3 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y1 ) @ Y3 ) ) @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) @ Y1 ) @ ( Y4 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ ( Y5 @ Y2 @ Y3 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y4 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y3 @ Y2 ) @ Y3 ) ) @ Y1 ) ) @ Y3 ) @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y3 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y4 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y3 ) ) ) @ ( Y4 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y4 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y3 ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y3 ) ) ) ) @ Y3 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y4 @ Y1 ) ) @ Y1 ) ) ) @ Y3 ) @ Y1 ) )
= Y1 )
@ ( Y0 @ ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f205]) ).
thf(f205,plain,
~ ( c_not
@ ! [X0: $i > $i > $i,X2: $i > $i,X4: $i,X5: $i,X6: $i,X7: $i > $o] :
( c_and
@ ( ( X0 @ ( X0 @ X5 @ ( X0 @ X4 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X6 @ ( X0 @ ( X0 @ X5 @ ( X0 @ X5 @ ( X0 @ ( X0 @ X5 @ ( X0 @ ( X2 @ X5 ) @ ( X0 @ ( X0 @ X4 @ ( X0 @ X6 @ ( X0 @ X6 @ X6 ) ) ) @ X5 ) ) ) @ ( X0 @ ( X2 @ ( X0 @ ( X0 @ ( X2 @ X4 ) @ X5 ) @ ( X0 @ X5 @ X5 ) ) ) @ ( X0 @ X6 @ ( X0 @ X6 @ ( X0 @ ( X0 @ ( X0 @ X5 @ ( X0 @ ( X0 @ X5 @ ( X0 @ ( X2 @ X6 ) @ X4 ) ) @ ( X2 @ ( X0 @ X4 @ X5 ) ) ) ) @ X6 ) @ ( X2 @ ( X0 @ ( X0 @ X4 @ ( X0 @ X5 @ ( X0 @ ( X2 @ ( X0 @ X5 @ X4 ) ) @ X5 ) ) ) @ ( X0 @ ( X0 @ ( X0 @ X6 @ ( X0 @ ( X2 @ X5 ) @ X6 ) ) @ X6 ) @ ( X2 @ ( X2 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X5 @ ( X0 @ ( X0 @ X6 @ ( X0 @ ( X0 @ X4 @ X5 ) @ X4 ) ) @ X6 ) ) @ X4 ) @ ( X0 @ X4 @ ( X0 @ X5 @ X5 ) ) ) @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X6 @ ( X0 @ X5 @ X5 ) ) @ ( X2 @ ( X2 @ ( X0 @ X4 @ ( X2 @ ( X2 @ ( X0 @ X4 @ X5 ) ) ) ) ) ) ) @ X5 ) @ X6 ) @ ( X0 @ X6 @ X4 ) ) ) ) @ X5 ) @ X5 ) @ ( X2 @ X6 ) ) ) ) @ ( X0 @ ( X0 @ ( X2 @ ( X0 @ ( X2 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X4 @ ( X0 @ ( X2 @ ( X2 @ ( X0 @ ( X0 @ X5 @ X6 ) @ X4 ) ) ) @ ( X2 @ ( X0 @ X5 @ X5 ) ) ) ) @ X5 ) @ ( X2 @ X5 ) ) @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X5 @ X4 ) @ ( X2 @ ( X2 @ ( X2 @ X4 ) ) ) ) @ X4 ) @ X6 ) @ X5 ) ) ) @ ( X0 @ ( X0 @ ( X0 @ X6 @ X5 ) @ ( X2 @ X6 ) ) @ X6 ) ) ) @ X4 ) @ X6 ) )
= X6 )
@ ( X7 @ ( X2 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,negated_conjecture,
~ ( c_not
@ ! [X1: $i > $i > $i,X0: $i > $i > $o,X4: $i > $i,X2: $i > $o,X7: $i,X5: $i,X6: $i,X3: $i > $o] :
( c_and
@ ( ( 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 ) )
= X6 )
@ ? [X8: $i] : ( X3 @ ( X4 @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
thf(f109,conjecture,
( c_not
@ ! [X1: $i > $i > $i,X0: $i > $i > $o,X4: $i > $i,X2: $i > $o,X7: $i,X5: $i,X6: $i,X3: $i > $o] :
( c_and
@ ( ( 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 ) )
= X6 )
@ ? [X8: $i] : ( X3 @ ( X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',conj) ).
thf(f763,plain,
( ! [X3: $i,X1: $i > $o,X5: $i > $i] :
( ( X1 @ ( X5 @ X3 ) )
= $true )
| ~ spl9_18 ),
inference(avatar_component_clause,[status(thm)],[f762]) ).
thf(f762,definition,
( spl9_18
<=> ! [X5: $i > $i,X1: $i > $o,X3: $i] :
( ( X1 @ ( X5 @ X3 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_18])],[avatar_definition]) ).
thf(f791,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[status(thm)],[f790]) ).
thf(f790,plain,
( $false
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f786]) ).
thf(f786,plain,
( ( $false = $true )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f554,f695]) ).
thf(f695,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f694]) ).
thf(f694,definition,
( spl9_2
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f764,plain,
( spl9_18
| spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f552,f694,f762]) ).
thf(f552,plain,
! [X3: $i,X1: $i > $o,X7: $o,X5: $i > $i] :
( ( ( X1 @ ( X5 @ X3 ) )
= $true )
| ( $true = X7 ) ),
inference(binary_proxy_clausification,[status(thm)],[f548]) ).
thf(f548,plain,
! [X3: $i,X1: $i > $o,X7: $o,X5: $i > $i] :
( ( $false
= ( ( X1 @ ( X5 @ X3 ) )
=> X7 ) )
| ( $true = X7 ) ),
inference(binary_proxy_clausification,[status(thm)],[f547]) ).
thf(f547,plain,
! [X2: $i,X3: $i,X1: $i > $o,X6: $i > $i > $i,X7: $o,X4: $i,X5: $i > $i] :
( ( $true = X7 )
| ( ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X3 ) @ ( X6 @ ( X6 @ X4 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X5 @ X4 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X2 ) @ X4 ) ) @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( X5 @ ( X6 @ ( X6 @ X4 @ ( X6 @ X3 @ ( X6 @ ( X5 @ ( X6 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X5 @ X3 ) @ X2 ) ) @ X2 ) @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( X6 @ X4 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X5 @ ( X5 @ ( X6 @ X4 @ ( X5 @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( X5 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X5 @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X4 @ ( X6 @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X4 ) ) ) @ ( X5 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X5 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X4 ) @ ( X5 @ ( X5 @ ( X5 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X5 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( X5 @ X3 ) )
=> X7 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f546]) ).
thf(f546,plain,
! [X2: $i,X3: $i,X1: $i > $o,X6: $i > $i > $i,X7: $o,X4: $i,X5: $i > $i] :
( $true
= ( ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X3 ) @ ( X6 @ ( X6 @ X4 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X5 @ X4 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X2 ) @ X4 ) ) @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( X5 @ ( X6 @ ( X6 @ X4 @ ( X6 @ X3 @ ( X6 @ ( X5 @ ( X6 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X5 @ X3 ) @ X2 ) ) @ X2 ) @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( X6 @ X4 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X5 @ ( X5 @ ( X6 @ X4 @ ( X5 @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( X5 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X5 @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X4 @ ( X6 @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X4 ) ) ) @ ( X5 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X5 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X4 ) @ ( X5 @ ( X5 @ ( X5 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X5 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( X5 @ X3 ) )
=> X7 ) )
=> X7 ) ),
inference(beta_eta_normalization,[status(thm)],[f545]) ).
thf(f545,plain,
! [X2: $i,X3: $i,X1: $i > $o,X6: $i > $i > $i,X7: $o,X4: $i,X5: $i > $i] :
( $true
= ( ^ [Y0: $o] :
( ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X3 ) @ ( X6 @ ( X6 @ X4 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X5 @ X4 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X2 ) @ X4 ) ) @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( X5 @ ( X6 @ ( X6 @ X4 @ ( X6 @ X3 @ ( X6 @ ( X5 @ ( X6 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X5 @ X3 ) @ X2 ) ) @ X2 ) @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( X6 @ X4 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X5 @ ( X5 @ ( X6 @ X4 @ ( X5 @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( X5 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X5 @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X4 @ ( X6 @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X4 ) ) ) @ ( X5 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X5 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X4 ) @ ( X5 @ ( X5 @ ( X5 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X5 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( X5 @ X3 ) )
=> Y0 ) )
=> Y0 )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f544]) ).
thf(f544,plain,
! [X2: $i,X3: $i,X1: $i > $o,X6: $i > $i > $i,X4: $i,X5: $i > $i] :
( ( !! @ $o
@ ^ [Y0: $o] :
( ( ( ( X6 @ ( X6 @ X3 @ ( X6 @ X4 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X3 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X3 ) @ ( X6 @ ( X6 @ X4 @ ( X6 @ X2 @ ( X6 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X5 @ X4 ) @ X3 ) @ ( X6 @ X3 @ X3 ) ) ) @ ( X6 @ X2 @ ( X6 @ X2 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X5 @ X2 ) @ X4 ) ) @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( X5 @ ( X6 @ ( X6 @ X4 @ ( X6 @ X3 @ ( X6 @ ( X5 @ ( X6 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X5 @ X3 ) @ X2 ) ) @ X2 ) @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ ( X6 @ ( X6 @ X2 @ ( X6 @ ( X6 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( X6 @ X4 @ ( X6 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X2 @ ( X6 @ X3 @ X3 ) ) @ ( X5 @ ( X5 @ ( X6 @ X4 @ ( X5 @ ( X5 @ ( X6 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( X6 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( X5 @ X2 ) ) ) ) @ ( X6 @ ( X6 @ ( X5 @ ( X6 @ ( X5 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X4 @ ( X6 @ ( X5 @ ( X5 @ ( X6 @ ( X6 @ X3 @ X2 ) @ X4 ) ) ) @ ( X5 @ ( X6 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X5 @ X3 ) ) @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ ( X6 @ X3 @ X4 ) @ ( X5 @ ( X5 @ ( X5 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( X6 @ ( X6 @ ( X6 @ X2 @ X3 ) @ ( X5 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( X5 @ X3 ) )
=> Y0 ) )
=> Y0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f543]) ).
thf(f543,plain,
! [X2: $i,X3: $i,X1: $i > $o,X6: $i > $i > $i,X4: $i,X5: $i > $i] :
( ( ^ [Y0: $i > $i > $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( ( ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X4 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X5 @ X3 ) @ ( Y0 @ ( Y0 @ X4 @ ( Y0 @ X2 @ ( Y0 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y0 @ ( X5 @ ( Y0 @ ( Y0 @ ( X5 @ X4 ) @ X3 ) @ ( Y0 @ X3 @ X3 ) ) ) @ ( Y0 @ X2 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X5 @ X2 ) @ X4 ) ) @ ( X5 @ ( Y0 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( X5 @ ( Y0 @ ( Y0 @ X4 @ ( Y0 @ X3 @ ( Y0 @ ( X5 @ ( Y0 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( X5 @ X3 ) @ X2 ) ) @ X2 ) @ ( X5 @ ( X5 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( Y0 @ X4 @ ( Y0 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ X3 @ X3 ) ) @ ( X5 @ ( X5 @ ( Y0 @ X4 @ ( X5 @ ( X5 @ ( Y0 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y0 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( X5 @ X2 ) ) ) ) @ ( Y0 @ ( Y0 @ ( X5 @ ( Y0 @ ( X5 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X4 @ ( Y0 @ ( X5 @ ( X5 @ ( Y0 @ ( Y0 @ X3 @ X2 ) @ X4 ) ) ) @ ( X5 @ ( Y0 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X5 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ X4 ) @ ( X5 @ ( X5 @ ( X5 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ X3 ) @ ( X5 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( X5 @ X3 ) )
=> Y1 ) )
=> Y1 ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f542]) ).
thf(f542,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i > $i] :
( ( !! @ ( $i > $i > $i )
@ ^ [Y0: $i > $i > $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( ( ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X4 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X5 @ X3 ) @ ( Y0 @ ( Y0 @ X4 @ ( Y0 @ X2 @ ( Y0 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y0 @ ( X5 @ ( Y0 @ ( Y0 @ ( X5 @ X4 ) @ X3 ) @ ( Y0 @ X3 @ X3 ) ) ) @ ( Y0 @ X2 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( X5 @ X2 ) @ X4 ) ) @ ( X5 @ ( Y0 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( X5 @ ( Y0 @ ( Y0 @ X4 @ ( Y0 @ X3 @ ( Y0 @ ( X5 @ ( Y0 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( X5 @ X3 ) @ X2 ) ) @ X2 ) @ ( X5 @ ( X5 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ ( Y0 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( Y0 @ X4 @ ( Y0 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ ( Y0 @ X3 @ X3 ) ) @ ( X5 @ ( X5 @ ( Y0 @ X4 @ ( X5 @ ( X5 @ ( Y0 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y0 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( X5 @ X2 ) ) ) ) @ ( Y0 @ ( Y0 @ ( X5 @ ( Y0 @ ( X5 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X4 @ ( Y0 @ ( X5 @ ( X5 @ ( Y0 @ ( Y0 @ X3 @ X2 ) @ X4 ) ) ) @ ( X5 @ ( Y0 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( X5 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ X3 @ X4 ) @ ( X5 @ ( X5 @ ( X5 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( Y0 @ ( Y0 @ ( Y0 @ X2 @ X3 ) @ ( X5 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( X5 @ X3 ) )
=> Y1 ) )
=> Y1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f541]) ).
thf(f541,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i,X5: $i > $i] :
( ( ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( ( ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X4 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y0 @ X3 ) @ ( Y1 @ ( Y1 @ X4 @ ( Y1 @ X2 @ ( Y1 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y1 @ ( Y0 @ ( Y1 @ ( Y1 @ ( Y0 @ X4 ) @ X3 ) @ ( Y1 @ X3 @ X3 ) ) ) @ ( Y1 @ X2 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y0 @ X2 ) @ X4 ) ) @ ( Y0 @ ( Y1 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( Y0 @ ( Y1 @ ( Y1 @ X4 @ ( Y1 @ X3 @ ( Y1 @ ( Y0 @ ( Y1 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y0 @ X3 ) @ X2 ) ) @ X2 ) @ ( Y0 @ ( Y0 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( Y1 @ X4 @ ( Y1 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ X3 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y1 @ X4 @ ( Y0 @ ( Y0 @ ( Y1 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y1 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( Y0 @ X2 ) ) ) ) @ ( Y1 @ ( Y1 @ ( Y0 @ ( Y1 @ ( Y0 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X4 @ ( Y1 @ ( Y0 @ ( Y0 @ ( Y1 @ ( Y1 @ X3 @ X2 ) @ X4 ) ) ) @ ( Y0 @ ( Y1 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( Y0 @ X3 ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ X4 ) @ ( Y0 @ ( Y0 @ ( Y0 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ X3 ) @ ( Y0 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( Y0 @ X3 ) )
=> Y2 ) )
=> Y2 ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f540]) ).
thf(f540,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y1: $i > $i > $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( ( ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X4 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y0 @ X3 ) @ ( Y1 @ ( Y1 @ X4 @ ( Y1 @ X2 @ ( Y1 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y1 @ ( Y0 @ ( Y1 @ ( Y1 @ ( Y0 @ X4 ) @ X3 ) @ ( Y1 @ X3 @ X3 ) ) ) @ ( Y1 @ X2 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y0 @ X2 ) @ X4 ) ) @ ( Y0 @ ( Y1 @ X4 @ X3 ) ) ) ) @ X2 ) @ ( Y0 @ ( Y1 @ ( Y1 @ X4 @ ( Y1 @ X3 @ ( Y1 @ ( Y0 @ ( Y1 @ X3 @ X4 ) ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y0 @ X3 ) @ X2 ) ) @ X2 ) @ ( Y0 @ ( Y0 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ ( Y1 @ X4 @ X3 ) @ X4 ) ) @ X2 ) ) @ X4 ) @ ( Y1 @ X4 @ ( Y1 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ ( Y1 @ X3 @ X3 ) ) @ ( Y0 @ ( Y0 @ ( Y1 @ X4 @ ( Y0 @ ( Y0 @ ( Y1 @ X4 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y1 @ X2 @ X4 ) ) ) ) @ X3 ) @ X3 ) @ ( Y0 @ X2 ) ) ) ) @ ( Y1 @ ( Y1 @ ( Y0 @ ( Y1 @ ( Y0 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X4 @ ( Y1 @ ( Y0 @ ( Y0 @ ( Y1 @ ( Y1 @ X3 @ X2 ) @ X4 ) ) ) @ ( Y0 @ ( Y1 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( Y0 @ X3 ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ X3 @ X4 ) @ ( Y0 @ ( Y0 @ ( Y0 @ X4 ) ) ) ) @ X4 ) @ X2 ) @ X3 ) ) ) @ ( Y1 @ ( Y1 @ ( Y1 @ X2 @ X3 ) @ ( Y0 @ X2 ) ) @ X2 ) ) ) @ X4 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( Y0 @ X3 ) )
=> Y2 ) )
=> Y2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f539]) ).
thf(f539,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( ( ( Y2 @ ( Y2 @ X3 @ ( Y2 @ Y0 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y1 @ X3 ) @ ( Y2 @ ( Y2 @ Y0 @ ( Y2 @ X2 @ ( Y2 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y2 @ ( Y1 @ ( Y2 @ ( Y2 @ ( Y1 @ Y0 ) @ X3 ) @ ( Y2 @ X3 @ X3 ) ) ) @ ( Y2 @ X2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y1 @ X2 ) @ Y0 ) ) @ ( Y1 @ ( Y2 @ Y0 @ X3 ) ) ) ) @ X2 ) @ ( Y1 @ ( Y2 @ ( Y2 @ Y0 @ ( Y2 @ X3 @ ( Y2 @ ( Y1 @ ( Y2 @ X3 @ Y0 ) ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y1 @ X3 ) @ X2 ) ) @ X2 ) @ ( Y1 @ ( Y1 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ Y0 @ X3 ) @ Y0 ) ) @ X2 ) ) @ Y0 ) @ ( Y2 @ Y0 @ ( Y2 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ X3 @ X3 ) ) @ ( Y1 @ ( Y1 @ ( Y2 @ Y0 @ ( Y1 @ ( Y1 @ ( Y2 @ Y0 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y2 @ X2 @ Y0 ) ) ) ) @ X3 ) @ X3 ) @ ( Y1 @ X2 ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y1 @ ( Y2 @ ( Y1 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ Y0 @ ( Y2 @ ( Y1 @ ( Y1 @ ( Y2 @ ( Y2 @ X3 @ X2 ) @ Y0 ) ) ) @ ( Y1 @ ( Y2 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( Y1 @ X3 ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ Y0 ) @ ( Y1 @ ( Y1 @ ( Y1 @ Y0 ) ) ) ) @ Y0 ) @ X2 ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ X3 ) @ ( Y1 @ X2 ) ) @ X2 ) ) ) @ Y0 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( Y1 @ X3 ) )
=> Y3 ) )
=> Y3 ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f538]) ).
thf(f538,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y2: $i > $i > $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( ( ( Y2 @ ( Y2 @ X3 @ ( Y2 @ Y0 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y1 @ X3 ) @ ( Y2 @ ( Y2 @ Y0 @ ( Y2 @ X2 @ ( Y2 @ X2 @ X2 ) ) ) @ X3 ) ) ) @ ( Y2 @ ( Y1 @ ( Y2 @ ( Y2 @ ( Y1 @ Y0 ) @ X3 ) @ ( Y2 @ X3 @ X3 ) ) ) @ ( Y2 @ X2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y1 @ X2 ) @ Y0 ) ) @ ( Y1 @ ( Y2 @ Y0 @ X3 ) ) ) ) @ X2 ) @ ( Y1 @ ( Y2 @ ( Y2 @ Y0 @ ( Y2 @ X3 @ ( Y2 @ ( Y1 @ ( Y2 @ X3 @ Y0 ) ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y1 @ X3 ) @ X2 ) ) @ X2 ) @ ( Y1 @ ( Y1 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ ( Y2 @ Y0 @ X3 ) @ Y0 ) ) @ X2 ) ) @ Y0 ) @ ( Y2 @ Y0 @ ( Y2 @ X3 @ X3 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ ( Y2 @ X3 @ X3 ) ) @ ( Y1 @ ( Y1 @ ( Y2 @ Y0 @ ( Y1 @ ( Y1 @ ( Y2 @ Y0 @ X3 ) ) ) ) ) ) ) @ X3 ) @ X2 ) @ ( Y2 @ X2 @ Y0 ) ) ) ) @ X3 ) @ X3 ) @ ( Y1 @ X2 ) ) ) ) @ ( Y2 @ ( Y2 @ ( Y1 @ ( Y2 @ ( Y1 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ Y0 @ ( Y2 @ ( Y1 @ ( Y1 @ ( Y2 @ ( Y2 @ X3 @ X2 ) @ Y0 ) ) ) @ ( Y1 @ ( Y2 @ X3 @ X3 ) ) ) ) @ X3 ) @ ( Y1 @ X3 ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ X3 @ Y0 ) @ ( Y1 @ ( Y1 @ ( Y1 @ Y0 ) ) ) ) @ Y0 ) @ X2 ) @ X3 ) ) ) @ ( Y2 @ ( Y2 @ ( Y2 @ X2 @ X3 ) @ ( Y1 @ X2 ) ) @ X2 ) ) ) @ Y0 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( Y1 @ X3 ) )
=> Y3 ) )
=> Y3 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f537]) ).
thf(f537,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y3: $i > $i > $i] :
( !! @ $o
@ ^ [Y4: $o] :
( ( ( ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ Y1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ Y1 @ ( Y3 @ X2 @ ( Y3 @ X2 @ X2 ) ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y2 @ ( Y3 @ ( Y3 @ ( Y2 @ Y1 ) @ Y0 ) @ ( Y3 @ Y0 @ Y0 ) ) ) @ ( Y3 @ X2 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y2 @ X2 ) @ Y1 ) ) @ ( Y2 @ ( Y3 @ Y1 @ Y0 ) ) ) ) @ X2 ) @ ( Y2 @ ( Y3 @ ( Y3 @ Y1 @ ( Y3 @ Y0 @ ( Y3 @ ( Y2 @ ( Y3 @ Y0 @ Y1 ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y2 @ Y0 ) @ X2 ) ) @ X2 ) @ ( Y2 @ ( Y2 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ Y1 @ Y0 ) @ Y1 ) ) @ X2 ) ) @ Y1 ) @ ( Y3 @ Y1 @ ( Y3 @ Y0 @ Y0 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ Y0 @ Y0 ) ) @ ( Y2 @ ( Y2 @ ( Y3 @ Y1 @ ( Y2 @ ( Y2 @ ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) @ Y0 ) @ X2 ) @ ( Y3 @ X2 @ Y1 ) ) ) ) @ Y0 ) @ Y0 ) @ ( Y2 @ X2 ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y2 @ ( Y3 @ ( Y2 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y1 @ ( Y3 @ ( Y2 @ ( Y2 @ ( Y3 @ ( Y3 @ Y0 @ X2 ) @ Y1 ) ) ) @ ( Y2 @ ( Y3 @ Y0 @ Y0 ) ) ) ) @ Y0 ) @ ( Y2 @ Y0 ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ Y1 ) @ ( Y2 @ ( Y2 @ ( Y2 @ Y1 ) ) ) ) @ Y1 ) @ X2 ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ Y0 ) @ ( Y2 @ X2 ) ) @ X2 ) ) ) @ Y1 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( Y2 @ Y0 ) )
=> Y4 ) )
=> Y4 ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f536]) ).
thf(f536,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y3: $i > $i > $i] :
( !! @ $o
@ ^ [Y4: $o] :
( ( ( ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ Y1 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y2 @ Y0 ) @ ( Y3 @ ( Y3 @ Y1 @ ( Y3 @ X2 @ ( Y3 @ X2 @ X2 ) ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y2 @ ( Y3 @ ( Y3 @ ( Y2 @ Y1 ) @ Y0 ) @ ( Y3 @ Y0 @ Y0 ) ) ) @ ( Y3 @ X2 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y2 @ X2 ) @ Y1 ) ) @ ( Y2 @ ( Y3 @ Y1 @ Y0 ) ) ) ) @ X2 ) @ ( Y2 @ ( Y3 @ ( Y3 @ Y1 @ ( Y3 @ Y0 @ ( Y3 @ ( Y2 @ ( Y3 @ Y0 @ Y1 ) ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y2 @ Y0 ) @ X2 ) ) @ X2 ) @ ( Y2 @ ( Y2 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ ( Y3 @ Y1 @ Y0 ) @ Y1 ) ) @ X2 ) ) @ Y1 ) @ ( Y3 @ Y1 @ ( Y3 @ Y0 @ Y0 ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ ( Y3 @ Y0 @ Y0 ) ) @ ( Y2 @ ( Y2 @ ( Y3 @ Y1 @ ( Y2 @ ( Y2 @ ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) @ Y0 ) @ X2 ) @ ( Y3 @ X2 @ Y1 ) ) ) ) @ Y0 ) @ Y0 ) @ ( Y2 @ X2 ) ) ) ) @ ( Y3 @ ( Y3 @ ( Y2 @ ( Y3 @ ( Y2 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y1 @ ( Y3 @ ( Y2 @ ( Y2 @ ( Y3 @ ( Y3 @ Y0 @ X2 ) @ Y1 ) ) ) @ ( Y2 @ ( Y3 @ Y0 @ Y0 ) ) ) ) @ Y0 ) @ ( Y2 @ Y0 ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ ( Y3 @ Y0 @ Y1 ) @ ( Y2 @ ( Y2 @ ( Y2 @ Y1 ) ) ) ) @ Y1 ) @ X2 ) @ Y0 ) ) ) @ ( Y3 @ ( Y3 @ ( Y3 @ X2 @ Y0 ) @ ( Y2 @ X2 ) ) @ X2 ) ) ) @ Y1 ) @ X2 ) )
= X2 )
=> ( ( X1 @ ( Y2 @ Y0 ) )
=> Y4 ) )
=> Y4 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f535]) ).
thf(f535,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y4: $i > $i > $i] :
( !! @ $o
@ ^ [Y5: $o] :
( ( ( ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ Y2 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y3 @ Y1 ) @ ( Y4 @ ( Y4 @ Y2 @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ Y0 ) ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y3 @ ( Y4 @ ( Y4 @ ( Y3 @ Y2 ) @ Y1 ) @ ( Y4 @ Y1 @ Y1 ) ) ) @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y3 @ Y0 ) @ Y2 ) ) @ ( Y3 @ ( Y4 @ Y2 @ Y1 ) ) ) ) @ Y0 ) @ ( Y3 @ ( Y4 @ ( Y4 @ Y2 @ ( Y4 @ Y1 @ ( Y4 @ ( Y3 @ ( Y4 @ Y1 @ Y2 ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y3 @ Y1 ) @ Y0 ) ) @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ Y2 @ Y1 ) @ Y2 ) ) @ Y0 ) ) @ Y2 ) @ ( Y4 @ Y2 @ ( Y4 @ Y1 @ Y1 ) ) ) @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ Y1 @ Y1 ) ) @ ( Y3 @ ( Y3 @ ( Y4 @ Y2 @ ( Y3 @ ( Y3 @ ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) @ Y1 ) @ Y0 ) @ ( Y4 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ Y1 ) @ ( Y3 @ Y0 ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y3 @ ( Y4 @ ( Y3 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y2 @ ( Y4 @ ( Y3 @ ( Y3 @ ( Y4 @ ( Y4 @ Y1 @ Y0 ) @ Y2 ) ) ) @ ( Y3 @ ( Y4 @ Y1 @ Y1 ) ) ) ) @ Y1 ) @ ( Y3 @ Y1 ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ Y2 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y2 ) ) ) ) @ Y2 ) @ Y0 ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ Y1 ) @ ( Y3 @ Y0 ) ) @ Y0 ) ) ) @ Y2 ) @ Y0 ) )
= Y0 )
=> ( ( X1 @ ( Y3 @ Y1 ) )
=> Y5 ) )
=> Y5 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f534]) ).
thf(f534,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y4: $i > $i > $i] :
( !! @ $o
@ ^ [Y5: $o] :
( ( ( ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ Y2 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y3 @ Y1 ) @ ( Y4 @ ( Y4 @ Y2 @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ Y0 ) ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y3 @ ( Y4 @ ( Y4 @ ( Y3 @ Y2 ) @ Y1 ) @ ( Y4 @ Y1 @ Y1 ) ) ) @ ( Y4 @ Y0 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y3 @ Y0 ) @ Y2 ) ) @ ( Y3 @ ( Y4 @ Y2 @ Y1 ) ) ) ) @ Y0 ) @ ( Y3 @ ( Y4 @ ( Y4 @ Y2 @ ( Y4 @ Y1 @ ( Y4 @ ( Y3 @ ( Y4 @ Y1 @ Y2 ) ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y3 @ Y1 ) @ Y0 ) ) @ Y0 ) @ ( Y3 @ ( Y3 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ ( Y4 @ Y2 @ Y1 ) @ Y2 ) ) @ Y0 ) ) @ Y2 ) @ ( Y4 @ Y2 @ ( Y4 @ Y1 @ Y1 ) ) ) @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ ( Y4 @ Y1 @ Y1 ) ) @ ( Y3 @ ( Y3 @ ( Y4 @ Y2 @ ( Y3 @ ( Y3 @ ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) @ Y1 ) @ Y0 ) @ ( Y4 @ Y0 @ Y2 ) ) ) ) @ Y1 ) @ Y1 ) @ ( Y3 @ Y0 ) ) ) ) @ ( Y4 @ ( Y4 @ ( Y3 @ ( Y4 @ ( Y3 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y2 @ ( Y4 @ ( Y3 @ ( Y3 @ ( Y4 @ ( Y4 @ Y1 @ Y0 ) @ Y2 ) ) ) @ ( Y3 @ ( Y4 @ Y1 @ Y1 ) ) ) ) @ Y1 ) @ ( Y3 @ Y1 ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ ( Y4 @ Y1 @ Y2 ) @ ( Y3 @ ( Y3 @ ( Y3 @ Y2 ) ) ) ) @ Y2 ) @ Y0 ) @ Y1 ) ) ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y0 @ Y1 ) @ ( Y3 @ Y0 ) ) @ Y0 ) ) ) @ Y2 ) @ Y0 ) )
= Y0 )
=> ( ( X1 @ ( Y3 @ Y1 ) )
=> Y5 ) )
=> Y5 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f533]) ).
thf(f533,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( !! @ $o
@ ^ [Y6: $o] :
( ( ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y2 ) @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y4 @ Y3 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y1 ) @ Y3 ) ) @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) @ Y1 ) @ ( Y4 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ ( Y5 @ Y2 @ Y3 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y4 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y3 @ Y2 ) @ Y3 ) ) @ Y1 ) ) @ Y3 ) @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y3 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y4 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y3 ) ) ) @ ( Y4 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y4 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y3 ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y3 ) ) ) ) @ Y3 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y4 @ Y1 ) ) @ Y1 ) ) ) @ Y3 ) @ Y1 ) )
= Y1 )
=> ( ( Y0 @ ( Y4 @ Y2 ) )
=> Y6 ) )
=> Y6 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f532]) ).
thf(f532,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( !! @ ( $i > $i > $i )
@ ^ [Y5: $i > $i > $i] :
( !! @ $o
@ ^ [Y6: $o] :
( ( ( ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y3 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y2 ) @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ Y1 ) ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y4 @ Y3 ) @ Y2 ) @ ( Y5 @ Y2 @ Y2 ) ) ) @ ( Y5 @ Y1 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ Y1 ) @ Y3 ) ) @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) @ Y1 ) @ ( Y4 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ ( Y5 @ ( Y4 @ ( Y5 @ Y2 @ Y3 ) ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y4 @ Y2 ) @ Y1 ) ) @ Y1 ) @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ ( Y5 @ Y3 @ Y2 ) @ Y3 ) ) @ Y1 ) ) @ Y3 ) @ ( Y5 @ Y3 @ ( Y5 @ Y2 @ Y2 ) ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ ( Y5 @ Y2 @ Y2 ) ) @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ ( Y4 @ ( Y4 @ ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) @ Y2 ) @ Y1 ) @ ( Y5 @ Y1 @ Y3 ) ) ) ) @ Y2 ) @ Y2 ) @ ( Y4 @ Y1 ) ) ) ) @ ( Y5 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y4 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y3 @ ( Y5 @ ( Y4 @ ( Y4 @ ( Y5 @ ( Y5 @ Y2 @ Y1 ) @ Y3 ) ) ) @ ( Y4 @ ( Y5 @ Y2 @ Y2 ) ) ) ) @ Y2 ) @ ( Y4 @ Y2 ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ ( Y5 @ Y2 @ Y3 ) @ ( Y4 @ ( Y4 @ ( Y4 @ Y3 ) ) ) ) @ Y3 ) @ Y1 ) @ Y2 ) ) ) @ ( Y5 @ ( Y5 @ ( Y5 @ Y1 @ Y2 ) @ ( Y4 @ Y1 ) ) @ Y1 ) ) ) @ Y3 ) @ Y1 ) )
= Y1 )
=> ( ( Y0 @ ( Y4 @ Y2 ) )
=> Y6 ) )
=> Y6 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO877^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n019.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 14:49:54 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.48 ---- Original DTF file ---
% 0.18/0.48 thf(spec,logic,$$dhol).
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 % File : SYO877^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.48 % Domain : Syntactic
% 0.18/0.48 % Problem : ProofGold problem Random3_25_neg_th0
% 0.18/0.48 % Version : Especial.
% 0.18/0.48 % English :
% 0.18/0.48
% 0.18/0.48 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.18/0.48 % Source : [Urb20]
% 0.18/0.48 % Names : Random3_25_neg_th0.p [Urb20]
% 0.18/0.48
% 0.18/0.48 % Status : Theorem
% 0.18/0.48 % Rating : 0.67 v9.1.0, 0.75 v9.0.0, 0.80 v8.2.0, 0.77 v8.1.0, 0.64 v7.5.0
% 0.18/0.48 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.18/0.48 % Number of atoms : 482 ( 136 equ; 0 cnn)
% 0.18/0.48 % Maximal formula atoms : 5 ( 4 avg)
% 0.18/0.48 % Number of connectives : 1306 ( 0 ~; 0 |; 0 &;1217 @)
% 0.18/0.48 % ( 0 <=>; 89 =>; 0 <=; 0 <~>)
% 0.18/0.48 % Maximal formula depth : 15 ( 2 avg)
% 0.18/0.48 % Number of types : 2 ( 0 usr)
% 0.18/0.48 % Number of type conns : 564 ( 564 >; 0 *; 0 +; 0 <<)
% 0.18/0.48 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.18/0.48 % Number of variables : 414 ( 275 ^; 101 !; 38 ?; 414 :)
% 0.18/0.48 % SPC : TH0_THM_EQU_NAR
% 0.18/0.48
% 0.18/0.48 % Comments : See https://proofgold.org
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 thf(c_Eps_i_tp,type,
% 0.18/0.48 c_Eps_i: ( $i > $o ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_False_tp,type,
% 0.18/0.48 c_False: $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_True_tp,type,
% 0.18/0.48 c_True: $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_not_tp,type,
% 0.18/0.48 c_not: $o > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_and_tp,type,
% 0.18/0.48 c_and: $o > $o > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_or_tp,type,
% 0.18/0.48 c_or: $o > $o > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_iff_tp,type,
% 0.18/0.48 c_iff: $o > $o > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_In_tp,type,
% 0.18/0.48 c_In: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_Subq_tp,type,
% 0.18/0.48 c_Subq: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_Empty_tp,type,
% 0.18/0.48 c_Empty: $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Union_tp,type,
% 0.18/0.48 c_Union: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Power_tp,type,
% 0.18/0.48 c_Power: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Repl_tp,type,
% 0.18/0.48 c_Repl: $i > ( $i > $i ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_TransSet_tp,type,
% 0.18/0.48 c_TransSet: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_atleast2_tp,type,
% 0.18/0.48 c_atleast2: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_atleast3_tp,type,
% 0.18/0.48 c_atleast3: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_atleast4_tp,type,
% 0.18/0.48 c_atleast4: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_atleast5_tp,type,
% 0.18/0.48 c_atleast5: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_atleast6_tp,type,
% 0.18/0.48 c_atleast6: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_exactly2_tp,type,
% 0.18/0.48 c_exactly2: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_exactly3_tp,type,
% 0.18/0.48 c_exactly3: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_exactly4_tp,type,
% 0.18/0.48 c_exactly4: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_exactly5_tp,type,
% 0.18/0.48 c_exactly5: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_exu_i_tp,type,
% 0.18/0.48 c_exu_i: ( $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_reflexive_i_tp,type,
% 0.18/0.48 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_irreflexive_i_tp,type,
% 0.18/0.48 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_symmetric_i_tp,type,
% 0.18/0.48 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_antisymmetric_i_tp,type,
% 0.18/0.48 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_transitive_i_tp,type,
% 0.18/0.48 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_eqreln_i_tp,type,
% 0.18/0.48 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_per_i_tp,type,
% 0.18/0.48 c_per_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_linear_i_tp,type,
% 0.18/0.48 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_trichotomous_or_i_tp,type,
% 0.18/0.48 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_partialorder_i_tp,type,
% 0.18/0.48 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_totalorder_i_tp,type,
% 0.18/0.48 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_strictpartialorder_i_tp,type,
% 0.18/0.48 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_stricttotalorder_i_tp,type,
% 0.18/0.48 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_If_i_tp,type,
% 0.18/0.48 c_If_i: $o > $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_exactly1of2_tp,type,
% 0.18/0.48 c_exactly1of2: $o > $o > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_exactly1of3_tp,type,
% 0.18/0.48 c_exactly1of3: $o > $o > $o > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_nIn_tp,type,
% 0.18/0.48 c_nIn: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_nSubq_tp,type,
% 0.18/0.48 c_nSubq: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_UPair_tp,type,
% 0.18/0.48 c_UPair: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Sing_tp,type,
% 0.18/0.48 c_Sing: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_binunion_tp,type,
% 0.18/0.48 c_binunion: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_SetAdjoin_tp,type,
% 0.18/0.48 c_SetAdjoin: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_famunion_tp,type,
% 0.18/0.48 c_famunion: $i > ( $i > $i ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Sep_tp,type,
% 0.18/0.48 c_Sep: $i > ( $i > $o ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_ReplSep_tp,type,
% 0.18/0.48 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_binintersect_tp,type,
% 0.18/0.48 c_binintersect: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_setminus_tp,type,
% 0.18/0.48 c_setminus: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_inj_tp,type,
% 0.18/0.48 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_bij_tp,type,
% 0.18/0.48 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_atleastp_tp,type,
% 0.18/0.48 c_atleastp: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_equip_tp,type,
% 0.18/0.48 c_equip: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_In_rec_poly_G_i_tp,type,
% 0.18/0.48 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_In_rec_poly_i_tp,type,
% 0.18/0.48 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_ordsucc_tp,type,
% 0.18/0.48 c_ordsucc: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_nat_p_tp,type,
% 0.18/0.48 c_nat_p: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_nat_primrec_tp,type,
% 0.18/0.48 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_add_nat_tp,type,
% 0.18/0.48 c_add_nat: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_mul_nat_tp,type,
% 0.18/0.48 c_mul_nat: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_ordinal_tp,type,
% 0.18/0.48 c_ordinal: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_V__tp,type,
% 0.18/0.48 c_V_: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Inj1_tp,type,
% 0.18/0.48 c_Inj1: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Inj0_tp,type,
% 0.18/0.48 c_Inj0: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Unj_tp,type,
% 0.18/0.48 c_Unj: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_combine_funcs_tp,type,
% 0.18/0.48 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_setsum_tp,type,
% 0.18/0.48 c_setsum: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_proj0_tp,type,
% 0.18/0.48 c_proj0: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_proj1_tp,type,
% 0.18/0.48 c_proj1: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_binrep_tp,type,
% 0.18/0.48 c_binrep: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_lam_tp,type,
% 0.18/0.48 c_lam: $i > ( $i > $i ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_setprod_tp,type,
% 0.18/0.48 c_setprod: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_ap_tp,type,
% 0.18/0.48 c_ap: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_setsum_p_tp,type,
% 0.18/0.48 c_setsum_p: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_tuple_p_tp,type,
% 0.18/0.48 c_tuple_p: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_Pi_tp,type,
% 0.18/0.48 c_Pi: $i > ( $i > $i ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_setexp_tp,type,
% 0.18/0.48 c_setexp: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_Sep2_tp,type,
% 0.18/0.48 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_set_of_pairs_tp,type,
% 0.18/0.48 c_set_of_pairs: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_lam2_tp,type,
% 0.18/0.48 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_PNoEq__tp,type,
% 0.18/0.48 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_PNoLt__tp,type,
% 0.18/0.48 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_PNoLt_tp,type,
% 0.18/0.48 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_PNoLe_tp,type,
% 0.18/0.48 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_PNo_downc_tp,type,
% 0.18/0.48 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_PNo_upc_tp,type,
% 0.18/0.48 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_SNoElts__tp,type,
% 0.18/0.48 c_SNoElts_: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_SNo__tp,type,
% 0.18/0.48 c_SNo_: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_PSNo_tp,type,
% 0.18/0.48 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_SNo_tp,type,
% 0.18/0.48 c_SNo: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_SNoLev_tp,type,
% 0.18/0.48 c_SNoLev: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(c_SNoEq__tp,type,
% 0.18/0.48 c_SNoEq_: $i > $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_SNoLt_tp,type,
% 0.18/0.48 c_SNoLt: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_SNoLe_tp,type,
% 0.18/0.48 c_SNoLe: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_binop_on_tp,type,
% 0.18/0.48 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_Loop_tp,type,
% 0.18/0.48 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_Loop_with_defs_tp,type,
% 0.18/0.48 c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_Loop_with_defs_cex1_tp,type,
% 0.18/0.48 c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_Loop_with_defs_cex2_tp,type,
% 0.18/0.48 c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_combinator_tp,type,
% 0.18/0.48 c_combinator: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_combinator_equiv_tp,type,
% 0.18/0.48 c_combinator_equiv: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(c_equip_mod_tp,type,
% 0.18/0.48 c_equip_mod: $i > $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(ax1,axiom,
% 0.18/0.48 ! [X0: $i > $o,X1: $i] :
% 0.18/0.48 ( ( X0 @ X1 )
% 0.18/0.48 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax2,axiom,
% 0.18/0.48 ! [X0: $o] :
% 0.18/0.48 ( ( c_not @ ( c_not @ X0 ) )
% 0.18/0.48 => X0 ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax3,axiom,
% 0.18/0.48 ! [X0: $o,X1: $o] :
% 0.18/0.48 ( ( c_iff @ X0 @ X1 )
% 0.18/0.48 => ( X0 = X1 ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax4,axiom,
% 0.18/0.48 ! [X0: $i,X1: $i] :
% 0.18/0.48 ( ( c_Subq @ X0 @ X1 )
% 0.18/0.48 => ( ( c_Subq @ X1 @ X0 )
% 0.18/0.48 => ( X0 = X1 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax5,axiom,
% 0.18/0.48 ( c_not
% 0.18/0.48 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax6,axiom,
% 0.18/0.48 ! [X0: $i,X1: $i] :
% 0.18/0.48 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.18/0.48 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax7,axiom,
% 0.18/0.48 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax8,axiom,
% 0.18/0.48 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.18/0.48 ( c_iff
% 0.18/0.48 @ ( c_In @ X2
% 0.18/0.48 @ ( c_Repl @ X0
% 0.18/0.48 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.18/0.48 @ ? [X3: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X3 @ X0 )
% 0.18/0.48 @ ( X2
% 0.18/0.48 = ( X1 @ X3 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax9,axiom,
% 0.18/0.48 ! [X0: $i > $o] :
% 0.18/0.48 ( ! [X1: $i] :
% 0.18/0.48 ( ( X0 @ X1 )
% 0.18/0.48 => ! [X2: $i] :
% 0.18/0.48 ( ( c_In @ X2 @ X1 )
% 0.18/0.48 => ( X0 @ X2 ) ) )
% 0.18/0.48 => ( ( X0 @ c_Empty )
% 0.18/0.48 => ( ! [X1: $i] :
% 0.18/0.48 ( ( X0 @ X1 )
% 0.18/0.48 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.18/0.48 => ( ! [X1: $i] :
% 0.18/0.48 ( ( X0 @ X1 )
% 0.18/0.48 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.18/0.48 => ( ! [X1: $i] :
% 0.18/0.48 ( ( X0 @ X1 )
% 0.18/0.48 => ! [X2: $i > $i] :
% 0.18/0.48 ( ! [X3: $i] :
% 0.18/0.48 ( ( c_In @ X3 @ X1 )
% 0.18/0.48 => ( X0 @ ( X2 @ X3 ) ) )
% 0.18/0.48 => ( X0
% 0.18/0.48 @ ( c_Repl @ X1
% 0.18/0.48 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.18/0.48 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax10,axiom,
% 0.18/0.48 ! [X0: $i > $o] :
% 0.18/0.48 ( ! [X1: $i] :
% 0.18/0.48 ( ! [X2: $i] :
% 0.18/0.48 ( ( c_In @ X2 @ X1 )
% 0.18/0.48 => ( X0 @ X2 ) )
% 0.18/0.48 => ( X0 @ X1 ) )
% 0.18/0.48 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax11,axiom,
% 0.18/0.48 ( c_False
% 0.18/0.48 = ( ! [X0: $o] : X0 ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax12,axiom,
% 0.18/0.48 ( c_True
% 0.18/0.48 = ( ! [X0: $o] :
% 0.18/0.48 ( X0
% 0.18/0.48 => X0 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax13,axiom,
% 0.18/0.48 ( c_not
% 0.18/0.48 = ( ^ [X0: $o] :
% 0.18/0.48 ( X0
% 0.18/0.48 => c_False ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax14,axiom,
% 0.18/0.48 ( c_and
% 0.18/0.48 = ( ^ [X0: $o,X1: $o] :
% 0.18/0.48 ! [X2: $o] :
% 0.18/0.48 ( ( X0
% 0.18/0.48 => ( X1
% 0.18/0.48 => X2 ) )
% 0.18/0.48 => X2 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax15,axiom,
% 0.18/0.48 ( c_or
% 0.18/0.48 = ( ^ [X0: $o,X1: $o] :
% 0.18/0.48 ! [X2: $o] :
% 0.18/0.48 ( ( X0
% 0.18/0.48 => X2 )
% 0.18/0.48 => ( ( X1
% 0.18/0.48 => X2 )
% 0.18/0.48 => X2 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax16,axiom,
% 0.18/0.48 ( c_iff
% 0.18/0.48 = ( ^ [X0: $o,X1: $o] :
% 0.18/0.48 ( c_and
% 0.18/0.48 @ ( X0
% 0.18/0.48 => X1 )
% 0.18/0.48 @ ( X1
% 0.18/0.48 => X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax17,axiom,
% 0.18/0.48 ( c_Subq
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ! [X2: $i] :
% 0.18/0.48 ( ( c_In @ X2 @ X0 )
% 0.18/0.48 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax18,axiom,
% 0.18/0.48 ( c_TransSet
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ! [X1: $i] :
% 0.18/0.48 ( ( c_In @ X1 @ X0 )
% 0.18/0.48 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax19,axiom,
% 0.18/0.48 ( c_atleast2
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax20,axiom,
% 0.18/0.48 ( c_atleast3
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax21,axiom,
% 0.18/0.48 ( c_atleast4
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax22,axiom,
% 0.18/0.48 ( c_atleast5
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax23,axiom,
% 0.18/0.48 ( c_atleast6
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax24,axiom,
% 0.18/0.48 ( c_exactly2
% 0.18/0.48 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax25,axiom,
% 0.18/0.48 ( c_exactly3
% 0.18/0.48 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax26,axiom,
% 0.18/0.48 ( c_exactly4
% 0.18/0.48 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax27,axiom,
% 0.18/0.48 ( c_exactly5
% 0.18/0.48 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax28,axiom,
% 0.18/0.48 ( c_exu_i
% 0.18/0.48 = ( ^ [X0: $i > $o] :
% 0.18/0.48 ( c_and
% 0.18/0.48 @ ? [X1: $i] : ( X0 @ X1 )
% 0.18/0.48 @ ! [X1: $i,X2: $i] :
% 0.18/0.48 ( ( X0 @ X1 )
% 0.18/0.48 => ( ( X0 @ X2 )
% 0.18/0.48 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax29,axiom,
% 0.18/0.48 ( c_reflexive_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] :
% 0.18/0.48 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax30,axiom,
% 0.18/0.48 ( c_irreflexive_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] :
% 0.18/0.48 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax31,axiom,
% 0.18/0.48 ( c_symmetric_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] :
% 0.18/0.48 ! [X1: $i,X2: $i] :
% 0.18/0.48 ( ( X0 @ X1 @ X2 )
% 0.18/0.48 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax32,axiom,
% 0.18/0.48 ( c_antisymmetric_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] :
% 0.18/0.48 ! [X1: $i,X2: $i] :
% 0.18/0.48 ( ( X0 @ X1 @ X2 )
% 0.18/0.48 => ( ( X0 @ X2 @ X1 )
% 0.18/0.48 => ( X1 = X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax33,axiom,
% 0.18/0.48 ( c_transitive_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] :
% 0.18/0.48 ! [X1: $i,X2: $i,X3: $i] :
% 0.18/0.48 ( ( X0 @ X1 @ X2 )
% 0.18/0.48 => ( ( X0 @ X2 @ X3 )
% 0.18/0.48 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax34,axiom,
% 0.18/0.48 ( c_eqreln_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax35,axiom,
% 0.18/0.48 ( c_per_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax36,axiom,
% 0.18/0.48 ( c_linear_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] :
% 0.18/0.48 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax37,axiom,
% 0.18/0.48 ( c_trichotomous_or_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] :
% 0.18/0.48 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax38,axiom,
% 0.18/0.48 ( c_partialorder_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax39,axiom,
% 0.18/0.48 ( c_totalorder_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax40,axiom,
% 0.18/0.48 ( c_strictpartialorder_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax41,axiom,
% 0.18/0.48 ( c_stricttotalorder_i
% 0.18/0.48 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax42,axiom,
% 0.18/0.48 ( c_If_i
% 0.18/0.48 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.18/0.48 ( c_Eps_i
% 0.18/0.48 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax43,axiom,
% 0.18/0.48 ( c_exactly1of2
% 0.18/0.48 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax44,axiom,
% 0.18/0.48 ( c_exactly1of3
% 0.18/0.48 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax45,axiom,
% 0.18/0.48 ( c_nIn
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax46,axiom,
% 0.18/0.48 ( c_nSubq
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax47,axiom,
% 0.18/0.48 ( c_UPair
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.18/0.48 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax48,axiom,
% 0.18/0.48 ( c_Sing
% 0.18/0.48 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax49,axiom,
% 0.18/0.48 ( c_binunion
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax50,axiom,
% 0.18/0.48 ( c_SetAdjoin
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax51,axiom,
% 0.18/0.48 ( c_famunion
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i] :
% 0.18/0.48 ( c_Union
% 0.18/0.48 @ ( c_Repl @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax52,axiom,
% 0.18/0.48 ( c_Sep
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $o] :
% 0.18/0.48 ( c_If_i
% 0.18/0.48 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.18/0.48 @ ( c_Repl @ X0
% 0.18/0.48 @ ^ [X2: $i] :
% 0.18/0.48 ( ^ [X3: $i] :
% 0.18/0.48 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.18/0.48 @ ( c_Eps_i
% 0.18/0.48 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.18/0.48 @ X2 ) )
% 0.18/0.48 @ c_Empty ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax53,axiom,
% 0.18/0.48 ( c_ReplSep
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.18/0.48 ( c_Repl
% 0.18/0.48 @ ( c_Sep @ X0
% 0.18/0.48 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.18/0.48 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax54,axiom,
% 0.18/0.48 ( c_binintersect
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_Sep @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax55,axiom,
% 0.18/0.48 ( c_setminus
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_Sep @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax56,axiom,
% 0.18/0.48 ( c_inj
% 0.18/0.48 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.18/0.48 ( c_and
% 0.18/0.48 @ ! [X3: $i] :
% 0.18/0.48 ( ( c_In @ X3 @ X0 )
% 0.18/0.48 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.18/0.48 @ ! [X3: $i] :
% 0.18/0.48 ( ( c_In @ X3 @ X0 )
% 0.18/0.48 => ! [X4: $i] :
% 0.18/0.48 ( ( c_In @ X4 @ X0 )
% 0.18/0.48 => ( ( ( X2 @ X3 )
% 0.18/0.48 = ( X2 @ X4 ) )
% 0.18/0.48 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax57,axiom,
% 0.18/0.48 ( c_bij
% 0.18/0.48 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.18/0.48 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.18/0.48 @ ! [X3: $i] :
% 0.18/0.48 ( ( c_In @ X3 @ X1 )
% 0.18/0.48 => ? [X4: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X4 @ X0 )
% 0.18/0.48 @ ( ( X2 @ X4 )
% 0.18/0.48 = X3 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax58,axiom,
% 0.18/0.48 ( c_atleastp
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax59,axiom,
% 0.18/0.48 ( c_equip
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax60,axiom,
% 0.18/0.48 ( c_In_rec_poly_G_i
% 0.18/0.48 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.18/0.48 ! [X3: $i > $i > $o] :
% 0.18/0.48 ( ! [X4: $i,X5: $i > $i] :
% 0.18/0.48 ( ! [X6: $i] :
% 0.18/0.48 ( ( c_In @ X6 @ X4 )
% 0.18/0.48 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.18/0.48 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.18/0.48 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax61,axiom,
% 0.18/0.48 ( c_In_rec_poly_i
% 0.18/0.48 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.18/0.48 ( c_Eps_i
% 0.18/0.48 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax62,axiom,
% 0.18/0.48 ( c_ordsucc
% 0.18/0.48 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax63,axiom,
% 0.18/0.48 ( c_nat_p
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ! [X1: $i > $o] :
% 0.18/0.48 ( ( X1 @ c_Empty )
% 0.18/0.48 => ( ! [X2: $i] :
% 0.18/0.48 ( ( X1 @ X2 )
% 0.18/0.48 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.18/0.48 => ( X1 @ X0 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax64,axiom,
% 0.18/0.48 ( c_nat_primrec
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.18/0.48 ( c_In_rec_poly_i
% 0.18/0.48 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax65,axiom,
% 0.18/0.48 ( c_add_nat
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_nat_primrec @ X0
% 0.18/0.48 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.18/0.48 @ X1 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax66,axiom,
% 0.18/0.48 ( c_mul_nat
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_nat_primrec @ c_Empty
% 0.18/0.48 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.18/0.48 @ X1 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax67,axiom,
% 0.18/0.48 ( c_ordinal
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ( c_and @ ( c_TransSet @ X0 )
% 0.18/0.48 @ ! [X1: $i] :
% 0.18/0.48 ( ( c_In @ X1 @ X0 )
% 0.18/0.48 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax68,axiom,
% 0.18/0.48 ( c_V_
% 0.18/0.48 = ( c_In_rec_poly_i
% 0.18/0.48 @ ^ [X0: $i,X1: $i > $i] :
% 0.18/0.48 ( c_famunion @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax69,axiom,
% 0.18/0.48 ( c_Inj1
% 0.18/0.48 = ( c_In_rec_poly_i
% 0.18/0.48 @ ^ [X0: $i,X1: $i > $i] :
% 0.18/0.48 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.18/0.48 @ ( c_Repl @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax70,axiom,
% 0.18/0.48 ( c_Inj0
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ( c_Repl @ X0
% 0.18/0.48 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax71,axiom,
% 0.18/0.48 ( c_Unj
% 0.18/0.48 = ( c_In_rec_poly_i
% 0.18/0.48 @ ^ [X0: $i,X1: $i > $i] :
% 0.18/0.48 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.18/0.48 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax72,axiom,
% 0.18/0.48 ( c_combine_funcs
% 0.18/0.48 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.18/0.48 ( c_If_i
% 0.18/0.48 @ ( X4
% 0.18/0.48 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.18/0.48 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.18/0.48 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax73,axiom,
% 0.18/0.48 ( c_setsum
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_binunion
% 0.18/0.48 @ ( c_Repl @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.18/0.48 @ ( c_Repl @ X1
% 0.18/0.48 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax74,axiom,
% 0.18/0.48 ( c_proj0
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ( c_ReplSep @ X0
% 0.18/0.48 @ ^ [X1: $i] :
% 0.18/0.48 ? [X2: $i] :
% 0.18/0.48 ( ( c_Inj0 @ X2 )
% 0.18/0.48 = X1 )
% 0.18/0.48 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax75,axiom,
% 0.18/0.48 ( c_proj1
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ( c_ReplSep @ X0
% 0.18/0.48 @ ^ [X1: $i] :
% 0.18/0.48 ? [X2: $i] :
% 0.18/0.48 ( ( c_Inj1 @ X2 )
% 0.18/0.48 = X1 )
% 0.18/0.48 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax76,axiom,
% 0.18/0.48 ( c_binrep
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax77,axiom,
% 0.18/0.48 ( c_lam
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i] :
% 0.18/0.48 ( c_famunion @ X0
% 0.18/0.48 @ ^ [X2: $i] :
% 0.18/0.48 ( c_Repl @ ( X1 @ X2 )
% 0.18/0.48 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax78,axiom,
% 0.18/0.48 ( c_setprod
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_lam @ X0
% 0.18/0.48 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax79,axiom,
% 0.18/0.48 ( c_ap
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_ReplSep @ X0
% 0.18/0.48 @ ^ [X2: $i] :
% 0.18/0.48 ? [X3: $i] :
% 0.18/0.48 ( X2
% 0.18/0.48 = ( c_setsum @ X1 @ X3 ) )
% 0.18/0.48 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax80,axiom,
% 0.18/0.48 ( c_setsum_p
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.18/0.48 = X0 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax81,axiom,
% 0.18/0.48 ( c_tuple_p
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ! [X2: $i] :
% 0.18/0.48 ( ( c_In @ X2 @ X1 )
% 0.18/0.48 => ? [X3: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X3 @ X0 )
% 0.18/0.48 @ ? [X4: $i] :
% 0.18/0.48 ( X2
% 0.18/0.48 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax82,axiom,
% 0.18/0.48 ( c_Pi
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i] :
% 0.18/0.48 ( c_Sep
% 0.18/0.48 @ ( c_Power
% 0.18/0.48 @ ( c_lam @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.18/0.48 @ ^ [X2: $i] :
% 0.18/0.48 ! [X3: $i] :
% 0.18/0.48 ( ( c_In @ X3 @ X0 )
% 0.18/0.48 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax83,axiom,
% 0.18/0.48 ( c_setexp
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_Pi @ X1
% 0.18/0.48 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax84,axiom,
% 0.18/0.48 ( c_Sep2
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.18/0.48 ( c_Sep
% 0.18/0.48 @ ( c_lam @ X0
% 0.18/0.48 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.18/0.48 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax85,axiom,
% 0.18/0.48 ( c_set_of_pairs
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ! [X1: $i] :
% 0.18/0.48 ( ( c_In @ X1 @ X0 )
% 0.18/0.48 => ? [X2: $i,X3: $i] :
% 0.18/0.48 ( X1
% 0.18/0.48 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.18/0.48 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax86,axiom,
% 0.18/0.48 ( c_lam2
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.18/0.48 ( c_lam @ X0
% 0.18/0.48 @ ^ [X3: $i] :
% 0.18/0.48 ( c_lam @ ( X1 @ X3 )
% 0.18/0.48 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax87,axiom,
% 0.18/0.48 ( c_PNoEq_
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.18/0.48 ! [X3: $i] :
% 0.18/0.48 ( ( c_In @ X3 @ X0 )
% 0.18/0.48 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax88,axiom,
% 0.18/0.48 ( c_PNoLt_
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.18/0.48 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax89,axiom,
% 0.18/0.48 ( c_PNoLt
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax90,axiom,
% 0.18/0.48 ( c_PNoLe
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax91,axiom,
% 0.18/0.48 ( c_PNo_downc
% 0.18/0.48 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.18/0.48 ? [X3: $i] :
% 0.18/0.48 ( c_and @ ( c_ordinal @ X3 )
% 0.18/0.48 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax92,axiom,
% 0.18/0.48 ( c_PNo_upc
% 0.18/0.48 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.18/0.48 ? [X3: $i] :
% 0.18/0.48 ( c_and @ ( c_ordinal @ X3 )
% 0.18/0.48 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax93,axiom,
% 0.18/0.48 ( c_SNoElts_
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ( c_binunion @ X0
% 0.18/0.48 @ ( c_Repl @ X0
% 0.18/0.48 @ ^ [X1: $i] :
% 0.18/0.48 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.18/0.48 @ X1 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax94,axiom,
% 0.18/0.48 ( c_SNo_
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.18/0.48 @ ! [X2: $i] :
% 0.18/0.48 ( ( c_In @ X2 @ X0 )
% 0.18/0.48 => ( c_exactly1of2
% 0.18/0.48 @ ( c_In
% 0.18/0.48 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.18/0.48 @ X2 )
% 0.18/0.48 @ X1 )
% 0.18/0.48 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax95,axiom,
% 0.18/0.48 ( c_PSNo
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $o] :
% 0.18/0.48 ( c_binunion
% 0.18/0.48 @ ( c_Sep @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.18/0.48 @ ( c_ReplSep @ X0
% 0.18/0.48 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.18/0.48 @ ^ [X2: $i] :
% 0.18/0.48 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.18/0.48 @ X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax96,axiom,
% 0.18/0.48 ( c_SNo
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax97,axiom,
% 0.18/0.48 ( c_SNoLev
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ( c_Eps_i
% 0.18/0.48 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax98,axiom,
% 0.18/0.48 ( c_SNoEq_
% 0.18/0.48 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.18/0.48 ( c_PNoEq_ @ X0
% 0.18/0.48 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.18/0.48 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax99,axiom,
% 0.18/0.48 ( c_SNoLt
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.18/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.18/0.48 @ ( c_SNoLev @ X1 )
% 0.18/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax100,axiom,
% 0.18/0.48 ( c_SNoLe
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.18/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.18/0.48 @ ( c_SNoLev @ X1 )
% 0.18/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax101,axiom,
% 0.18/0.48 ( c_binop_on
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.18/0.48 ! [X2: $i] :
% 0.18/0.48 ( ( c_In @ X2 @ X0 )
% 0.18/0.48 => ! [X3: $i] :
% 0.18/0.48 ( ( c_In @ X3 @ X0 )
% 0.18/0.48 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax102,axiom,
% 0.18/0.48 ( c_Loop
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.18/0.48 ( c_and
% 0.18/0.48 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.18/0.48 @ ! [X5: $i] :
% 0.18/0.48 ( ( c_In @ X5 @ X0 )
% 0.18/0.48 => ( c_and
% 0.18/0.48 @ ( ( X1 @ X4 @ X5 )
% 0.18/0.48 = X5 )
% 0.18/0.48 @ ( ( X1 @ X5 @ X4 )
% 0.18/0.48 = X5 ) ) ) )
% 0.18/0.48 @ ! [X5: $i] :
% 0.18/0.48 ( ( c_In @ X5 @ X0 )
% 0.18/0.48 => ! [X6: $i] :
% 0.18/0.48 ( ( c_In @ X6 @ X0 )
% 0.18/0.48 => ( c_and
% 0.18/0.48 @ ( c_and
% 0.18/0.48 @ ( c_and
% 0.18/0.48 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.18/0.48 = X6 )
% 0.18/0.48 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.18/0.48 = X6 ) )
% 0.18/0.48 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.18/0.48 = X5 ) )
% 0.18/0.48 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.18/0.48 = X5 ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax103,axiom,
% 0.18/0.48 ( c_Loop_with_defs
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.18/0.48 ( c_and
% 0.18/0.48 @ ( c_and
% 0.18/0.48 @ ( c_and
% 0.18/0.48 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.18/0.48 @ ! [X14: $i] :
% 0.18/0.48 ( ( c_In @ X14 @ X0 )
% 0.18/0.48 => ! [X15: $i] :
% 0.18/0.48 ( ( c_In @ X15 @ X0 )
% 0.18/0.48 => ( ( X5 @ X14 @ X15 )
% 0.18/0.48 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.18/0.48 @ ! [X14: $i] :
% 0.18/0.48 ( ( c_In @ X14 @ X0 )
% 0.18/0.48 => ! [X15: $i] :
% 0.18/0.48 ( ( c_In @ X15 @ X0 )
% 0.18/0.48 => ! [X16: $i] :
% 0.18/0.48 ( ( c_In @ X16 @ X0 )
% 0.18/0.48 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.18/0.48 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.18/0.48 @ ! [X14: $i] :
% 0.18/0.48 ( ( c_In @ X14 @ X0 )
% 0.18/0.48 => ! [X15: $i] :
% 0.18/0.48 ( ( c_In @ X15 @ X0 )
% 0.18/0.48 => ( c_and
% 0.18/0.48 @ ( c_and
% 0.18/0.48 @ ( c_and
% 0.18/0.48 @ ( c_and
% 0.18/0.48 @ ( ( X7 @ X14 @ X15 )
% 0.18/0.48 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.18/0.48 @ ( ( X10 @ X14 @ X15 )
% 0.18/0.48 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.18/0.48 @ ( ( X11 @ X14 @ X15 )
% 0.18/0.48 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.18/0.48 @ ( ( X12 @ X14 @ X15 )
% 0.18/0.48 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.18/0.48 @ ( ( X13 @ X14 @ X15 )
% 0.18/0.48 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.18/0.48 @ ! [X14: $i] :
% 0.18/0.48 ( ( c_In @ X14 @ X0 )
% 0.18/0.48 => ! [X15: $i] :
% 0.18/0.48 ( ( c_In @ X15 @ X0 )
% 0.18/0.48 => ! [X16: $i] :
% 0.18/0.48 ( ( c_In @ X16 @ X0 )
% 0.18/0.48 => ( c_and
% 0.18/0.48 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.18/0.48 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.18/0.48 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.18/0.48 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax104,axiom,
% 0.18/0.48 ( c_Loop_with_defs_cex1
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.18/0.48 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.18/0.48 @ ? [X14: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X14 @ X0 )
% 0.18/0.48 @ ? [X15: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X15 @ X0 )
% 0.18/0.48 @ ? [X16: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X16 @ X0 )
% 0.18/0.48 @ ? [X17: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X17 @ X0 )
% 0.18/0.48 @ ( c_not
% 0.18/0.48 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.18/0.48 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax105,axiom,
% 0.18/0.48 ( c_Loop_with_defs_cex2
% 0.18/0.48 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.18/0.48 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.18/0.48 @ ? [X14: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X14 @ X0 )
% 0.18/0.48 @ ? [X15: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X15 @ X0 )
% 0.18/0.48 @ ? [X16: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X16 @ X0 )
% 0.18/0.48 @ ? [X17: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X17 @ X0 )
% 0.18/0.48 @ ? [X18: $i] :
% 0.18/0.48 ( c_and @ ( c_In @ X18 @ X0 )
% 0.18/0.48 @ ( c_not
% 0.18/0.48 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.18/0.48 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax106,axiom,
% 0.18/0.48 ( c_combinator
% 0.18/0.48 = ( ^ [X0: $i] :
% 0.18/0.48 ! [X1: $i > $o] :
% 0.18/0.48 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.18/0.48 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.18/0.48 => ( ! [X2: $i,X3: $i] :
% 0.18/0.48 ( ( X1 @ X2 )
% 0.18/0.48 => ( ( X1 @ X3 )
% 0.18/0.48 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.18/0.48 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax107,axiom,
% 0.18/0.48 ( c_combinator_equiv
% 0.18/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.18/0.48 ! [X2: $i > $i > $o] :
% 0.18/0.48 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.18/0.48 ( ( c_per_i @ X2 )
% 0.18/0.48 => ( ! [X6: $i] :
% 0.18/0.48 ( ( c_combinator @ X6 )
% 0.18/0.48 => ( X2 @ X6 @ X6 ) )
% 0.18/0.48 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.18/0.48 ( ( c_combinator @ X6 )
% 0.18/0.48 => ( ( c_combinator @ X7 )
% 0.18/0.48 => ( ( c_combinator @ X8 )
% 0.18/0.48 => ( ( c_combinator @ X9 )
% 0.18/0.48 => ( ( X2 @ X6 @ X8 )
% 0.18/0.48 => ( ( X2 @ X7 @ X9 )
% 0.18/0.48 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.18/0.48 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.18/0.48 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.18/0.48 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.18/0.48 @ ( c_Inj0 @ c_Empty )
% 0.18/0.48 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.18/0.48 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ax108,axiom,
% 0.18/0.48 ( c_equip_mod
% 0.18/0.48 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.18/0.48 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(conj,conjecture,
% 0.18/0.48 ( c_not
% 0.18/0.48 @ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i] :
% 0.18/0.48 ( c_and
% 0.18/0.48 @ ( X6
% 0.18/0.48 = ( 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 ) ) )
% 0.18/0.48 @ ? [X8: $i] : ( X3 @ ( X4 @ X5 ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 ------------------------
% 2.53/1.68 ---- Embedded in THF ---
% 2.53/1.68 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.53/1.68 %%% Generated on Tue Feb 24 14:49:55 EST 2026
% 2.53/1.68 %%% using '$$dhol' embedding, version 1.3.0.
% 2.53/1.68 %%% Logic specification used:
% 2.53/1.68 %%% thf(spec, logic, $$dhol).
% 2.53/1.68
% 2.53/1.68 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2DTF30472.p
% See solution above
% 2.53/1.68 ------------------------
% 2.74/1.71 ---- Cleaned THF ---
% 2.74/1.71 thf(c_Eps_i_tp,type,
% 2.74/1.71 c_Eps_i: ( $i > $o ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_False_tp,type,
% 2.74/1.71 c_False: $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_True_tp,type,
% 2.74/1.71 c_True: $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_not_tp,type,
% 2.74/1.71 c_not: $o > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_and_tp,type,
% 2.74/1.71 c_and: $o > $o > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_or_tp,type,
% 2.74/1.71 c_or: $o > $o > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_iff_tp,type,
% 2.74/1.71 c_iff: $o > $o > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_In_tp,type,
% 2.74/1.71 c_In: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_Subq_tp,type,
% 2.74/1.71 c_Subq: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_Empty_tp,type,
% 2.74/1.71 c_Empty: $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Union_tp,type,
% 2.74/1.71 c_Union: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Power_tp,type,
% 2.74/1.71 c_Power: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Repl_tp,type,
% 2.74/1.71 c_Repl: $i > ( $i > $i ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_TransSet_tp,type,
% 2.74/1.71 c_TransSet: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_atleast2_tp,type,
% 2.74/1.71 c_atleast2: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_atleast3_tp,type,
% 2.74/1.71 c_atleast3: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_atleast4_tp,type,
% 2.74/1.71 c_atleast4: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_atleast5_tp,type,
% 2.74/1.71 c_atleast5: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_atleast6_tp,type,
% 2.74/1.71 c_atleast6: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_exactly2_tp,type,
% 2.74/1.71 c_exactly2: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_exactly3_tp,type,
% 2.74/1.71 c_exactly3: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_exactly4_tp,type,
% 2.74/1.71 c_exactly4: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_exactly5_tp,type,
% 2.74/1.71 c_exactly5: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_exu_i_tp,type,
% 2.74/1.71 c_exu_i: ( $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_reflexive_i_tp,type,
% 2.74/1.71 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_irreflexive_i_tp,type,
% 2.74/1.71 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_symmetric_i_tp,type,
% 2.74/1.71 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_antisymmetric_i_tp,type,
% 2.74/1.71 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_transitive_i_tp,type,
% 2.74/1.71 c_transitive_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_eqreln_i_tp,type,
% 2.74/1.71 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_per_i_tp,type,
% 2.74/1.71 c_per_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_linear_i_tp,type,
% 2.74/1.71 c_linear_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_trichotomous_or_i_tp,type,
% 2.74/1.71 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_partialorder_i_tp,type,
% 2.74/1.71 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_totalorder_i_tp,type,
% 2.74/1.71 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_strictpartialorder_i_tp,type,
% 2.74/1.71 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_stricttotalorder_i_tp,type,
% 2.74/1.71 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_If_i_tp,type,
% 2.74/1.71 c_If_i: $o > $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_exactly1of2_tp,type,
% 2.74/1.71 c_exactly1of2: $o > $o > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_exactly1of3_tp,type,
% 2.74/1.71 c_exactly1of3: $o > $o > $o > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_nIn_tp,type,
% 2.74/1.71 c_nIn: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_nSubq_tp,type,
% 2.74/1.71 c_nSubq: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_UPair_tp,type,
% 2.74/1.71 c_UPair: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Sing_tp,type,
% 2.74/1.71 c_Sing: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_binunion_tp,type,
% 2.74/1.71 c_binunion: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_SetAdjoin_tp,type,
% 2.74/1.71 c_SetAdjoin: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_famunion_tp,type,
% 2.74/1.71 c_famunion: $i > ( $i > $i ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Sep_tp,type,
% 2.74/1.71 c_Sep: $i > ( $i > $o ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_ReplSep_tp,type,
% 2.74/1.71 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_binintersect_tp,type,
% 2.74/1.71 c_binintersect: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_setminus_tp,type,
% 2.74/1.71 c_setminus: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_inj_tp,type,
% 2.74/1.71 c_inj: $i > $i > ( $i > $i ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_bij_tp,type,
% 2.74/1.71 c_bij: $i > $i > ( $i > $i ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_atleastp_tp,type,
% 2.74/1.71 c_atleastp: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_equip_tp,type,
% 2.74/1.71 c_equip: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_In_rec_poly_G_i_tp,type,
% 2.74/1.71 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_In_rec_poly_i_tp,type,
% 2.74/1.71 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_ordsucc_tp,type,
% 2.74/1.71 c_ordsucc: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_nat_p_tp,type,
% 2.74/1.71 c_nat_p: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_nat_primrec_tp,type,
% 2.74/1.71 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_add_nat_tp,type,
% 2.74/1.71 c_add_nat: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_mul_nat_tp,type,
% 2.74/1.71 c_mul_nat: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_ordinal_tp,type,
% 2.74/1.71 c_ordinal: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_V__tp,type,
% 2.74/1.71 c_V_: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Inj1_tp,type,
% 2.74/1.71 c_Inj1: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Inj0_tp,type,
% 2.74/1.71 c_Inj0: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Unj_tp,type,
% 2.74/1.71 c_Unj: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_combine_funcs_tp,type,
% 2.74/1.71 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_setsum_tp,type,
% 2.74/1.71 c_setsum: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_proj0_tp,type,
% 2.74/1.71 c_proj0: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_proj1_tp,type,
% 2.74/1.71 c_proj1: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_binrep_tp,type,
% 2.74/1.71 c_binrep: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_lam_tp,type,
% 2.74/1.71 c_lam: $i > ( $i > $i ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_setprod_tp,type,
% 2.74/1.71 c_setprod: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_ap_tp,type,
% 2.74/1.71 c_ap: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_setsum_p_tp,type,
% 2.74/1.71 c_setsum_p: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_tuple_p_tp,type,
% 2.74/1.71 c_tuple_p: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_Pi_tp,type,
% 2.74/1.71 c_Pi: $i > ( $i > $i ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_setexp_tp,type,
% 2.74/1.71 c_setexp: $i > $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_Sep2_tp,type,
% 2.74/1.71 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_set_of_pairs_tp,type,
% 2.74/1.71 c_set_of_pairs: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_lam2_tp,type,
% 2.74/1.71 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_PNoEq__tp,type,
% 2.74/1.71 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_PNoLt__tp,type,
% 2.74/1.71 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_PNoLt_tp,type,
% 2.74/1.71 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_PNoLe_tp,type,
% 2.74/1.71 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_PNo_downc_tp,type,
% 2.74/1.71 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_PNo_upc_tp,type,
% 2.74/1.71 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_SNoElts__tp,type,
% 2.74/1.71 c_SNoElts_: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_SNo__tp,type,
% 2.74/1.71 c_SNo_: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_PSNo_tp,type,
% 2.74/1.71 c_PSNo: $i > ( $i > $o ) > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_SNo_tp,type,
% 2.74/1.71 c_SNo: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_SNoLev_tp,type,
% 2.74/1.71 c_SNoLev: $i > $i ).
% 2.74/1.71
% 2.74/1.71 thf(c_SNoEq__tp,type,
% 2.74/1.71 c_SNoEq_: $i > $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_SNoLt_tp,type,
% 2.74/1.71 c_SNoLt: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_SNoLe_tp,type,
% 2.74/1.71 c_SNoLe: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_binop_on_tp,type,
% 2.74/1.71 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_Loop_tp,type,
% 2.74/1.71 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_Loop_with_defs_tp,type,
% 2.74/1.71 c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_Loop_with_defs_cex1_tp,type,
% 2.74/1.71 c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_Loop_with_defs_cex2_tp,type,
% 2.74/1.71 c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_combinator_tp,type,
% 2.74/1.71 c_combinator: $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_combinator_equiv_tp,type,
% 2.74/1.71 c_combinator_equiv: $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(c_equip_mod_tp,type,
% 2.74/1.71 c_equip_mod: $i > $i > $i > $o ).
% 2.74/1.71
% 2.74/1.71 thf(ax1,axiom,
% 2.74/1.71 ! [X0: $i > $o,X1: $i] :
% 2.74/1.71 ( ( X0 @ X1 )
% 2.74/1.71 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax2,axiom,
% 2.74/1.71 ! [X0: $o] :
% 2.74/1.71 ( ( c_not @ ( c_not @ X0 ) )
% 2.74/1.71 => X0 ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax3,axiom,
% 2.74/1.71 ! [X0: $o,X1: $o] :
% 2.74/1.71 ( ( c_iff @ X0 @ X1 )
% 2.74/1.71 => ( X0 = X1 ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax4,axiom,
% 2.74/1.71 ! [X0: $i,X1: $i] :
% 2.74/1.71 ( ( c_Subq @ X0 @ X1 )
% 2.74/1.71 => ( ( c_Subq @ X1 @ X0 )
% 2.74/1.71 => ( X0 = X1 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax5,axiom,
% 2.74/1.71 ( c_not
% 2.74/1.71 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax6,axiom,
% 2.74/1.71 ! [X0: $i,X1: $i] :
% 2.74/1.71 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 2.74/1.71 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax7,axiom,
% 2.74/1.71 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax8,axiom,
% 2.74/1.71 ! [X0: $i,X1: $i > $i,X2: $i] :
% 2.74/1.71 ( c_iff
% 2.74/1.71 @ ( c_In @ X2
% 2.74/1.71 @ ( c_Repl @ X0
% 2.74/1.71 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 2.74/1.71 @ ? [X3: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X3 @ X0 )
% 2.74/1.71 @ ( X2
% 2.74/1.71 = ( X1 @ X3 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax9,axiom,
% 2.74/1.71 ! [X0: $i > $o] :
% 2.74/1.71 ( ! [X1: $i] :
% 2.74/1.71 ( ( X0 @ X1 )
% 2.74/1.71 => ! [X2: $i] :
% 2.74/1.71 ( ( c_In @ X2 @ X1 )
% 2.74/1.71 => ( X0 @ X2 ) ) )
% 2.74/1.71 => ( ( X0 @ c_Empty )
% 2.74/1.71 => ( ! [X1: $i] :
% 2.74/1.71 ( ( X0 @ X1 )
% 2.74/1.71 => ( X0 @ ( c_Union @ X1 ) ) )
% 2.74/1.71 => ( ! [X1: $i] :
% 2.74/1.71 ( ( X0 @ X1 )
% 2.74/1.71 => ( X0 @ ( c_Power @ X1 ) ) )
% 2.74/1.71 => ( ! [X1: $i] :
% 2.74/1.71 ( ( X0 @ X1 )
% 2.74/1.71 => ! [X2: $i > $i] :
% 2.74/1.71 ( ! [X3: $i] :
% 2.74/1.71 ( ( c_In @ X3 @ X1 )
% 2.74/1.71 => ( X0 @ ( X2 @ X3 ) ) )
% 2.74/1.71 => ( X0
% 2.74/1.71 @ ( c_Repl @ X1
% 2.74/1.71 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 2.74/1.71 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax10,axiom,
% 2.74/1.71 ! [X0: $i > $o] :
% 2.74/1.71 ( ! [X1: $i] :
% 2.74/1.71 ( ! [X2: $i] :
% 2.74/1.71 ( ( c_In @ X2 @ X1 )
% 2.74/1.71 => ( X0 @ X2 ) )
% 2.74/1.71 => ( X0 @ X1 ) )
% 2.74/1.71 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax11,axiom,
% 2.74/1.71 ( c_False
% 2.74/1.71 = ( ! [X0: $o] : X0 ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax12,axiom,
% 2.74/1.71 ( c_True
% 2.74/1.71 = ( ! [X0: $o] :
% 2.74/1.71 ( X0
% 2.74/1.71 => X0 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax13,axiom,
% 2.74/1.71 ( c_not
% 2.74/1.71 = ( ^ [X0: $o] :
% 2.74/1.71 ( X0
% 2.74/1.71 => c_False ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax14,axiom,
% 2.74/1.71 ( c_and
% 2.74/1.71 = ( ^ [X0: $o,X1: $o] :
% 2.74/1.71 ! [X2: $o] :
% 2.74/1.71 ( ( X0
% 2.74/1.71 => ( X1
% 2.74/1.71 => X2 ) )
% 2.74/1.71 => X2 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax15,axiom,
% 2.74/1.71 ( c_or
% 2.74/1.71 = ( ^ [X0: $o,X1: $o] :
% 2.74/1.71 ! [X2: $o] :
% 2.74/1.71 ( ( X0
% 2.74/1.71 => X2 )
% 2.74/1.71 => ( ( X1
% 2.74/1.71 => X2 )
% 2.74/1.71 => X2 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax16,axiom,
% 2.74/1.71 ( c_iff
% 2.74/1.71 = ( ^ [X0: $o,X1: $o] :
% 2.74/1.71 ( c_and
% 2.74/1.71 @ ( X0
% 2.74/1.71 => X1 )
% 2.74/1.71 @ ( X1
% 2.74/1.71 => X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax17,axiom,
% 2.74/1.71 ( c_Subq
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ! [X2: $i] :
% 2.74/1.71 ( ( c_In @ X2 @ X0 )
% 2.74/1.71 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax18,axiom,
% 2.74/1.71 ( c_TransSet
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ! [X1: $i] :
% 2.74/1.71 ( ( c_In @ X1 @ X0 )
% 2.74/1.71 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax19,axiom,
% 2.74/1.71 ( c_atleast2
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax20,axiom,
% 2.74/1.71 ( c_atleast3
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax21,axiom,
% 2.74/1.71 ( c_atleast4
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax22,axiom,
% 2.74/1.71 ( c_atleast5
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax23,axiom,
% 2.74/1.71 ( c_atleast6
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax24,axiom,
% 2.74/1.71 ( c_exactly2
% 2.74/1.71 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax25,axiom,
% 2.74/1.71 ( c_exactly3
% 2.74/1.71 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax26,axiom,
% 2.74/1.71 ( c_exactly4
% 2.74/1.71 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax27,axiom,
% 2.74/1.71 ( c_exactly5
% 2.74/1.71 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax28,axiom,
% 2.74/1.71 ( c_exu_i
% 2.74/1.71 = ( ^ [X0: $i > $o] :
% 2.74/1.71 ( c_and
% 2.74/1.71 @ ? [X1: $i] : ( X0 @ X1 )
% 2.74/1.71 @ ! [X1: $i,X2: $i] :
% 2.74/1.71 ( ( X0 @ X1 )
% 2.74/1.71 => ( ( X0 @ X2 )
% 2.74/1.71 => ( X1 = X2 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax29,axiom,
% 2.74/1.71 ( c_reflexive_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] :
% 2.74/1.71 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax30,axiom,
% 2.74/1.71 ( c_irreflexive_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] :
% 2.74/1.71 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax31,axiom,
% 2.74/1.71 ( c_symmetric_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] :
% 2.74/1.71 ! [X1: $i,X2: $i] :
% 2.74/1.71 ( ( X0 @ X1 @ X2 )
% 2.74/1.71 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax32,axiom,
% 2.74/1.71 ( c_antisymmetric_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] :
% 2.74/1.71 ! [X1: $i,X2: $i] :
% 2.74/1.71 ( ( X0 @ X1 @ X2 )
% 2.74/1.71 => ( ( X0 @ X2 @ X1 )
% 2.74/1.71 => ( X1 = X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax33,axiom,
% 2.74/1.71 ( c_transitive_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] :
% 2.74/1.71 ! [X1: $i,X2: $i,X3: $i] :
% 2.74/1.71 ( ( X0 @ X1 @ X2 )
% 2.74/1.71 => ( ( X0 @ X2 @ X3 )
% 2.74/1.71 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax34,axiom,
% 2.74/1.71 ( c_eqreln_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax35,axiom,
% 2.74/1.71 ( c_per_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax36,axiom,
% 2.74/1.71 ( c_linear_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] :
% 2.74/1.71 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax37,axiom,
% 2.74/1.71 ( c_trichotomous_or_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] :
% 2.74/1.71 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax38,axiom,
% 2.74/1.71 ( c_partialorder_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax39,axiom,
% 2.74/1.71 ( c_totalorder_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax40,axiom,
% 2.74/1.71 ( c_strictpartialorder_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax41,axiom,
% 2.74/1.71 ( c_stricttotalorder_i
% 2.74/1.71 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax42,axiom,
% 2.74/1.71 ( c_If_i
% 2.74/1.71 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 2.74/1.71 ( c_Eps_i
% 2.74/1.71 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax43,axiom,
% 2.74/1.71 ( c_exactly1of2
% 2.74/1.71 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax44,axiom,
% 2.74/1.71 ( c_exactly1of3
% 2.74/1.71 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax45,axiom,
% 2.74/1.71 ( c_nIn
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax46,axiom,
% 2.74/1.71 ( c_nSubq
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax47,axiom,
% 2.74/1.71 ( c_UPair
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 2.74/1.71 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax48,axiom,
% 2.74/1.71 ( c_Sing
% 2.74/1.71 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax49,axiom,
% 2.74/1.71 ( c_binunion
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax50,axiom,
% 2.74/1.71 ( c_SetAdjoin
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax51,axiom,
% 2.74/1.71 ( c_famunion
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i] :
% 2.74/1.71 ( c_Union
% 2.74/1.71 @ ( c_Repl @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax52,axiom,
% 2.74/1.71 ( c_Sep
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $o] :
% 2.74/1.71 ( c_If_i
% 2.74/1.71 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 2.74/1.71 @ ( c_Repl @ X0
% 2.74/1.71 @ ^ [X2: $i] :
% 2.74/1.71 ( ^ [X3: $i] :
% 2.74/1.71 ( c_If_i @ ( X1 @ X3 ) @ X3
% 2.74/1.71 @ ( c_Eps_i
% 2.74/1.71 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 2.74/1.71 @ X2 ) )
% 2.74/1.71 @ c_Empty ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax53,axiom,
% 2.74/1.71 ( c_ReplSep
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 2.74/1.71 ( c_Repl
% 2.74/1.71 @ ( c_Sep @ X0
% 2.74/1.71 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.74/1.71 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax54,axiom,
% 2.74/1.71 ( c_binintersect
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_Sep @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax55,axiom,
% 2.74/1.71 ( c_setminus
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_Sep @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax56,axiom,
% 2.74/1.71 ( c_inj
% 2.74/1.71 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.74/1.71 ( c_and
% 2.74/1.71 @ ! [X3: $i] :
% 2.74/1.71 ( ( c_In @ X3 @ X0 )
% 2.74/1.71 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 2.74/1.71 @ ! [X3: $i] :
% 2.74/1.71 ( ( c_In @ X3 @ X0 )
% 2.74/1.71 => ! [X4: $i] :
% 2.74/1.71 ( ( c_In @ X4 @ X0 )
% 2.74/1.71 => ( ( ( X2 @ X3 )
% 2.74/1.71 = ( X2 @ X4 ) )
% 2.74/1.71 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax57,axiom,
% 2.74/1.71 ( c_bij
% 2.74/1.71 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.74/1.71 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 2.74/1.71 @ ! [X3: $i] :
% 2.74/1.71 ( ( c_In @ X3 @ X1 )
% 2.74/1.71 => ? [X4: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X4 @ X0 )
% 2.74/1.71 @ ( ( X2 @ X4 )
% 2.74/1.71 = X3 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax58,axiom,
% 2.74/1.71 ( c_atleastp
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax59,axiom,
% 2.74/1.71 ( c_equip
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax60,axiom,
% 2.74/1.71 ( c_In_rec_poly_G_i
% 2.74/1.71 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 2.74/1.71 ! [X3: $i > $i > $o] :
% 2.74/1.71 ( ! [X4: $i,X5: $i > $i] :
% 2.74/1.71 ( ! [X6: $i] :
% 2.74/1.71 ( ( c_In @ X6 @ X4 )
% 2.74/1.71 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 2.74/1.71 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 2.74/1.71 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax61,axiom,
% 2.74/1.71 ( c_In_rec_poly_i
% 2.74/1.71 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 2.74/1.71 ( c_Eps_i
% 2.74/1.71 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax62,axiom,
% 2.74/1.71 ( c_ordsucc
% 2.74/1.71 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax63,axiom,
% 2.74/1.71 ( c_nat_p
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ! [X1: $i > $o] :
% 2.74/1.71 ( ( X1 @ c_Empty )
% 2.74/1.71 => ( ! [X2: $i] :
% 2.74/1.71 ( ( X1 @ X2 )
% 2.74/1.71 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 2.74/1.71 => ( X1 @ X0 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax64,axiom,
% 2.74/1.71 ( c_nat_primrec
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.74/1.71 ( c_In_rec_poly_i
% 2.74/1.71 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax65,axiom,
% 2.74/1.71 ( c_add_nat
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_nat_primrec @ X0
% 2.74/1.71 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 2.74/1.71 @ X1 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax66,axiom,
% 2.74/1.71 ( c_mul_nat
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_nat_primrec @ c_Empty
% 2.74/1.71 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 2.74/1.71 @ X1 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax67,axiom,
% 2.74/1.71 ( c_ordinal
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ( c_and @ ( c_TransSet @ X0 )
% 2.74/1.71 @ ! [X1: $i] :
% 2.74/1.71 ( ( c_In @ X1 @ X0 )
% 2.74/1.71 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax68,axiom,
% 2.74/1.71 ( c_V_
% 2.74/1.71 = ( c_In_rec_poly_i
% 2.74/1.71 @ ^ [X0: $i,X1: $i > $i] :
% 2.74/1.71 ( c_famunion @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax69,axiom,
% 2.74/1.71 ( c_Inj1
% 2.74/1.71 = ( c_In_rec_poly_i
% 2.74/1.71 @ ^ [X0: $i,X1: $i > $i] :
% 2.74/1.71 ( c_binunion @ ( c_Sing @ c_Empty )
% 2.74/1.71 @ ( c_Repl @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax70,axiom,
% 2.74/1.71 ( c_Inj0
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ( c_Repl @ X0
% 2.74/1.71 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax71,axiom,
% 2.74/1.71 ( c_Unj
% 2.74/1.71 = ( c_In_rec_poly_i
% 2.74/1.71 @ ^ [X0: $i,X1: $i > $i] :
% 2.74/1.71 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 2.74/1.71 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax72,axiom,
% 2.74/1.71 ( c_combine_funcs
% 2.74/1.71 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 2.74/1.71 ( c_If_i
% 2.74/1.71 @ ( X4
% 2.74/1.71 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 2.74/1.71 @ ( X2 @ ( c_Unj @ X4 ) )
% 2.74/1.71 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax73,axiom,
% 2.74/1.71 ( c_setsum
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_binunion
% 2.74/1.71 @ ( c_Repl @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 2.74/1.71 @ ( c_Repl @ X1
% 2.74/1.71 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax74,axiom,
% 2.74/1.71 ( c_proj0
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ( c_ReplSep @ X0
% 2.74/1.71 @ ^ [X1: $i] :
% 2.74/1.71 ? [X2: $i] :
% 2.74/1.71 ( ( c_Inj0 @ X2 )
% 2.74/1.71 = X1 )
% 2.74/1.71 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax75,axiom,
% 2.74/1.71 ( c_proj1
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ( c_ReplSep @ X0
% 2.74/1.71 @ ^ [X1: $i] :
% 2.74/1.71 ? [X2: $i] :
% 2.74/1.71 ( ( c_Inj1 @ X2 )
% 2.74/1.71 = X1 )
% 2.74/1.71 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax76,axiom,
% 2.74/1.71 ( c_binrep
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax77,axiom,
% 2.74/1.71 ( c_lam
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i] :
% 2.74/1.71 ( c_famunion @ X0
% 2.74/1.71 @ ^ [X2: $i] :
% 2.74/1.71 ( c_Repl @ ( X1 @ X2 )
% 2.74/1.71 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax78,axiom,
% 2.74/1.71 ( c_setprod
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_lam @ X0
% 2.74/1.71 @ ^ [X2: $i] : X1 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax79,axiom,
% 2.74/1.71 ( c_ap
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_ReplSep @ X0
% 2.74/1.71 @ ^ [X2: $i] :
% 2.74/1.71 ? [X3: $i] :
% 2.74/1.71 ( X2
% 2.74/1.71 = ( c_setsum @ X1 @ X3 ) )
% 2.74/1.71 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax80,axiom,
% 2.74/1.71 ( c_setsum_p
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 2.74/1.71 = X0 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax81,axiom,
% 2.74/1.71 ( c_tuple_p
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ! [X2: $i] :
% 2.74/1.71 ( ( c_In @ X2 @ X1 )
% 2.74/1.71 => ? [X3: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X3 @ X0 )
% 2.74/1.71 @ ? [X4: $i] :
% 2.74/1.71 ( X2
% 2.74/1.71 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax82,axiom,
% 2.74/1.71 ( c_Pi
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i] :
% 2.74/1.71 ( c_Sep
% 2.74/1.71 @ ( c_Power
% 2.74/1.71 @ ( c_lam @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 2.74/1.71 @ ^ [X2: $i] :
% 2.74/1.71 ! [X3: $i] :
% 2.74/1.71 ( ( c_In @ X3 @ X0 )
% 2.74/1.71 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax83,axiom,
% 2.74/1.71 ( c_setexp
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_Pi @ X1
% 2.74/1.71 @ ^ [X2: $i] : X0 ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax84,axiom,
% 2.74/1.71 ( c_Sep2
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 2.74/1.71 ( c_Sep
% 2.74/1.71 @ ( c_lam @ X0
% 2.74/1.71 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.74/1.71 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax85,axiom,
% 2.74/1.71 ( c_set_of_pairs
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ! [X1: $i] :
% 2.74/1.71 ( ( c_In @ X1 @ X0 )
% 2.74/1.71 => ? [X2: $i,X3: $i] :
% 2.74/1.71 ( X1
% 2.74/1.71 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 2.74/1.71 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax86,axiom,
% 2.74/1.71 ( c_lam2
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 2.74/1.71 ( c_lam @ X0
% 2.74/1.71 @ ^ [X3: $i] :
% 2.74/1.71 ( c_lam @ ( X1 @ X3 )
% 2.74/1.71 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax87,axiom,
% 2.74/1.71 ( c_PNoEq_
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.74/1.71 ! [X3: $i] :
% 2.74/1.71 ( ( c_In @ X3 @ X0 )
% 2.74/1.71 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax88,axiom,
% 2.74/1.71 ( c_PNoLt_
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.74/1.71 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax89,axiom,
% 2.74/1.71 ( c_PNoLt
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax90,axiom,
% 2.74/1.71 ( c_PNoLe
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax91,axiom,
% 2.74/1.71 ( c_PNo_downc
% 2.74/1.71 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.74/1.71 ? [X3: $i] :
% 2.74/1.71 ( c_and @ ( c_ordinal @ X3 )
% 2.74/1.71 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax92,axiom,
% 2.74/1.71 ( c_PNo_upc
% 2.74/1.71 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.74/1.71 ? [X3: $i] :
% 2.74/1.71 ( c_and @ ( c_ordinal @ X3 )
% 2.74/1.71 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax93,axiom,
% 2.74/1.71 ( c_SNoElts_
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ( c_binunion @ X0
% 2.74/1.71 @ ( c_Repl @ X0
% 2.74/1.71 @ ^ [X1: $i] :
% 2.74/1.71 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.74/1.71 @ X1 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax94,axiom,
% 2.74/1.71 ( c_SNo_
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 2.74/1.71 @ ! [X2: $i] :
% 2.74/1.71 ( ( c_In @ X2 @ X0 )
% 2.74/1.71 => ( c_exactly1of2
% 2.74/1.71 @ ( c_In
% 2.74/1.71 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.74/1.71 @ X2 )
% 2.74/1.71 @ X1 )
% 2.74/1.71 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax95,axiom,
% 2.74/1.71 ( c_PSNo
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $o] :
% 2.74/1.71 ( c_binunion
% 2.74/1.71 @ ( c_Sep @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 2.74/1.71 @ ( c_ReplSep @ X0
% 2.74/1.71 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 2.74/1.71 @ ^ [X2: $i] :
% 2.74/1.71 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.74/1.71 @ X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax96,axiom,
% 2.74/1.71 ( c_SNo
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax97,axiom,
% 2.74/1.71 ( c_SNoLev
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ( c_Eps_i
% 2.74/1.71 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax98,axiom,
% 2.74/1.71 ( c_SNoEq_
% 2.74/1.71 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.74/1.71 ( c_PNoEq_ @ X0
% 2.74/1.71 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 2.74/1.71 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax99,axiom,
% 2.74/1.71 ( c_SNoLt
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 2.74/1.71 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.74/1.71 @ ( c_SNoLev @ X1 )
% 2.74/1.71 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax100,axiom,
% 2.74/1.71 ( c_SNoLe
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 2.74/1.71 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.74/1.71 @ ( c_SNoLev @ X1 )
% 2.74/1.71 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax101,axiom,
% 2.74/1.71 ( c_binop_on
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.74/1.71 ! [X2: $i] :
% 2.74/1.71 ( ( c_In @ X2 @ X0 )
% 2.74/1.71 => ! [X3: $i] :
% 2.74/1.71 ( ( c_In @ X3 @ X0 )
% 2.74/1.71 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax102,axiom,
% 2.74/1.71 ( c_Loop
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 2.74/1.71 ( c_and
% 2.74/1.71 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 2.74/1.71 @ ! [X5: $i] :
% 2.74/1.71 ( ( c_In @ X5 @ X0 )
% 2.74/1.71 => ( c_and
% 2.74/1.71 @ ( ( X1 @ X4 @ X5 )
% 2.74/1.71 = X5 )
% 2.74/1.71 @ ( ( X1 @ X5 @ X4 )
% 2.74/1.71 = X5 ) ) ) )
% 2.74/1.71 @ ! [X5: $i] :
% 2.74/1.71 ( ( c_In @ X5 @ X0 )
% 2.74/1.71 => ! [X6: $i] :
% 2.74/1.71 ( ( c_In @ X6 @ X0 )
% 2.74/1.71 => ( c_and
% 2.74/1.71 @ ( c_and
% 2.74/1.71 @ ( c_and
% 2.74/1.71 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 2.74/1.71 = X6 )
% 2.74/1.71 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 2.74/1.71 = X6 ) )
% 2.74/1.71 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 2.74/1.71 = X5 ) )
% 2.74/1.71 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 2.74/1.71 = X5 ) ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax103,axiom,
% 2.74/1.71 ( c_Loop_with_defs
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.74/1.71 ( c_and
% 2.74/1.71 @ ( c_and
% 2.74/1.71 @ ( c_and
% 2.74/1.71 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 2.74/1.71 @ ! [X14: $i] :
% 2.74/1.71 ( ( c_In @ X14 @ X0 )
% 2.74/1.71 => ! [X15: $i] :
% 2.74/1.71 ( ( c_In @ X15 @ X0 )
% 2.74/1.71 => ( ( X5 @ X14 @ X15 )
% 2.74/1.71 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 2.74/1.71 @ ! [X14: $i] :
% 2.74/1.71 ( ( c_In @ X14 @ X0 )
% 2.74/1.71 => ! [X15: $i] :
% 2.74/1.71 ( ( c_In @ X15 @ X0 )
% 2.74/1.71 => ! [X16: $i] :
% 2.74/1.71 ( ( c_In @ X16 @ X0 )
% 2.74/1.71 => ( ( X6 @ X14 @ X15 @ X16 )
% 2.74/1.71 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 2.74/1.71 @ ! [X14: $i] :
% 2.74/1.71 ( ( c_In @ X14 @ X0 )
% 2.74/1.71 => ! [X15: $i] :
% 2.74/1.71 ( ( c_In @ X15 @ X0 )
% 2.74/1.71 => ( c_and
% 2.74/1.71 @ ( c_and
% 2.74/1.71 @ ( c_and
% 2.74/1.71 @ ( c_and
% 2.74/1.71 @ ( ( X7 @ X14 @ X15 )
% 2.74/1.71 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 2.74/1.71 @ ( ( X10 @ X14 @ X15 )
% 2.74/1.71 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 2.74/1.71 @ ( ( X11 @ X14 @ X15 )
% 2.74/1.71 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 2.74/1.71 @ ( ( X12 @ X14 @ X15 )
% 2.74/1.71 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 2.74/1.71 @ ( ( X13 @ X14 @ X15 )
% 2.74/1.71 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 2.74/1.71 @ ! [X14: $i] :
% 2.74/1.71 ( ( c_In @ X14 @ X0 )
% 2.74/1.71 => ! [X15: $i] :
% 2.74/1.71 ( ( c_In @ X15 @ X0 )
% 2.74/1.71 => ! [X16: $i] :
% 2.74/1.71 ( ( c_In @ X16 @ X0 )
% 2.74/1.71 => ( c_and
% 2.74/1.71 @ ( ( X8 @ X14 @ X15 @ X16 )
% 2.74/1.71 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 2.74/1.71 @ ( ( X9 @ X14 @ X15 @ X16 )
% 2.74/1.71 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax104,axiom,
% 2.74/1.71 ( c_Loop_with_defs_cex1
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.74/1.71 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.74/1.71 @ ? [X14: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X14 @ X0 )
% 2.74/1.71 @ ? [X15: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X15 @ X0 )
% 2.74/1.71 @ ? [X16: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X16 @ X0 )
% 2.74/1.71 @ ? [X17: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X17 @ X0 )
% 2.74/1.71 @ ( c_not
% 2.74/1.71 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 2.74/1.71 = X4 ) ) ) ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax105,axiom,
% 2.74/1.71 ( c_Loop_with_defs_cex2
% 2.74/1.71 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.74/1.71 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.74/1.71 @ ? [X14: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X14 @ X0 )
% 2.74/1.71 @ ? [X15: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X15 @ X0 )
% 2.74/1.71 @ ? [X16: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X16 @ X0 )
% 2.74/1.71 @ ? [X17: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X17 @ X0 )
% 2.74/1.71 @ ? [X18: $i] :
% 2.74/1.71 ( c_and @ ( c_In @ X18 @ X0 )
% 2.74/1.71 @ ( c_not
% 2.74/1.71 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 2.74/1.71 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax106,axiom,
% 2.74/1.71 ( c_combinator
% 2.74/1.71 = ( ^ [X0: $i] :
% 2.74/1.71 ! [X1: $i > $o] :
% 2.74/1.71 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 2.74/1.71 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 2.74/1.71 => ( ! [X2: $i,X3: $i] :
% 2.74/1.71 ( ( X1 @ X2 )
% 2.74/1.71 => ( ( X1 @ X3 )
% 2.74/1.71 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 2.74/1.71 => ( X1 @ X0 ) ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax107,axiom,
% 2.74/1.71 ( c_combinator_equiv
% 2.74/1.71 = ( ^ [X0: $i,X1: $i] :
% 2.74/1.71 ! [X2: $i > $i > $o] :
% 2.74/1.71 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 2.74/1.71 ( ( c_per_i @ X2 )
% 2.74/1.71 => ( ! [X6: $i] :
% 2.74/1.71 ( ( c_combinator @ X6 )
% 2.74/1.71 => ( X2 @ X6 @ X6 ) )
% 2.74/1.71 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.74/1.71 ( ( c_combinator @ X6 )
% 2.74/1.71 => ( ( c_combinator @ X7 )
% 2.74/1.71 => ( ( c_combinator @ X8 )
% 2.74/1.71 => ( ( c_combinator @ X9 )
% 2.74/1.71 => ( ( X2 @ X6 @ X8 )
% 2.74/1.71 => ( ( X2 @ X7 @ X9 )
% 2.74/1.71 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 2.74/1.71 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 2.74/1.71 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 2.74/1.71 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 2.74/1.71 @ ( c_Inj0 @ c_Empty )
% 2.74/1.71 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 2.74/1.71 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(ax108,axiom,
% 2.74/1.71 ( c_equip_mod
% 2.74/1.71 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.74/1.71 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 2.74/1.71
% 2.74/1.71 thf(conj,conjecture,
% 2.74/1.71 ( c_not
% 2.74/1.71 @ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i] :
% 2.74/1.71 ( c_and
% 2.74/1.71 @ ( X6
% 2.74/1.71 = ( 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 ) ) )
% 2.74/1.71 @ ? [X8: $i] : ( X3 @ ( X4 @ X5 ) ) ) ) ).
% 2.74/1.71 ------------------------
% 2.74/1.74 % (30584)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/27Mi)
% 2.74/1.74 % (30588)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/18Mi)
% 2.74/1.74 % (30582)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/183Mi)
% 2.74/1.74 % (30586)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/2Mi)
% 2.74/1.74 % (30587)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/275Mi)
% 2.74/1.74 % (30585)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/2Mi)
% 2.74/1.74 % (30583)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/4Mi)
% 2.74/1.74 % (30585)Instruction limit reached!
% 2.74/1.74 % (30585)------------------------------
% 2.74/1.74 % (30585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.74 % (30585)Termination reason: Unknown
% 2.74/1.74 % (30585)Termination phase: shuffling
% 2.74/1.74
% 2.74/1.74 % (30586)Instruction limit reached!
% 2.74/1.74 % (30586)------------------------------
% 2.74/1.74 % (30586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.74 % (30585)Memory used [KB]: 1279
% 2.74/1.74 % (30585)Time elapsed: 0.003 s
% 2.74/1.74 % (30585)Instructions burned: 2 (million)
% 2.74/1.74 % (30585)------------------------------
% 2.74/1.74 % (30585)------------------------------
% 2.74/1.74 % (30586)Termination reason: Unknown
% 2.74/1.74 % (30586)Termination phase: shuffling
% 2.74/1.74
% 2.74/1.74 % (30586)Memory used [KB]: 1279
% 2.74/1.74 % (30586)Time elapsed: 0.003 s
% 2.74/1.74 % (30586)Instructions burned: 2 (million)
% 2.74/1.74 % (30586)------------------------------
% 2.74/1.74 % (30586)------------------------------
% 2.74/1.74 % (30583)Instruction limit reached!
% 2.74/1.74 % (30583)------------------------------
% 2.74/1.74 % (30583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.74 % (30583)Termination reason: Unknown
% 2.74/1.74 % (30583)Termination phase: shuffling
% 2.74/1.74
% 2.74/1.74 % (30583)Memory used [KB]: 1279
% 2.74/1.74 % (30583)Time elapsed: 0.004 s
% 2.74/1.74 % (30583)Instructions burned: 4 (million)
% 2.74/1.74 % (30583)------------------------------
% 2.74/1.74 % (30583)------------------------------
% 2.74/1.75 % (30588)Instruction limit reached!
% 2.74/1.75 % (30588)------------------------------
% 2.74/1.75 % (30588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.75 % (30588)Termination reason: Unknown
% 2.74/1.75 % (30588)Termination phase: shuffling
% 2.74/1.75
% 2.74/1.75 % (30588)Memory used [KB]: 1535
% 2.74/1.75 % (30588)Time elapsed: 0.010 s
% 2.74/1.75 % (30588)Instructions burned: 18 (million)
% 2.74/1.75 % (30588)------------------------------
% 2.74/1.75 % (30588)------------------------------
% 2.74/1.75 % (30584)Instruction limit reached!
% 2.74/1.75 % (30584)------------------------------
% 2.74/1.75 % (30584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.75 % (30584)Termination reason: Unknown
% 2.74/1.75 % (30584)Termination phase: Property scanning
% 2.74/1.75
% 2.74/1.75 % (30584)Memory used [KB]: 1535
% 2.74/1.75 % (30584)Time elapsed: 0.015 s
% 2.74/1.75 % (30584)Instructions burned: 28 (million)
% 2.74/1.75 % (30584)------------------------------
% 2.74/1.75 % (30584)------------------------------
% 2.74/1.76 % (30587)Refutation not found, incomplete strategy
% 2.74/1.76 % (30587)------------------------------
% 2.74/1.76 % (30587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.76 % (30587)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.76
% 2.74/1.76
% 2.74/1.76 % (30587)Memory used [KB]: 6012
% 2.74/1.76 % (30587)Time elapsed: 0.018 s
% 2.74/1.76 % (30587)Instructions burned: 35 (million)
% 2.74/1.76 % (30587)------------------------------
% 2.74/1.76 % (30587)------------------------------
% 2.74/1.76 % (30590)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/37Mi)
% 2.74/1.76 % (30589)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/3Mi)
% 2.74/1.76 % (30591)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/15Mi)
% 2.74/1.76 % (30589)Instruction limit reached!
% 2.74/1.76 % (30589)------------------------------
% 2.74/1.76 % (30589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.76 % (30589)Termination reason: Unknown
% 2.74/1.76 % (30589)Termination phase: shuffling
% 2.74/1.76
% 2.74/1.76 % (30589)Memory used [KB]: 1279
% 2.74/1.76 % (30589)Time elapsed: 0.003 s
% 2.74/1.76 % (30589)Instructions burned: 3 (million)
% 2.74/1.76 % (30589)------------------------------
% 2.74/1.76 % (30589)------------------------------
% 2.74/1.77 % (30592)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/3Mi)
% 2.74/1.77 % (30591)Instruction limit reached!
% 2.74/1.77 % (30591)------------------------------
% 2.74/1.77 % (30591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.77 % (30591)Termination reason: Unknown
% 2.74/1.77 % (30591)Termination phase: shuffling
% 2.74/1.77
% 2.74/1.77 % (30591)Memory used [KB]: 1535
% 2.74/1.77 % (30591)Time elapsed: 0.009 s
% 2.74/1.77 % (30591)Instructions burned: 16 (million)
% 2.74/1.77 % (30591)------------------------------
% 2.74/1.77 % (30591)------------------------------
% 2.74/1.77 % (30592)Instruction limit reached!
% 2.74/1.77 % (30592)------------------------------
% 2.74/1.77 % (30592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.77 % (30592)Termination reason: Unknown
% 2.74/1.77 % (30592)Termination phase: shuffling
% 2.74/1.77
% 2.74/1.77 % (30592)Memory used [KB]: 1279
% 2.74/1.77 % (30592)Time elapsed: 0.003 s
% 2.74/1.77 % (30592)Instructions burned: 3 (million)
% 2.74/1.77 % (30592)------------------------------
% 2.74/1.77 % (30592)------------------------------
% 2.74/1.77 % (30593)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/1041Mi)
% 2.74/1.78 % (30594)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/7Mi)
% 2.74/1.78 % (30590)Instruction limit reached!
% 2.74/1.78 % (30590)------------------------------
% 2.74/1.78 % (30590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.78 % (30590)Termination reason: Unknown
% 2.74/1.78 % (30590)Termination phase: Property scanning
% 2.74/1.78
% 2.74/1.78 % (30590)Memory used [KB]: 1535
% 2.74/1.78 % (30590)Time elapsed: 0.018 s
% 2.74/1.78 % (30590)Instructions burned: 37 (million)
% 2.74/1.78 % (30590)------------------------------
% 2.74/1.78 % (30590)------------------------------
% 2.74/1.78 % (30595)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/16Mi)
% 2.74/1.78 % (30594)Instruction limit reached!
% 2.74/1.78 % (30594)------------------------------
% 2.74/1.78 % (30594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.78 % (30594)Termination reason: Unknown
% 2.74/1.78 % (30594)Termination phase: shuffling
% 2.74/1.78
% 2.74/1.78 % (30594)Memory used [KB]: 1279
% 2.74/1.78 % (30594)Time elapsed: 0.005 s
% 2.74/1.78 % (30594)Instructions burned: 7 (million)
% 2.74/1.78 % (30594)------------------------------
% 2.74/1.78 % (30594)------------------------------
% 2.74/1.78 % (30596)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/3Mi)
% 2.74/1.78 % (30597)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/3Mi)
% 2.74/1.78 % (30595)Instruction limit reached!
% 2.74/1.78 % (30595)------------------------------
% 2.74/1.78 % (30595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.78 % (30595)Termination reason: Unknown
% 2.74/1.78 % (30595)Termination phase: shuffling
% 2.74/1.78
% 2.74/1.78 % (30595)Memory used [KB]: 1535
% 2.74/1.78 % (30595)Time elapsed: 0.009 s
% 2.74/1.78 % (30595)Instructions burned: 17 (million)
% 2.74/1.78 % (30595)------------------------------
% 2.74/1.78 % (30595)------------------------------
% 2.74/1.78 % (30596)Instruction limit reached!
% 2.74/1.78 % (30596)------------------------------
% 2.74/1.78 % (30596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.78 % (30596)Termination reason: Unknown
% 2.74/1.78 % (30596)Termination phase: shuffling
% 2.74/1.78
% 2.74/1.78 % (30596)Memory used [KB]: 1279
% 2.74/1.78 % (30596)Time elapsed: 0.003 s
% 2.74/1.78 % (30596)Instructions burned: 3 (million)
% 2.74/1.78 % (30596)------------------------------
% 2.74/1.78 % (30596)------------------------------
% 2.74/1.78 % (30597)Instruction limit reached!
% 2.74/1.78 % (30597)------------------------------
% 2.74/1.78 % (30597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.78 % (30597)Termination reason: Unknown
% 2.74/1.78 % (30597)Termination phase: shuffling
% 2.74/1.78
% 2.74/1.78 % (30597)Memory used [KB]: 1279
% 2.74/1.78 % (30597)Time elapsed: 0.003 s
% 2.74/1.78 % (30597)Instructions burned: 3 (million)
% 2.74/1.78 % (30597)------------------------------
% 2.74/1.78 % (30597)------------------------------
% 2.74/1.79 % (30582)First to succeed.
% 2.74/1.79 % (30598)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/7Mi)
% 2.74/1.79 % (30599)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/3Mi)
% 2.74/1.79 % (30598)Instruction limit reached!
% 2.74/1.79 % (30598)------------------------------
% 2.74/1.79 % (30598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.79 % (30598)Termination reason: Unknown
% 2.74/1.79 % (30598)Termination phase: shuffling
% 2.74/1.79
% 2.74/1.79 % (30598)Memory used [KB]: 1279
% 2.74/1.79 % (30598)Time elapsed: 0.005 s
% 2.74/1.79 % (30598)Instructions burned: 7 (million)
% 2.74/1.79 % (30598)------------------------------
% 2.74/1.79 % (30598)------------------------------
% 2.74/1.80 % (30599)Instruction limit reached!
% 2.74/1.80 % (30599)------------------------------
% 2.74/1.80 % (30599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.80 % (30599)Termination reason: Unknown
% 2.74/1.80 % (30599)Termination phase: shuffling
% 2.74/1.80
% 2.74/1.80 % (30599)Memory used [KB]: 1279
% 2.74/1.80 % (30599)Time elapsed: 0.003 s
% 2.74/1.80 % (30599)Instructions burned: 3 (million)
% 2.74/1.80 % (30599)------------------------------
% 2.74/1.80 % (30599)------------------------------
% 2.78/1.80 % (30600)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/4Mi)
% 2.78/1.80 % (30601)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/18Mi)
% 2.78/1.80 % (30602)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30472 for (2999ds/710Mi)
% 2.78/1.80 % (30582)Refutation found. Thanks to Tanya!
% 2.78/1.80 % SZS status Theorem for DTF2THF_30472
% 2.78/1.80 % SZS output start Proof for DTF2THF_30472
% 2.78/1.80 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i).
% 2.78/1.80 thf(func_def_3, type, c_not: $o > $o).
% 2.78/1.80 thf(func_def_4, type, c_and: $o > $o > $o).
% 2.78/1.80 thf(func_def_5, type, c_or: $o > $o > $o).
% 2.78/1.80 thf(func_def_6, type, c_iff: $o > $o > $o).
% 2.78/1.80 thf(func_def_7, type, c_In: $i > $i > $o).
% 2.78/1.80 thf(func_def_8, type, c_Subq: $i > $i > $o).
% 2.78/1.80 thf(func_def_10, type, c_Union: $i > $i).
% 2.78/1.80 thf(func_def_11, type, c_Power: $i > $i).
% 2.78/1.80 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i).
% 2.78/1.80 thf(func_def_13, type, c_TransSet: $i > $o).
% 2.78/1.80 thf(func_def_14, type, c_atleast2: $i > $o).
% 2.78/1.80 thf(func_def_15, type, c_atleast3: $i > $o).
% 2.78/1.80 thf(func_def_16, type, c_atleast4: $i > $o).
% 2.78/1.80 thf(func_def_17, type, c_atleast5: $i > $o).
% 2.78/1.80 thf(func_def_18, type, c_atleast6: $i > $o).
% 2.78/1.80 thf(func_def_19, type, c_exactly2: $i > $o).
% 2.78/1.80 thf(func_def_20, type, c_exactly3: $i > $o).
% 2.78/1.80 thf(func_def_21, type, c_exactly4: $i > $o).
% 2.78/1.80 thf(func_def_22, type, c_exactly5: $i > $o).
% 2.78/1.80 thf(func_def_23, type, c_exu_i: ($i > $o) > $o).
% 2.78/1.80 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o).
% 2.78/1.80 thf(func_def_37, type, c_If_i: $o > $i > $i > $i).
% 2.78/1.80 thf(func_def_38, type, c_exactly1of2: $o > $o > $o).
% 2.78/1.80 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o).
% 2.78/1.80 thf(func_def_40, type, c_nIn: $i > $i > $o).
% 2.78/1.80 thf(func_def_41, type, c_nSubq: $i > $i > $o).
% 2.78/1.80 thf(func_def_42, type, c_UPair: $i > $i > $i).
% 2.78/1.80 thf(func_def_43, type, c_Sing: $i > $i).
% 2.78/1.80 thf(func_def_44, type, c_binunion: $i > $i > $i).
% 2.78/1.80 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i).
% 2.78/1.80 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i).
% 2.78/1.80 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i).
% 2.78/1.80 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i).
% 2.78/1.80 thf(func_def_49, type, c_binintersect: $i > $i > $i).
% 2.78/1.80 thf(func_def_50, type, c_setminus: $i > $i > $i).
% 2.78/1.80 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o).
% 2.78/1.80 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o).
% 2.78/1.80 thf(func_def_53, type, c_atleastp: $i > $i > $o).
% 2.78/1.80 thf(func_def_54, type, c_equip: $i > $i > $o).
% 2.78/1.80 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o).
% 2.78/1.80 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i).
% 2.78/1.80 thf(func_def_57, type, c_ordsucc: $i > $i).
% 2.78/1.80 thf(func_def_58, type, c_nat_p: $i > $o).
% 2.78/1.80 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i).
% 2.78/1.80 thf(func_def_60, type, c_add_nat: $i > $i > $i).
% 2.78/1.80 thf(func_def_61, type, c_mul_nat: $i > $i > $i).
% 2.78/1.80 thf(func_def_62, type, c_ordinal: $i > $o).
% 2.78/1.80 thf(func_def_63, type, c_V_: $i > $i).
% 2.78/1.80 thf(func_def_64, type, c_Inj1: $i > $i).
% 2.78/1.80 thf(func_def_65, type, c_Inj0: $i > $i).
% 2.78/1.80 thf(func_def_66, type, c_Unj: $i > $i).
% 2.78/1.80 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i).
% 2.78/1.80 thf(func_def_68, type, c_setsum: $i > $i > $i).
% 2.78/1.80 thf(func_def_69, type, c_proj0: $i > $i).
% 2.78/1.80 thf(func_def_70, type, c_proj1: $i > $i).
% 2.78/1.80 thf(func_def_71, type, c_binrep: $i > $i > $i).
% 2.78/1.80 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i).
% 2.78/1.80 thf(func_def_73, type, c_setprod: $i > $i > $i).
% 2.78/1.80 thf(func_def_74, type, c_ap: $i > $i > $i).
% 2.78/1.80 thf(func_def_75, type, c_setsum_p: $i > $o).
% 2.78/1.80 thf(func_def_76, type, c_tuple_p: $i > $i > $o).
% 2.78/1.80 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i).
% 2.78/1.80 thf(func_def_78, type, c_setexp: $i > $i > $i).
% 2.78/1.80 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i).
% 2.78/1.80 thf(func_def_80, type, c_set_of_pairs: $i > $o).
% 2.78/1.80 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i).
% 2.78/1.80 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o).
% 2.78/1.80 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o).
% 2.78/1.80 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o).
% 2.78/1.80 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o).
% 2.78/1.80 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 2.78/1.80 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 2.78/1.80 thf(func_def_88, type, c_SNoElts_: $i > $i).
% 2.78/1.80 thf(func_def_89, type, c_SNo_: $i > $i > $o).
% 2.78/1.80 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i).
% 2.78/1.80 thf(func_def_91, type, c_SNo: $i > $o).
% 2.78/1.80 thf(func_def_92, type, c_SNoLev: $i > $i).
% 2.78/1.80 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o).
% 2.78/1.80 thf(func_def_94, type, c_SNoLt: $i > $i > $o).
% 2.78/1.80 thf(func_def_95, type, c_SNoLe: $i > $i > $o).
% 2.78/1.80 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o).
% 2.78/1.80 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o).
% 2.78/1.80 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).
% 2.78/1.80 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).
% 2.78/1.80 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).
% 2.78/1.80 thf(func_def_101, type, c_combinator: $i > $o).
% 2.78/1.80 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o).
% 2.78/1.80 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o).
% 2.78/1.80 thf(func_def_131, type, sP0: ($i > $o) > $o).
% 2.78/1.80 thf(func_def_132, type, sP1: ($i > $o) > $o).
% 2.78/1.80 thf(func_def_133, type, sK2: ($i > $o) > $i).
% 2.78/1.80 thf(func_def_134, type, sK3: ($i > $o) > $i).
% 2.78/1.80 thf(func_def_135, type, sK4: ($i > $o) > $i).
% 2.78/1.80 thf(func_def_136, type, sK5: ($i > $o) > $i > $i).
% 2.78/1.80 thf(func_def_137, type, sK6: ($i > $o) > $i).
% 2.78/1.80 thf(func_def_138, type, sK7: ($i > $o) > $i).
% 2.78/1.80 thf(func_def_139, type, sK8: ($i > $o) > $i).
% 2.78/1.80 thf(func_def_142, type, sK11: $i > $i > $i).
% 2.78/1.80 thf(func_def_143, type, sK12: $i > $i > $i).
% 2.78/1.80 thf(func_def_144, type, sK13: $i > $i > $i).
% 2.78/1.80 thf(func_def_145, type, sK14: $i > $i > $i).
% 2.78/1.80 thf(func_def_146, type, sK15: $i > $i > $i > $o).
% 2.78/1.80 thf(func_def_147, type, sK16: $o > $o > $o).
% 2.78/1.80 thf(func_def_148, type, sK17: $o > $o > $o).
% 2.78/1.80 thf(func_def_149, type, sK18: $i > $i > $i).
% 2.78/1.80 thf(func_def_150, type, sK19: ($i > $i) > $i > $i > $i).
% 2.78/1.80 thf(func_def_151, type, sK20: ($i > $i) > $i > $i > $i > $o).
% 2.78/1.80 thf(func_def_154, type, ph22: !>[X0: $tType]:(X0)).
% 2.78/1.80 thf(f848,plain,(
% 2.78/1.80 $false),
% 2.78/1.80 inference(avatar_sat_refutation,[status(thm)],[f764,f791,f845])).
% 2.78/1.80 thf(f845,plain,(
% 2.78/1.80 ~spl9_18),
% 2.78/1.80 inference(avatar_contradiction_clause,[status(thm)],[f844])).
% 2.78/1.80 thf(f844,plain,(
% 2.78/1.80 $false | ~spl9_18),
% 2.78/1.80 inference(trivial_inequality_removal,[status(thm)],[f826])).
% 2.78/1.80 thf(f826,plain,(
% 2.78/1.80 ($false = $true) | ~spl9_18),
% 2.78/1.80 inference(superposition,[status(thm)],[f763,f554])).
% 2.78/1.80 thf(f554,plain,(
% 2.78/1.80 ($false = sK10)),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f553])).
% 2.78/1.80 thf(f553,plain,(
% 2.78/1.80 ($false = ((^[Y0 : $o]: (Y0)) @ sK10))),
% 2.78/1.80 inference(sigma_clausification,[status(thm)],[f531])).
% 2.78/1.80 thf(f531,plain,(
% 2.78/1.80 ((!! @ $o @ (^[Y0 : $o]: (Y0))) = $false)),
% 2.78/1.80 inference(binary_proxy_clausification,[status(thm)],[f530])).
% 2.78/1.80 thf(f530,plain,(
% 2.78/1.80 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (!! @ $o @ (^[Y6 : $o]: ((((Y5 @ (Y5 @ Y2 @ (Y5 @ Y3 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y2) @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y1 @ (Y5 @ Y1 @ Y1))) @ Y2))) @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y4 @ Y3) @ Y2) @ (Y5 @ Y2 @ Y2))) @ (Y5 @ Y1 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y1) @ Y3)) @ (Y4 @ (Y5 @ Y3 @ Y2)))) @ Y1) @ (Y4 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ (Y5 @ Y2 @ Y3)) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y4 @ Y2) @ Y1)) @ Y1) @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y3 @ Y2) @ Y3)) @ Y1)) @ Y3) @ (Y5 @ Y3 @ (Y5 @ Y2 @ Y2))) @ Y1))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ Y2 @ Y2)) @ (Y4 @ (Y4 @ (Y5 @ Y3 @ (Y4 @ (Y4 @ (Y5 @ Y3 @ Y2))))))) @ Y2) @ Y1) @ (Y5 @ Y1 @ Y3)))) @ Y2) @ Y2) @ (Y4 @ Y1)))) @ (Y5 @ (Y5 @ (Y4 @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ Y2 @ Y1) @ Y3))) @ (Y4 @ (Y5 @ Y2 @ Y2)))) @ Y2) @ (Y4 @ Y2)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y3)))) @ Y3) @ Y1) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ Y2) @ (Y4 @ Y1)) @ Y1))) @ Y3) @ Y1)) = Y1) => ((Y0 @ (Y4 @ Y2)) => Y6)) => Y6))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) != $true)),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f524])).
% 2.78/1.80 thf(f524,plain,(
% 2.78/1.80 (((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((Y5 @ (Y5 @ Y2 @ (Y5 @ Y3 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y2) @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y1 @ (Y5 @ Y1 @ Y1))) @ Y2))) @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y4 @ Y3) @ Y2) @ (Y5 @ Y2 @ Y2))) @ (Y5 @ Y1 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y1) @ Y3)) @ (Y4 @ (Y5 @ Y3 @ Y2)))) @ Y1) @ (Y4 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ (Y5 @ Y2 @ Y3)) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y4 @ Y2) @ Y1)) @ Y1) @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y3 @ Y2) @ Y3)) @ Y1)) @ Y3) @ (Y5 @ Y3 @ (Y5 @ Y2 @ Y2))) @ Y1))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ Y2 @ Y2)) @ (Y4 @ (Y4 @ (Y5 @ Y3 @ (Y4 @ (Y4 @ (Y5 @ Y3 @ Y2))))))) @ Y2) @ Y1) @ (Y5 @ Y1 @ Y3)))) @ Y2) @ Y2) @ (Y4 @ Y1)))) @ (Y5 @ (Y5 @ (Y4 @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ Y2 @ Y1) @ Y3))) @ (Y4 @ (Y5 @ Y2 @ Y2)))) @ Y2) @ (Y4 @ Y2)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y3)))) @ Y3) @ Y1) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ Y2) @ (Y4 @ Y1)) @ Y1))) @ Y3) @ Y1)) = Y1) @ (Y0 @ (Y4 @ Y2)))))))))))))))) != $true)),
% 2.78/1.80 inference(definition_unfolding,[status(thm)],[f403,f435,f382])).
% 2.78/1.80 thf(f382,plain,(
% 2.78/1.80 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 2.78/1.80 inference(cnf_transformation,[status(thm)],[f228])).
% 2.78/1.80 thf(f228,plain,(
% 2.78/1.80 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 2.78/1.80 inference(fool_elimination,[status(thm)],[f227])).
% 2.78/1.80 thf(f227,plain,(
% 2.78/1.80 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 2.78/1.80 inference(rectify,[status(thm)],[f14])).
% 2.78/1.80 thf(f14,axiom,(
% 2.78/1.80 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 2.78/1.80 file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',ax14)).
% 2.78/1.80 thf(f435,plain,(
% 2.78/1.80 (c_not = (^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))))),
% 2.78/1.80 inference(definition_unfolding,[status(thm)],[f375,f409])).
% 2.78/1.80 thf(f409,plain,(
% 2.78/1.80 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 2.78/1.80 inference(cnf_transformation,[status(thm)],[f246])).
% 2.78/1.80 thf(f246,plain,(
% 2.78/1.80 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 2.78/1.80 inference(fool_elimination,[status(thm)],[f245])).
% 2.78/1.80 thf(f245,plain,(
% 2.78/1.80 (c_False = ! [X0 : $o] : X0)),
% 2.78/1.80 inference(rectify,[status(thm)],[f11])).
% 2.78/1.80 thf(f11,axiom,(
% 2.78/1.80 (c_False = ! [X0 : $o] : X0)),
% 2.78/1.80 file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',ax11)).
% 2.78/1.80 thf(f375,plain,(
% 2.78/1.80 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 2.78/1.80 inference(cnf_transformation,[status(thm)],[f193])).
% 2.78/1.80 thf(f193,plain,(
% 2.78/1.80 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 2.78/1.80 inference(fool_elimination,[status(thm)],[f192])).
% 2.78/1.80 thf(f192,plain,(
% 2.78/1.80 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 2.78/1.80 inference(rectify,[status(thm)],[f13])).
% 2.78/1.80 thf(f13,axiom,(
% 2.78/1.80 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 2.78/1.80 file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',ax13)).
% 2.78/1.80 thf(f403,plain,(
% 2.78/1.80 ($true != (c_not @ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (c_and @ ((Y5 @ (Y5 @ Y2 @ (Y5 @ Y3 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y2) @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y1 @ (Y5 @ Y1 @ Y1))) @ Y2))) @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y4 @ Y3) @ Y2) @ (Y5 @ Y2 @ Y2))) @ (Y5 @ Y1 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y1) @ Y3)) @ (Y4 @ (Y5 @ Y3 @ Y2)))) @ Y1) @ (Y4 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ (Y5 @ Y2 @ Y3)) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y4 @ Y2) @ Y1)) @ Y1) @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y3 @ Y2) @ Y3)) @ Y1)) @ Y3) @ (Y5 @ Y3 @ (Y5 @ Y2 @ Y2))) @ Y1))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ Y2 @ Y2)) @ (Y4 @ (Y4 @ (Y5 @ Y3 @ (Y4 @ (Y4 @ (Y5 @ Y3 @ Y2))))))) @ Y2) @ Y1) @ (Y5 @ Y1 @ Y3)))) @ Y2) @ Y2) @ (Y4 @ Y1)))) @ (Y5 @ (Y5 @ (Y4 @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ Y2 @ Y1) @ Y3))) @ (Y4 @ (Y5 @ Y2 @ Y2)))) @ Y2) @ (Y4 @ Y2)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y3)))) @ Y3) @ Y1) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ Y2) @ (Y4 @ Y1)) @ Y1))) @ Y3) @ Y1)) = Y1) @ (Y0 @ (Y4 @ Y2)))))))))))))))))),
% 2.78/1.80 inference(cnf_transformation,[status(thm)],[f288])).
% 2.78/1.80 thf(f288,plain,(
% 2.78/1.80 ($true != (c_not @ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (c_and @ ((Y5 @ (Y5 @ Y2 @ (Y5 @ Y3 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y2) @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y1 @ (Y5 @ Y1 @ Y1))) @ Y2))) @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y4 @ Y3) @ Y2) @ (Y5 @ Y2 @ Y2))) @ (Y5 @ Y1 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y1) @ Y3)) @ (Y4 @ (Y5 @ Y3 @ Y2)))) @ Y1) @ (Y4 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ (Y5 @ Y2 @ Y3)) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y4 @ Y2) @ Y1)) @ Y1) @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y3 @ Y2) @ Y3)) @ Y1)) @ Y3) @ (Y5 @ Y3 @ (Y5 @ Y2 @ Y2))) @ Y1))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ Y2 @ Y2)) @ (Y4 @ (Y4 @ (Y5 @ Y3 @ (Y4 @ (Y4 @ (Y5 @ Y3 @ Y2))))))) @ Y2) @ Y1) @ (Y5 @ Y1 @ Y3)))) @ Y2) @ Y2) @ (Y4 @ Y1)))) @ (Y5 @ (Y5 @ (Y4 @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ Y2 @ Y1) @ Y3))) @ (Y4 @ (Y5 @ Y2 @ Y2)))) @ Y2) @ (Y4 @ Y2)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y3)))) @ Y3) @ Y1) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ Y2) @ (Y4 @ Y1)) @ Y1))) @ Y3) @ Y1)) = Y1) @ (Y0 @ (Y4 @ Y2)))))))))))))))))),
% 2.78/1.80 inference(flattening,[status(thm)],[f206])).
% 2.78/1.80 thf(f206,plain,(
% 2.78/1.80 ~($true = (c_not @ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (c_and @ ((Y5 @ (Y5 @ Y2 @ (Y5 @ Y3 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y2) @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y1 @ (Y5 @ Y1 @ Y1))) @ Y2))) @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y4 @ Y3) @ Y2) @ (Y5 @ Y2 @ Y2))) @ (Y5 @ Y1 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y1) @ Y3)) @ (Y4 @ (Y5 @ Y3 @ Y2)))) @ Y1) @ (Y4 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ (Y5 @ Y2 @ Y3)) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y4 @ Y2) @ Y1)) @ Y1) @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y3 @ Y2) @ Y3)) @ Y1)) @ Y3) @ (Y5 @ Y3 @ (Y5 @ Y2 @ Y2))) @ Y1))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ Y2 @ Y2)) @ (Y4 @ (Y4 @ (Y5 @ Y3 @ (Y4 @ (Y4 @ (Y5 @ Y3 @ Y2))))))) @ Y2) @ Y1) @ (Y5 @ Y1 @ Y3)))) @ Y2) @ Y2) @ (Y4 @ Y1)))) @ (Y5 @ (Y5 @ (Y4 @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ Y2 @ Y1) @ Y3))) @ (Y4 @ (Y5 @ Y2 @ Y2)))) @ Y2) @ (Y4 @ Y2)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y3)))) @ Y3) @ Y1) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ Y2) @ (Y4 @ Y1)) @ Y1))) @ Y3) @ Y1)) = Y1) @ (Y0 @ (Y4 @ Y2)))))))))))))))))),
% 2.78/1.80 inference(fool_elimination,[status(thm)],[f205])).
% 2.78/1.80 thf(f205,plain,(
% 2.78/1.80 ~(c_not @ ! [X0 : $i > $i > $i,X2 : $i > $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i > $o] : (c_and @ ((X0 @ (X0 @ X5 @ (X0 @ X4 @ (X0 @ (X0 @ (X0 @ (X0 @ X6 @ (X0 @ (X0 @ X5 @ (X0 @ X5 @ (X0 @ (X0 @ X5 @ (X0 @ (X2 @ X5) @ (X0 @ (X0 @ X4 @ (X0 @ X6 @ (X0 @ X6 @ X6))) @ X5))) @ (X0 @ (X2 @ (X0 @ (X0 @ (X2 @ X4) @ X5) @ (X0 @ X5 @ X5))) @ (X0 @ X6 @ (X0 @ X6 @ (X0 @ (X0 @ (X0 @ X5 @ (X0 @ (X0 @ X5 @ (X0 @ (X2 @ X6) @ X4)) @ (X2 @ (X0 @ X4 @ X5)))) @ X6) @ (X2 @ (X0 @ (X0 @ X4 @ (X0 @ X5 @ (X0 @ (X2 @ (X0 @ X5 @ X4)) @ X5))) @ (X0 @ (X0 @ (X0 @ X6 @ (X0 @ (X2 @ X5) @ X6)) @ X6) @ (X2 @ (X2 @ (X0 @ (X0 @ (X0 @ (X0 @ X5 @ (X0 @ (X0 @ X6 @ (X0 @ (X0 @ X4 @ X5) @ X4)) @ X6)) @ X4) @ (X0 @ X4 @ (X0 @ X5 @ X5))) @ X6))))))))))))) @ (X0 @ (X0 @ (X0 @ (X0 @ (X0 @ X6 @ (X0 @ X5 @ X5)) @ (X2 @ (X2 @ (X0 @ X4 @ (X2 @ (X2 @ (X0 @ X4 @ X5))))))) @ X5) @ X6) @ (X0 @ X6 @ X4)))) @ X5) @ X5) @ (X2 @ X6)))) @ (X0 @ (X0 @ (X2 @ (X0 @ (X2 @ (X0 @ (X0 @ (X0 @ (X0 @ X4 @ (X0 @ (X2 @ (X2 @ (X0 @ (X0 @ X5 @ X6) @ X4))) @ (X2 @ (X0 @ X5 @ X5)))) @ X5) @ (X2 @ X5)) @ (X0 @ (X0 @ (X0 @ (X0 @ (X0 @ X5 @ X4) @ (X2 @ (X2 @ (X2 @ X4)))) @ X4) @ X6) @ X5))) @ (X0 @ (X0 @ (X0 @ X6 @ X5) @ (X2 @ X6)) @ X6))) @ X4) @ X6)) = X6) @ (X7 @ (X2 @ X5))))),
% 2.78/1.80 inference(rectify,[status(thm)],[f110])).
% 2.78/1.80 thf(f110,negated_conjecture,(
% 2.78/1.80 ~(c_not @ ! [X1 : $i > $i > $i,X0 : $i > $i > $o,X4 : $i > $i,X2 : $i > $o,X7 : $i,X5 : $i,X6 : $i,X3 : $i > $o] : (c_and @ ((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)) = X6) @ ? [X8 : $i] : (X3 @ (X4 @ X5))))),
% 2.78/1.80 inference(negated_conjecture,[status(cth)],[f109])).
% 2.78/1.80 thf(f109,conjecture,(
% 2.78/1.80 (c_not @ ! [X1 : $i > $i > $i,X0 : $i > $i > $o,X4 : $i > $i,X2 : $i > $o,X7 : $i,X5 : $i,X6 : $i,X3 : $i > $o] : (c_and @ ((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)) = X6) @ ? [X8 : $i] : (X3 @ (X4 @ X5))))),
% 2.78/1.80 file('/export/starexec/sandbox/tmp/tmp.vv0oIgGzul/DTF2THF_30472.p',conj)).
% 2.78/1.80 thf(f763,plain,(
% 2.78/1.80 ( ! [X3 : $i,X1 : $i > $o,X5 : $i > $i] : (((X1 @ (X5 @ X3)) = $true)) ) | ~spl9_18),
% 2.78/1.80 inference(avatar_component_clause,[status(thm)],[f762])).
% 2.78/1.80 thf(f762,definition,(
% 2.78/1.80 spl9_18 <=> ! [X5 : $i > $i,X1 : $i > $o,X3 : $i] : ((X1 @ (X5 @ X3)) = $true)),
% 2.78/1.80 introduced(definition,[new_symbols(naming,[spl9_18])],[avatar_definition])).
% 2.78/1.80 thf(f791,plain,(
% 2.78/1.80 ~spl9_2),
% 2.78/1.80 inference(avatar_contradiction_clause,[status(thm)],[f790])).
% 2.78/1.80 thf(f790,plain,(
% 2.78/1.80 $false | ~spl9_2),
% 2.78/1.80 inference(trivial_inequality_removal,[status(thm)],[f786])).
% 2.78/1.80 thf(f786,plain,(
% 2.78/1.80 ($false = $true) | ~spl9_2),
% 2.78/1.80 inference(superposition,[status(thm)],[f554,f695])).
% 2.78/1.80 thf(f695,plain,(
% 2.78/1.80 ( ! [X0 : $o] : (($true = X0)) ) | ~spl9_2),
% 2.78/1.80 inference(avatar_component_clause,[status(thm)],[f694])).
% 2.78/1.80 thf(f694,definition,(
% 2.78/1.80 spl9_2 <=> ! [X0 : $o] : ($true = X0)),
% 2.78/1.80 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 2.78/1.80 thf(f764,plain,(
% 2.78/1.80 spl9_18 | spl9_2),
% 2.78/1.80 inference(avatar_split_clause,[status(thm)],[f552,f694,f762])).
% 2.78/1.80 thf(f552,plain,(
% 2.78/1.80 ( ! [X3 : $i,X1 : $i > $o,X7 : $o,X5 : $i > $i] : (((X1 @ (X5 @ X3)) = $true) | ($true = X7)) )),
% 2.78/1.80 inference(binary_proxy_clausification,[status(thm)],[f548])).
% 2.78/1.80 thf(f548,plain,(
% 2.78/1.80 ( ! [X3 : $i,X1 : $i > $o,X7 : $o,X5 : $i > $i] : (($false = ((X1 @ (X5 @ X3)) => X7)) | ($true = X7)) )),
% 2.78/1.80 inference(binary_proxy_clausification,[status(thm)],[f547])).
% 2.78/1.80 thf(f547,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X6 : $i > $i > $i,X7 : $o,X4 : $i,X5 : $i > $i] : (($true = X7) | ((((X6 @ (X6 @ X3 @ (X6 @ X4 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X3 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X3) @ (X6 @ (X6 @ X4 @ (X6 @ X2 @ (X6 @ X2 @ X2))) @ X3))) @ (X6 @ (X5 @ (X6 @ (X6 @ (X5 @ X4) @ X3) @ (X6 @ X3 @ X3))) @ (X6 @ X2 @ (X6 @ X2 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X2) @ X4)) @ (X5 @ (X6 @ X4 @ X3)))) @ X2) @ (X5 @ (X6 @ (X6 @ X4 @ (X6 @ X3 @ (X6 @ (X5 @ (X6 @ X3 @ X4)) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X5 @ X3) @ X2)) @ X2) @ (X5 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (X6 @ X4 @ (X6 @ X3 @ X3))) @ X2))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ X3 @ X3)) @ (X5 @ (X5 @ (X6 @ X4 @ (X5 @ (X5 @ (X6 @ X4 @ X3))))))) @ X3) @ X2) @ (X6 @ X2 @ X4)))) @ X3) @ X3) @ (X5 @ X2)))) @ (X6 @ (X6 @ (X5 @ (X6 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X4 @ (X6 @ (X5 @ (X5 @ (X6 @ (X6 @ X3 @ X2) @ X4))) @ (X5 @ (X6 @ X3 @ X3)))) @ X3) @ (X5 @ X3)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X4)))) @ X4) @ X2) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ X3) @ (X5 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (X5 @ X3)) => X7)) = $false)) )),
% 2.78/1.80 inference(binary_proxy_clausification,[status(thm)],[f546])).
% 2.78/1.80 thf(f546,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X6 : $i > $i > $i,X7 : $o,X4 : $i,X5 : $i > $i] : (($true = ((((X6 @ (X6 @ X3 @ (X6 @ X4 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X3 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X3) @ (X6 @ (X6 @ X4 @ (X6 @ X2 @ (X6 @ X2 @ X2))) @ X3))) @ (X6 @ (X5 @ (X6 @ (X6 @ (X5 @ X4) @ X3) @ (X6 @ X3 @ X3))) @ (X6 @ X2 @ (X6 @ X2 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X2) @ X4)) @ (X5 @ (X6 @ X4 @ X3)))) @ X2) @ (X5 @ (X6 @ (X6 @ X4 @ (X6 @ X3 @ (X6 @ (X5 @ (X6 @ X3 @ X4)) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X5 @ X3) @ X2)) @ X2) @ (X5 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (X6 @ X4 @ (X6 @ X3 @ X3))) @ X2))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ X3 @ X3)) @ (X5 @ (X5 @ (X6 @ X4 @ (X5 @ (X5 @ (X6 @ X4 @ X3))))))) @ X3) @ X2) @ (X6 @ X2 @ X4)))) @ X3) @ X3) @ (X5 @ X2)))) @ (X6 @ (X6 @ (X5 @ (X6 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X4 @ (X6 @ (X5 @ (X5 @ (X6 @ (X6 @ X3 @ X2) @ X4))) @ (X5 @ (X6 @ X3 @ X3)))) @ X3) @ (X5 @ X3)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X4)))) @ X4) @ X2) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ X3) @ (X5 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (X5 @ X3)) => X7)) => X7))) )),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f545])).
% 2.78/1.80 thf(f545,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X6 : $i > $i > $i,X7 : $o,X4 : $i,X5 : $i > $i] : (($true = ((^[Y0 : $o]: ((((X6 @ (X6 @ X3 @ (X6 @ X4 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X3 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X3) @ (X6 @ (X6 @ X4 @ (X6 @ X2 @ (X6 @ X2 @ X2))) @ X3))) @ (X6 @ (X5 @ (X6 @ (X6 @ (X5 @ X4) @ X3) @ (X6 @ X3 @ X3))) @ (X6 @ X2 @ (X6 @ X2 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X2) @ X4)) @ (X5 @ (X6 @ X4 @ X3)))) @ X2) @ (X5 @ (X6 @ (X6 @ X4 @ (X6 @ X3 @ (X6 @ (X5 @ (X6 @ X3 @ X4)) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X5 @ X3) @ X2)) @ X2) @ (X5 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (X6 @ X4 @ (X6 @ X3 @ X3))) @ X2))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ X3 @ X3)) @ (X5 @ (X5 @ (X6 @ X4 @ (X5 @ (X5 @ (X6 @ X4 @ X3))))))) @ X3) @ X2) @ (X6 @ X2 @ X4)))) @ X3) @ X3) @ (X5 @ X2)))) @ (X6 @ (X6 @ (X5 @ (X6 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X4 @ (X6 @ (X5 @ (X5 @ (X6 @ (X6 @ X3 @ X2) @ X4))) @ (X5 @ (X6 @ X3 @ X3)))) @ X3) @ (X5 @ X3)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X4)))) @ X4) @ X2) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ X3) @ (X5 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (X5 @ X3)) => Y0)) => Y0)) @ X7))) )),
% 2.78/1.80 inference(pi_clausification,[status(thm)],[f544])).
% 2.78/1.80 thf(f544,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X6 : $i > $i > $i,X4 : $i,X5 : $i > $i] : (((!! @ $o @ (^[Y0 : $o]: ((((X6 @ (X6 @ X3 @ (X6 @ X4 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X3 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X3) @ (X6 @ (X6 @ X4 @ (X6 @ X2 @ (X6 @ X2 @ X2))) @ X3))) @ (X6 @ (X5 @ (X6 @ (X6 @ (X5 @ X4) @ X3) @ (X6 @ X3 @ X3))) @ (X6 @ X2 @ (X6 @ X2 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X3 @ (X6 @ (X5 @ X2) @ X4)) @ (X5 @ (X6 @ X4 @ X3)))) @ X2) @ (X5 @ (X6 @ (X6 @ X4 @ (X6 @ X3 @ (X6 @ (X5 @ (X6 @ X3 @ X4)) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ (X5 @ X3) @ X2)) @ X2) @ (X5 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X6 @ X2 @ (X6 @ (X6 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (X6 @ X4 @ (X6 @ X3 @ X3))) @ X2))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X2 @ (X6 @ X3 @ X3)) @ (X5 @ (X5 @ (X6 @ X4 @ (X5 @ (X5 @ (X6 @ X4 @ X3))))))) @ X3) @ X2) @ (X6 @ X2 @ X4)))) @ X3) @ X3) @ (X5 @ X2)))) @ (X6 @ (X6 @ (X5 @ (X6 @ (X5 @ (X6 @ (X6 @ (X6 @ (X6 @ X4 @ (X6 @ (X5 @ (X5 @ (X6 @ (X6 @ X3 @ X2) @ X4))) @ (X5 @ (X6 @ X3 @ X3)))) @ X3) @ (X5 @ X3)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X4)))) @ X4) @ X2) @ X3))) @ (X6 @ (X6 @ (X6 @ X2 @ X3) @ (X5 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (X5 @ X3)) => Y0)) => Y0))) = $true)) )),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f543])).
% 2.78/1.80 thf(f543,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X6 : $i > $i > $i,X4 : $i,X5 : $i > $i] : ((((^[Y0 : $i > $i > $i]: (!! @ $o @ (^[Y1 : $o]: ((((Y0 @ (Y0 @ X3 @ (Y0 @ X4 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X2 @ (Y0 @ (Y0 @ X3 @ (Y0 @ X3 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (X5 @ X3) @ (Y0 @ (Y0 @ X4 @ (Y0 @ X2 @ (Y0 @ X2 @ X2))) @ X3))) @ (Y0 @ (X5 @ (Y0 @ (Y0 @ (X5 @ X4) @ X3) @ (Y0 @ X3 @ X3))) @ (Y0 @ X2 @ (Y0 @ X2 @ (Y0 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (X5 @ X2) @ X4)) @ (X5 @ (Y0 @ X4 @ X3)))) @ X2) @ (X5 @ (Y0 @ (Y0 @ X4 @ (Y0 @ X3 @ (Y0 @ (X5 @ (Y0 @ X3 @ X4)) @ X3))) @ (Y0 @ (Y0 @ (Y0 @ X2 @ (Y0 @ (X5 @ X3) @ X2)) @ X2) @ (X5 @ (X5 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (Y0 @ X2 @ (Y0 @ (Y0 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (Y0 @ X4 @ (Y0 @ X3 @ X3))) @ X2))))))))))))) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X2 @ (Y0 @ X3 @ X3)) @ (X5 @ (X5 @ (Y0 @ X4 @ (X5 @ (X5 @ (Y0 @ X4 @ X3))))))) @ X3) @ X2) @ (Y0 @ X2 @ X4)))) @ X3) @ X3) @ (X5 @ X2)))) @ (Y0 @ (Y0 @ (X5 @ (Y0 @ (X5 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X4 @ (Y0 @ (X5 @ (X5 @ (Y0 @ (Y0 @ X3 @ X2) @ X4))) @ (X5 @ (Y0 @ X3 @ X3)))) @ X3) @ (X5 @ X3)) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X4)))) @ X4) @ X2) @ X3))) @ (Y0 @ (Y0 @ (Y0 @ X2 @ X3) @ (X5 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (X5 @ X3)) => Y1)) => Y1)))) @ X6) = $true)) )),
% 2.78/1.80 inference(pi_clausification,[status(thm)],[f542])).
% 2.78/1.80 thf(f542,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X4 : $i,X5 : $i > $i] : (((!! @ ($i > $i > $i) @ (^[Y0 : $i > $i > $i]: (!! @ $o @ (^[Y1 : $o]: ((((Y0 @ (Y0 @ X3 @ (Y0 @ X4 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X2 @ (Y0 @ (Y0 @ X3 @ (Y0 @ X3 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (X5 @ X3) @ (Y0 @ (Y0 @ X4 @ (Y0 @ X2 @ (Y0 @ X2 @ X2))) @ X3))) @ (Y0 @ (X5 @ (Y0 @ (Y0 @ (X5 @ X4) @ X3) @ (Y0 @ X3 @ X3))) @ (Y0 @ X2 @ (Y0 @ X2 @ (Y0 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (X5 @ X2) @ X4)) @ (X5 @ (Y0 @ X4 @ X3)))) @ X2) @ (X5 @ (Y0 @ (Y0 @ X4 @ (Y0 @ X3 @ (Y0 @ (X5 @ (Y0 @ X3 @ X4)) @ X3))) @ (Y0 @ (Y0 @ (Y0 @ X2 @ (Y0 @ (X5 @ X3) @ X2)) @ X2) @ (X5 @ (X5 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (Y0 @ X2 @ (Y0 @ (Y0 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (Y0 @ X4 @ (Y0 @ X3 @ X3))) @ X2))))))))))))) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X2 @ (Y0 @ X3 @ X3)) @ (X5 @ (X5 @ (Y0 @ X4 @ (X5 @ (X5 @ (Y0 @ X4 @ X3))))))) @ X3) @ X2) @ (Y0 @ X2 @ X4)))) @ X3) @ X3) @ (X5 @ X2)))) @ (Y0 @ (Y0 @ (X5 @ (Y0 @ (X5 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X4 @ (Y0 @ (X5 @ (X5 @ (Y0 @ (Y0 @ X3 @ X2) @ X4))) @ (X5 @ (Y0 @ X3 @ X3)))) @ X3) @ (X5 @ X3)) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X4)))) @ X4) @ X2) @ X3))) @ (Y0 @ (Y0 @ (Y0 @ X2 @ X3) @ (X5 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (X5 @ X3)) => Y1)) => Y1))))) = $true)) )),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f541])).
% 2.78/1.80 thf(f541,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X4 : $i,X5 : $i > $i] : ((((^[Y0 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: (!! @ $o @ (^[Y2 : $o]: ((((Y1 @ (Y1 @ X3 @ (Y1 @ X4 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X2 @ (Y1 @ (Y1 @ X3 @ (Y1 @ X3 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y0 @ X3) @ (Y1 @ (Y1 @ X4 @ (Y1 @ X2 @ (Y1 @ X2 @ X2))) @ X3))) @ (Y1 @ (Y0 @ (Y1 @ (Y1 @ (Y0 @ X4) @ X3) @ (Y1 @ X3 @ X3))) @ (Y1 @ X2 @ (Y1 @ X2 @ (Y1 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y0 @ X2) @ X4)) @ (Y0 @ (Y1 @ X4 @ X3)))) @ X2) @ (Y0 @ (Y1 @ (Y1 @ X4 @ (Y1 @ X3 @ (Y1 @ (Y0 @ (Y1 @ X3 @ X4)) @ X3))) @ (Y1 @ (Y1 @ (Y1 @ X2 @ (Y1 @ (Y0 @ X3) @ X2)) @ X2) @ (Y0 @ (Y0 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y1 @ X2 @ (Y1 @ (Y1 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (Y1 @ X4 @ (Y1 @ X3 @ X3))) @ X2))))))))))))) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X2 @ (Y1 @ X3 @ X3)) @ (Y0 @ (Y0 @ (Y1 @ X4 @ (Y0 @ (Y0 @ (Y1 @ X4 @ X3))))))) @ X3) @ X2) @ (Y1 @ X2 @ X4)))) @ X3) @ X3) @ (Y0 @ X2)))) @ (Y1 @ (Y1 @ (Y0 @ (Y1 @ (Y0 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X4 @ (Y1 @ (Y0 @ (Y0 @ (Y1 @ (Y1 @ X3 @ X2) @ X4))) @ (Y0 @ (Y1 @ X3 @ X3)))) @ X3) @ (Y0 @ X3)) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ X4) @ (Y0 @ (Y0 @ (Y0 @ X4)))) @ X4) @ X2) @ X3))) @ (Y1 @ (Y1 @ (Y1 @ X2 @ X3) @ (Y0 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (Y0 @ X3)) => Y2)) => Y2)))))) @ X5) = $true)) )),
% 2.78/1.80 inference(pi_clausification,[status(thm)],[f540])).
% 2.78/1.80 thf(f540,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X4 : $i] : (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: (!! @ $o @ (^[Y2 : $o]: ((((Y1 @ (Y1 @ X3 @ (Y1 @ X4 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X2 @ (Y1 @ (Y1 @ X3 @ (Y1 @ X3 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y0 @ X3) @ (Y1 @ (Y1 @ X4 @ (Y1 @ X2 @ (Y1 @ X2 @ X2))) @ X3))) @ (Y1 @ (Y0 @ (Y1 @ (Y1 @ (Y0 @ X4) @ X3) @ (Y1 @ X3 @ X3))) @ (Y1 @ X2 @ (Y1 @ X2 @ (Y1 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y0 @ X2) @ X4)) @ (Y0 @ (Y1 @ X4 @ X3)))) @ X2) @ (Y0 @ (Y1 @ (Y1 @ X4 @ (Y1 @ X3 @ (Y1 @ (Y0 @ (Y1 @ X3 @ X4)) @ X3))) @ (Y1 @ (Y1 @ (Y1 @ X2 @ (Y1 @ (Y0 @ X3) @ X2)) @ X2) @ (Y0 @ (Y0 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (Y1 @ X2 @ (Y1 @ (Y1 @ X4 @ X3) @ X4)) @ X2)) @ X4) @ (Y1 @ X4 @ (Y1 @ X3 @ X3))) @ X2))))))))))))) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X2 @ (Y1 @ X3 @ X3)) @ (Y0 @ (Y0 @ (Y1 @ X4 @ (Y0 @ (Y0 @ (Y1 @ X4 @ X3))))))) @ X3) @ X2) @ (Y1 @ X2 @ X4)))) @ X3) @ X3) @ (Y0 @ X2)))) @ (Y1 @ (Y1 @ (Y0 @ (Y1 @ (Y0 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X4 @ (Y1 @ (Y0 @ (Y0 @ (Y1 @ (Y1 @ X3 @ X2) @ X4))) @ (Y0 @ (Y1 @ X3 @ X3)))) @ X3) @ (Y0 @ X3)) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ X4) @ (Y0 @ (Y0 @ (Y0 @ X4)))) @ X4) @ X2) @ X3))) @ (Y1 @ (Y1 @ (Y1 @ X2 @ X3) @ (Y0 @ X2)) @ X2))) @ X4) @ X2)) = X2) => ((X1 @ (Y0 @ X3)) => Y2)) => Y2))))))) = $true)) )),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f539])).
% 2.78/1.80 thf(f539,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o,X4 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: (!! @ $o @ (^[Y3 : $o]: ((((Y2 @ (Y2 @ X3 @ (Y2 @ Y0 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ X3 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y1 @ X3) @ (Y2 @ (Y2 @ Y0 @ (Y2 @ X2 @ (Y2 @ X2 @ X2))) @ X3))) @ (Y2 @ (Y1 @ (Y2 @ (Y2 @ (Y1 @ Y0) @ X3) @ (Y2 @ X3 @ X3))) @ (Y2 @ X2 @ (Y2 @ X2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y1 @ X2) @ Y0)) @ (Y1 @ (Y2 @ Y0 @ X3)))) @ X2) @ (Y1 @ (Y2 @ (Y2 @ Y0 @ (Y2 @ X3 @ (Y2 @ (Y1 @ (Y2 @ X3 @ Y0)) @ X3))) @ (Y2 @ (Y2 @ (Y2 @ X2 @ (Y2 @ (Y1 @ X3) @ X2)) @ X2) @ (Y1 @ (Y1 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y2 @ X2 @ (Y2 @ (Y2 @ Y0 @ X3) @ Y0)) @ X2)) @ Y0) @ (Y2 @ Y0 @ (Y2 @ X3 @ X3))) @ X2))))))))))))) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X2 @ (Y2 @ X3 @ X3)) @ (Y1 @ (Y1 @ (Y2 @ Y0 @ (Y1 @ (Y1 @ (Y2 @ Y0 @ X3))))))) @ X3) @ X2) @ (Y2 @ X2 @ Y0)))) @ X3) @ X3) @ (Y1 @ X2)))) @ (Y2 @ (Y2 @ (Y1 @ (Y2 @ (Y1 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y0 @ (Y2 @ (Y1 @ (Y1 @ (Y2 @ (Y2 @ X3 @ X2) @ Y0))) @ (Y1 @ (Y2 @ X3 @ X3)))) @ X3) @ (Y1 @ X3)) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ Y0) @ (Y1 @ (Y1 @ (Y1 @ Y0)))) @ Y0) @ X2) @ X3))) @ (Y2 @ (Y2 @ (Y2 @ X2 @ X3) @ (Y1 @ X2)) @ X2))) @ Y0) @ X2)) = X2) => ((X1 @ (Y1 @ X3)) => Y3)) => Y3)))))))) @ X4))) )),
% 2.78/1.80 inference(pi_clausification,[status(thm)],[f538])).
% 2.78/1.80 thf(f538,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: (!! @ $o @ (^[Y3 : $o]: ((((Y2 @ (Y2 @ X3 @ (Y2 @ Y0 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ X3 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y1 @ X3) @ (Y2 @ (Y2 @ Y0 @ (Y2 @ X2 @ (Y2 @ X2 @ X2))) @ X3))) @ (Y2 @ (Y1 @ (Y2 @ (Y2 @ (Y1 @ Y0) @ X3) @ (Y2 @ X3 @ X3))) @ (Y2 @ X2 @ (Y2 @ X2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y1 @ X2) @ Y0)) @ (Y1 @ (Y2 @ Y0 @ X3)))) @ X2) @ (Y1 @ (Y2 @ (Y2 @ Y0 @ (Y2 @ X3 @ (Y2 @ (Y1 @ (Y2 @ X3 @ Y0)) @ X3))) @ (Y2 @ (Y2 @ (Y2 @ X2 @ (Y2 @ (Y1 @ X3) @ X2)) @ X2) @ (Y1 @ (Y1 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (Y2 @ X2 @ (Y2 @ (Y2 @ Y0 @ X3) @ Y0)) @ X2)) @ Y0) @ (Y2 @ Y0 @ (Y2 @ X3 @ X3))) @ X2))))))))))))) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X2 @ (Y2 @ X3 @ X3)) @ (Y1 @ (Y1 @ (Y2 @ Y0 @ (Y1 @ (Y1 @ (Y2 @ Y0 @ X3))))))) @ X3) @ X2) @ (Y2 @ X2 @ Y0)))) @ X3) @ X3) @ (Y1 @ X2)))) @ (Y2 @ (Y2 @ (Y1 @ (Y2 @ (Y1 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y0 @ (Y2 @ (Y1 @ (Y1 @ (Y2 @ (Y2 @ X3 @ X2) @ Y0))) @ (Y1 @ (Y2 @ X3 @ X3)))) @ X3) @ (Y1 @ X3)) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ Y0) @ (Y1 @ (Y1 @ (Y1 @ Y0)))) @ Y0) @ X2) @ X3))) @ (Y2 @ (Y2 @ (Y2 @ X2 @ X3) @ (Y1 @ X2)) @ X2))) @ Y0) @ X2)) = X2) => ((X1 @ (Y1 @ X3)) => Y3)) => Y3))))))))) = $true)) )),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f537])).
% 2.78/1.80 thf(f537,plain,(
% 2.78/1.80 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $o @ (^[Y4 : $o]: ((((Y3 @ (Y3 @ Y0 @ (Y3 @ Y1 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X2 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y2 @ Y0) @ (Y3 @ (Y3 @ Y1 @ (Y3 @ X2 @ (Y3 @ X2 @ X2))) @ Y0))) @ (Y3 @ (Y2 @ (Y3 @ (Y3 @ (Y2 @ Y1) @ Y0) @ (Y3 @ Y0 @ Y0))) @ (Y3 @ X2 @ (Y3 @ X2 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y2 @ X2) @ Y1)) @ (Y2 @ (Y3 @ Y1 @ Y0)))) @ X2) @ (Y2 @ (Y3 @ (Y3 @ Y1 @ (Y3 @ Y0 @ (Y3 @ (Y2 @ (Y3 @ Y0 @ Y1)) @ Y0))) @ (Y3 @ (Y3 @ (Y3 @ X2 @ (Y3 @ (Y2 @ Y0) @ X2)) @ X2) @ (Y2 @ (Y2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ X2 @ (Y3 @ (Y3 @ Y1 @ Y0) @ Y1)) @ X2)) @ Y1) @ (Y3 @ Y1 @ (Y3 @ Y0 @ Y0))) @ X2))))))))))))) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X2 @ (Y3 @ Y0 @ Y0)) @ (Y2 @ (Y2 @ (Y3 @ Y1 @ (Y2 @ (Y2 @ (Y3 @ Y1 @ Y0))))))) @ Y0) @ X2) @ (Y3 @ X2 @ Y1)))) @ Y0) @ Y0) @ (Y2 @ X2)))) @ (Y3 @ (Y3 @ (Y2 @ (Y3 @ (Y2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y1 @ (Y3 @ (Y2 @ (Y2 @ (Y3 @ (Y3 @ Y0 @ X2) @ Y1))) @ (Y2 @ (Y3 @ Y0 @ Y0)))) @ Y0) @ (Y2 @ Y0)) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ Y1) @ (Y2 @ (Y2 @ (Y2 @ Y1)))) @ Y1) @ X2) @ Y0))) @ (Y3 @ (Y3 @ (Y3 @ X2 @ Y0) @ (Y2 @ X2)) @ X2))) @ Y1) @ X2)) = X2) => ((X1 @ (Y2 @ Y0)) => Y4)) => Y4)))))))))) @ X3) = $true)) )),
% 2.78/1.80 inference(pi_clausification,[status(thm)],[f536])).
% 2.78/1.80 thf(f536,plain,(
% 2.78/1.80 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $o @ (^[Y4 : $o]: ((((Y3 @ (Y3 @ Y0 @ (Y3 @ Y1 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X2 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y2 @ Y0) @ (Y3 @ (Y3 @ Y1 @ (Y3 @ X2 @ (Y3 @ X2 @ X2))) @ Y0))) @ (Y3 @ (Y2 @ (Y3 @ (Y3 @ (Y2 @ Y1) @ Y0) @ (Y3 @ Y0 @ Y0))) @ (Y3 @ X2 @ (Y3 @ X2 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y2 @ X2) @ Y1)) @ (Y2 @ (Y3 @ Y1 @ Y0)))) @ X2) @ (Y2 @ (Y3 @ (Y3 @ Y1 @ (Y3 @ Y0 @ (Y3 @ (Y2 @ (Y3 @ Y0 @ Y1)) @ Y0))) @ (Y3 @ (Y3 @ (Y3 @ X2 @ (Y3 @ (Y2 @ Y0) @ X2)) @ X2) @ (Y2 @ (Y2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ X2 @ (Y3 @ (Y3 @ Y1 @ Y0) @ Y1)) @ X2)) @ Y1) @ (Y3 @ Y1 @ (Y3 @ Y0 @ Y0))) @ X2))))))))))))) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X2 @ (Y3 @ Y0 @ Y0)) @ (Y2 @ (Y2 @ (Y3 @ Y1 @ (Y2 @ (Y2 @ (Y3 @ Y1 @ Y0))))))) @ Y0) @ X2) @ (Y3 @ X2 @ Y1)))) @ Y0) @ Y0) @ (Y2 @ X2)))) @ (Y3 @ (Y3 @ (Y2 @ (Y3 @ (Y2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y1 @ (Y3 @ (Y2 @ (Y2 @ (Y3 @ (Y3 @ Y0 @ X2) @ Y1))) @ (Y2 @ (Y3 @ Y0 @ Y0)))) @ Y0) @ (Y2 @ Y0)) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ Y1) @ (Y2 @ (Y2 @ (Y2 @ Y1)))) @ Y1) @ X2) @ Y0))) @ (Y3 @ (Y3 @ (Y3 @ X2 @ Y0) @ (Y2 @ X2)) @ X2))) @ Y1) @ X2)) = X2) => ((X1 @ (Y2 @ Y0)) => Y4)) => Y4))))))))))) = $true)) )),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f535])).
% 2.78/1.80 thf(f535,plain,(
% 2.78/1.80 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: (!! @ $o @ (^[Y5 : $o]: ((((Y4 @ (Y4 @ Y1 @ (Y4 @ Y2 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y3 @ Y1) @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y0 @ (Y4 @ Y0 @ Y0))) @ Y1))) @ (Y4 @ (Y3 @ (Y4 @ (Y4 @ (Y3 @ Y2) @ Y1) @ (Y4 @ Y1 @ Y1))) @ (Y4 @ Y0 @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y3 @ Y0) @ Y2)) @ (Y3 @ (Y4 @ Y2 @ Y1)))) @ Y0) @ (Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y1 @ (Y4 @ (Y3 @ (Y4 @ Y1 @ Y2)) @ Y1))) @ (Y4 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ (Y3 @ Y1) @ Y0)) @ Y0) @ (Y3 @ (Y3 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ (Y4 @ Y2 @ Y1) @ Y2)) @ Y0)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y1 @ Y1))) @ Y0))))))))))))) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ Y1 @ Y1)) @ (Y3 @ (Y3 @ (Y4 @ Y2 @ (Y3 @ (Y3 @ (Y4 @ Y2 @ Y1))))))) @ Y1) @ Y0) @ (Y4 @ Y0 @ Y2)))) @ Y1) @ Y1) @ (Y3 @ Y0)))) @ (Y4 @ (Y4 @ (Y3 @ (Y4 @ (Y3 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ (Y3 @ (Y3 @ (Y4 @ (Y4 @ Y1 @ Y0) @ Y2))) @ (Y3 @ (Y4 @ Y1 @ Y1)))) @ Y1) @ (Y3 @ Y1)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ Y2) @ (Y3 @ (Y3 @ (Y3 @ Y2)))) @ Y2) @ Y0) @ Y1))) @ (Y4 @ (Y4 @ (Y4 @ Y0 @ Y1) @ (Y3 @ Y0)) @ Y0))) @ Y2) @ Y0)) = Y0) => ((X1 @ (Y3 @ Y1)) => Y5)) => Y5)))))))))))) @ X2) = $true)) )),
% 2.78/1.80 inference(pi_clausification,[status(thm)],[f534])).
% 2.78/1.80 thf(f534,plain,(
% 2.78/1.80 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: (!! @ $o @ (^[Y5 : $o]: ((((Y4 @ (Y4 @ Y1 @ (Y4 @ Y2 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y3 @ Y1) @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y0 @ (Y4 @ Y0 @ Y0))) @ Y1))) @ (Y4 @ (Y3 @ (Y4 @ (Y4 @ (Y3 @ Y2) @ Y1) @ (Y4 @ Y1 @ Y1))) @ (Y4 @ Y0 @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y3 @ Y0) @ Y2)) @ (Y3 @ (Y4 @ Y2 @ Y1)))) @ Y0) @ (Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y1 @ (Y4 @ (Y3 @ (Y4 @ Y1 @ Y2)) @ Y1))) @ (Y4 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ (Y3 @ Y1) @ Y0)) @ Y0) @ (Y3 @ (Y3 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ (Y4 @ Y2 @ Y1) @ Y2)) @ Y0)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y1 @ Y1))) @ Y0))))))))))))) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y0 @ (Y4 @ Y1 @ Y1)) @ (Y3 @ (Y3 @ (Y4 @ Y2 @ (Y3 @ (Y3 @ (Y4 @ Y2 @ Y1))))))) @ Y1) @ Y0) @ (Y4 @ Y0 @ Y2)))) @ Y1) @ Y1) @ (Y3 @ Y0)))) @ (Y4 @ (Y4 @ (Y3 @ (Y4 @ (Y3 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ (Y3 @ (Y3 @ (Y4 @ (Y4 @ Y1 @ Y0) @ Y2))) @ (Y3 @ (Y4 @ Y1 @ Y1)))) @ Y1) @ (Y3 @ Y1)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ Y2) @ (Y3 @ (Y3 @ (Y3 @ Y2)))) @ Y2) @ Y0) @ Y1))) @ (Y4 @ (Y4 @ (Y4 @ Y0 @ Y1) @ (Y3 @ Y0)) @ Y0))) @ Y2) @ Y0)) = Y0) => ((X1 @ (Y3 @ Y1)) => Y5)) => Y5))))))))))))))) )),
% 2.78/1.80 inference(beta_eta_normalization,[status(thm)],[f533])).
% 2.78/1.80 thf(f533,plain,(
% 2.78/1.80 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (!! @ $o @ (^[Y6 : $o]: ((((Y5 @ (Y5 @ Y2 @ (Y5 @ Y3 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y2) @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y1 @ (Y5 @ Y1 @ Y1))) @ Y2))) @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y4 @ Y3) @ Y2) @ (Y5 @ Y2 @ Y2))) @ (Y5 @ Y1 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y1) @ Y3)) @ (Y4 @ (Y5 @ Y3 @ Y2)))) @ Y1) @ (Y4 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ (Y5 @ Y2 @ Y3)) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y4 @ Y2) @ Y1)) @ Y1) @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y3 @ Y2) @ Y3)) @ Y1)) @ Y3) @ (Y5 @ Y3 @ (Y5 @ Y2 @ Y2))) @ Y1))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ Y2 @ Y2)) @ (Y4 @ (Y4 @ (Y5 @ Y3 @ (Y4 @ (Y4 @ (Y5 @ Y3 @ Y2))))))) @ Y2) @ Y1) @ (Y5 @ Y1 @ Y3)))) @ Y2) @ Y2) @ (Y4 @ Y1)))) @ (Y5 @ (Y5 @ (Y4 @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ Y2 @ Y1) @ Y3))) @ (Y4 @ (Y5 @ Y2 @ Y2)))) @ Y2) @ (Y4 @ Y2)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y3)))) @ Y3) @ Y1) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ Y2) @ (Y4 @ Y1)) @ Y1))) @ Y3) @ Y1)) = Y1) => ((Y0 @ (Y4 @ Y2)) => Y6)) => Y6)))))))))))))) @ X1))) )),
% 2.78/1.80 inference(pi_clausification,[status(thm)],[f532])).
% 2.78/1.80 thf(f532,plain,(
% 2.78/1.80 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (!! @ $o @ (^[Y6 : $o]: ((((Y5 @ (Y5 @ Y2 @ (Y5 @ Y3 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y2) @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y1 @ (Y5 @ Y1 @ Y1))) @ Y2))) @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y4 @ Y3) @ Y2) @ (Y5 @ Y2 @ Y2))) @ (Y5 @ Y1 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ Y1) @ Y3)) @ (Y4 @ (Y5 @ Y3 @ Y2)))) @ Y1) @ (Y4 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ Y2 @ (Y5 @ (Y4 @ (Y5 @ Y2 @ Y3)) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y4 @ Y2) @ Y1)) @ Y1) @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ (Y5 @ Y3 @ Y2) @ Y3)) @ Y1)) @ Y3) @ (Y5 @ Y3 @ (Y5 @ Y2 @ Y2))) @ Y1))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y1 @ (Y5 @ Y2 @ Y2)) @ (Y4 @ (Y4 @ (Y5 @ Y3 @ (Y4 @ (Y4 @ (Y5 @ Y3 @ Y2))))))) @ Y2) @ Y1) @ (Y5 @ Y1 @ Y3)))) @ Y2) @ Y2) @ (Y4 @ Y1)))) @ (Y5 @ (Y5 @ (Y4 @ (Y5 @ (Y4 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y3 @ (Y5 @ (Y4 @ (Y4 @ (Y5 @ (Y5 @ Y2 @ Y1) @ Y3))) @ (Y4 @ (Y5 @ Y2 @ Y2)))) @ Y2) @ (Y4 @ Y2)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y3)))) @ Y3) @ Y1) @ Y2))) @ (Y5 @ (Y5 @ (Y5 @ Y1 @ Y2) @ (Y4 @ Y1)) @ Y1))) @ Y3) @ Y1)) = Y1) => ((Y0 @ (Y4 @ Y2)) => Y6)) => Y6))))))))))))))))),
% 2.78/1.80 inference(binary_proxy_clausification,[status(thm)],[f530])).
% 2.78/1.80 % SZS output end Proof for DTF2THF_30472
% 2.78/1.80 % (30582)------------------------------
% 2.78/1.80 % (30582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.80 % (30582)Termination reason: Refutation
% 2.78/1.80
% 2.78/1.80 % (30582)Memory used [KB]: 6908
% 2.78/1.80 % (30582)Time elapsed: 0.059 s
% 2.78/1.80 % (30582)Instructions burned: 110 (million)
% 2.78/1.80 % (30582)------------------------------
% 2.78/1.80 % (30582)------------------------------
% 2.78/1.80 % (30581)Success in time 0.077 s
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