%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV529^1 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:41:28 AM UTC 2026
% Result : Theorem 7.52s 2.65s
% Output : Refutation 7.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 1163 ( 158 equ; 0 cnn)
% Maximal formula atoms : 68 ( 29 avg)
% Number of connectives : 2126 ( 57 ~; 57 |; 48 &;1876 @)
% ( 1 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1100 (1100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 115 ( 111 usr; 6 con; 0-14 aty)
% ( 0 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 875 ( 662 ^; 195 !; 18 ?; 875 :)
% 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,
diff:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > X1 ) > X0 ) ).
thf(func_def_132,type,
sK0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o ).
thf(func_def_133,type,
sK1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o ).
thf(func_def_134,type,
sK2: ( $i > $i ) > $i > $o ).
thf(func_def_135,type,
sK3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o ).
thf(func_def_136,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_139,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f1250,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f354,f1249]) ).
thf(f1249,plain,
spl6_2,
inference(avatar_contradiction_clause,[status(thm)],[f1248]) ).
thf(f1248,plain,
( $false
| spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1225]) ).
thf(f1225,plain,
( ( $true = $false )
| spl6_2 ),
inference(superposition,[status(thm)],[f877,f382]) ).
thf(f382,plain,
! [X1: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X1
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f380]) ).
thf(f380,plain,
! [X1: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true != $true )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X1
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) ),
inference(superposition,[status(thm)],[f316,f314]) ).
thf(f314,plain,
( $true
= ( sK2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) ),
inference(cnf_transformation,[status(thm)],[f298]) ).
thf(f298,plain,
( ! [X4: ( $i > $i > $i > $i ) > $i] :
( $true
= ( sK0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X4
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X5: $i > $i,X6: ( $i > $i > $i > $i ) > $i] :
( ( $true
!= ( c_In
@ ( X6
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( sK3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X5 @ ( X5 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( sK2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
& ! [X7: $i,X8: $i > ( $i > $i ) > $i] :
( $true
= ( sK1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X7
@ ^ [Y0: $i] :
( X8 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
& ! [X9: ( $i > ( $i > $i ) > $i > $i ) > $i,X10: $i] :
( ( $true
!= ( sK0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X10 ) )
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
& ! [X11: $i > $i > $i,X12: $i > $i > $i > $i,X13: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
!= ( sK2
@ ^ [Y0: $i] : Y0
@ ( X12 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X11 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X12 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X13
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X13
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
& ( ( c_False = $true )
| ( $true
!= ( sK3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( sK2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( sK1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ( c_False != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f296,f297]) ).
thf(f297,plain,
( ? [X0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X4: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X4
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X5: $i > $i,X6: ( $i > $i > $i > $i ) > $i] :
( ( $true
!= ( c_In
@ ( X6
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X5 @ ( X5 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
& ! [X7: $i,X8: $i > ( $i > $i ) > $i] :
( $true
= ( X1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X7
@ ^ [Y0: $i] :
( X8 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
& ! [X9: ( $i > ( $i > $i ) > $i > $i ) > $i,X10: $i] :
( ( $true
!= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X10 ) )
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
& ! [X11: $i > $i > $i,X12: $i > $i > $i > $i,X13: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( X12 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X11 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X12 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X13
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X13
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
& ( ( c_False = $true )
| ( $true
!= ( X3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( X1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ( c_False != $true ) )
=> ( ! [X4: ( $i > $i > $i > $i ) > $i] :
( $true
= ( sK0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X4
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X6: ( $i > $i > $i > $i ) > $i,X5: $i > $i] :
( ( $true
!= ( c_In
@ ( X6
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( sK3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X5 @ ( X5 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( sK2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
& ! [X8: $i > ( $i > $i ) > $i,X7: $i] :
( $true
= ( sK1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X7
@ ^ [Y0: $i] :
( X8 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
& ! [X10: $i,X9: ( $i > ( $i > $i ) > $i > $i ) > $i] :
( ( $true
!= ( sK0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X10 ) )
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
& ! [X13: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X12: $i > $i > $i > $i,X11: $i > $i > $i] :
( ( $true
!= ( sK2
@ ^ [Y0: $i] : Y0
@ ( X12 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X11 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X12 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X13
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X13
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
& ( ( c_False = $true )
| ( $true
!= ( sK3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( sK2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( sK1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ( c_False != $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f296,plain,
? [X0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X4: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X4
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X5: $i > $i,X6: ( $i > $i > $i > $i ) > $i] :
( ( $true
!= ( c_In
@ ( X6
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X5 @ ( X5 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
& ! [X7: $i,X8: $i > ( $i > $i ) > $i] :
( $true
= ( X1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X7
@ ^ [Y0: $i] :
( X8 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
& ! [X9: ( $i > ( $i > $i ) > $i > $i ) > $i,X10: $i] :
( ( $true
!= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X10 ) )
@ ( X9
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
& ! [X11: $i > $i > $i,X12: $i > $i > $i > $i,X13: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( X12 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X11 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X12 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X13
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X13
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
& ( ( c_False = $true )
| ( $true
!= ( X3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( X1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ( c_False != $true ) ),
inference(rectify,[status(thm)],[f293]) ).
thf(f293,plain,
? [X0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X7: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X7
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X10: $i > $i,X11: ( $i > $i > $i > $i ) > $i] :
( ( $true
!= ( c_In
@ ( X11
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X10 @ ( X10 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
& ! [X4: $i,X5: $i > ( $i > $i ) > $i] :
( $true
= ( X1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X4
@ ^ [Y0: $i] :
( X5 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
& ! [X8: ( $i > ( $i > $i ) > $i > $i ) > $i,X9: $i] :
( ( $true
!= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X9 ) )
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
& ! [X12: $i > $i > $i,X13: $i > $i > $i > $i,X14: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( X13 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X12 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X13 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X14
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X14
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
& ( ( c_False = $true )
| ( $true
!= ( X3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ! [X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( X1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ( c_False != $true ) ),
inference(flattening,[status(thm)],[f292]) ).
thf(f292,plain,
? [X0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ( c_False != $true )
& ! [X12: $i > $i > $i,X13: $i > $i > $i > $i,X14: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( X13 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X12 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X13 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X14
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X14
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
& ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
& ( ( c_False = $true )
| ( $true
!= ( X3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) ) )
& ! [X10: $i > $i,X11: ( $i > $i > $i > $i ) > $i] :
( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X10 @ ( X10 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) )
| ( $true
!= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
| ( $true
!= ( c_In
@ ( X11
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) ) )
& ! [X8: ( $i > ( $i > $i ) > $i > $i ) > $i,X9: $i] :
( ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) )
| ( $true
!= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
| ( $true
!= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X9 ) )
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) ) )
& ! [X7: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X7
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
& ! [X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true )
| ( $true
!= ( X1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
& ! [X4: $i,X5: $i > ( $i > $i ) > $i] :
( $true
= ( X1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X4
@ ^ [Y0: $i] :
( X5 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) ),
inference(ennf_transformation,[status(thm)],[f289]) ).
thf(f289,plain,
~ ! [X0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X4: $i,X5: $i > ( $i > $i ) > $i] :
( $true
= ( X1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X4
@ ^ [Y0: $i] :
( X5 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
=> ( ! [X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( $true
= ( X1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true ) )
=> ( ! [X7: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X7
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
=> ( ! [X8: ( $i > ( $i > $i ) > $i > $i ) > $i,X9: $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X9 ) )
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
=> ( ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X8
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
=> ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) ) )
=> ( ! [X10: $i > $i,X11: ( $i > $i > $i > $i ) > $i] :
( ( $true
= ( c_In
@ ( X11
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X10 @ ( X10 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) ) ) )
=> ( ( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
=> ( c_False = $true ) )
=> ( ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
=> ( ! [X12: $i > $i > $i,X13: $i > $i > $i > $i,X14: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( X13 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X12 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X13 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X14
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X14
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
=> ( c_False = $true ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f127]) ).
thf(f127,plain,
~ ! [X0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X5: $i,X6: $i > ( $i > $i ) > $i] :
( $true
= ( X1
@ ^ [Y0: $i > $i] : ( c_Inj0 @ ( Y0 @ c_Empty ) )
@ ^ [Y0: $i] : X5
@ ^ [Y0: $i] :
( X6 @ c_Empty
@ ^ [Y1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
=> ( ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( $true
= ( X1
@ ^ [Y0: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [Y1: ( $i > $i ) > $i,Y2: $i > $i,Y3: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Y0: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ Y0 ) )
@ ^ [Y0: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) )
= $true ) )
=> ( ! [X23: ( $i > $i > $i > $i ) > $i] :
( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ Y4 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] :
( c_setsum @ Y1
@ ( X23
@ ^ [Y2: $i,Y3: $i,Y4: $i] : c_Empty ) ) ) )
=> ( ! [X36: ( $i > ( $i > $i ) > $i > $i ) > $i,X38: $i] :
( ( $true
= ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X38 ) )
@ ( X36
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty ) ) )
=> ( ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X36
@ ^ [Y0: $i,Y1: $i > $i,Y2: $i] : c_Empty )
@ c_Empty )
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj1 @ c_Empty ) ) )
=> ( $true
= ( X0
@ ^ [Y0: $i > ( ( $i > $i ) > $i ) > $i,Y1: $i,Y2: $i,Y3: $i > $i,Y4: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) ) )
=> ( ! [X60: $i > $i,X61: ( $i > $i > $i > $i ) > $i] :
( ( $true
= ( c_In
@ ( X61
@ ^ [Y0: $i,Y1: $i,Y2: $i] : ( c_Inj1 @ Y1 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ Y1 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X60 @ ( X60 @ c_Empty ) ) ) )
@ ^ [Y0: $i > $i] : c_Empty ) ) ) )
=> ( ( ( $true
= ( X3
@ ^ [Y0: $i,Y1: $i] : Y0
@ ^ [Y0: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) ) )
=> ( c_False = $true ) )
=> ( ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( c_Inj0 @ c_Empty ) ) )
=> ( ! [X83: $i > $i > $i,X84: $i > $i > $i > $i,X86: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
= ( X2
@ ^ [Y0: $i] : Y0
@ ( X84 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X83 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X84 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X86
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
=> ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X86
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) )
=> ( c_False = $true ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f126]) ).
thf(f126,plain,
~ ! [X0: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X1: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X5: $i,X6: $i > ( $i > $i ) > $i] :
( X1
@ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
@ ^ [X9: $i] : X5
@ ^ [X10: $i] :
( X6 @ c_Empty
@ ^ [X11: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [X14: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( X1
@ ^ [X16: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X14
@ ^ [X17: ( $i > $i ) > $i,X18: $i > $i,X19: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X20: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X20 ) )
@ ^ [X21: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [X23: ( $i > $i > $i > $i ) > $i] :
( X0
@ ^ [X26: $i > ( ( $i > $i ) > $i ) > $i,X27: $i,X28: $i,X29: $i > $i,X30: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X30 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [X31: $i > $i,X32: $i] :
( c_setsum @ X32
@ ( X23
@ ^ [X33: $i,X34: $i,X35: $i] : c_Empty ) ) )
=> ( ! [X36: ( $i > ( $i > $i ) > $i > $i ) > $i,X38: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X38 ) )
@ ( X36
@ ^ [X40: $i,X41: $i > $i,X42: $i] : c_Empty ) )
=> ( ( X0
@ ^ [X43: $i > ( ( $i > $i ) > $i ) > $i,X44: $i,X45: $i,X46: $i > $i,X47: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X36
@ ^ [X48: $i,X49: $i > $i,X50: $i] : c_Empty )
@ c_Empty )
@ ^ [X51: $i > $i,X52: $i] : ( c_Inj1 @ c_Empty ) )
=> ( X0
@ ^ [X53: $i > ( ( $i > $i ) > $i ) > $i,X54: $i,X55: $i,X56: $i > $i,X57: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [X58: $i > $i,X59: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X60: $i > $i,X61: ( $i > $i > $i > $i ) > $i] :
( ( c_In
@ ( X61
@ ^ [X64: $i,X65: $i,X66: $i] : ( c_Inj1 @ X65 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X2
@ ^ [X67: $i] : X67
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( X3
@ ^ [X68: $i,X69: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X69 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X60 @ ( X60 @ c_Empty ) ) ) )
@ ^ [X70: $i > $i] : c_Empty ) ) )
=> ( ( ( X3
@ ^ [X75: $i,X76: $i] : X75
@ ^ [X77: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ( X2
@ ^ [X82: $i] : X82
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [X83: $i > $i > $i,X84: $i > $i > $i > $i,X86: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( X2
@ ^ [X87: $i] : X87
@ ( X84 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X83 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X84 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X86
@ ^ [X88: $i] : c_Empty
@ ^ [X89: $i > $i,X90: $i] : ( c_setsum @ X90 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X86
@ ^ [X91: $i] : X91
@ ^ [X92: $i > $i,X93: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,negated_conjecture,
~ ! [X2: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i] :
( X3
@ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
@ ^ [X8: $i] : X5
@ ^ [X8: $i] :
( X6 @ c_Empty
@ ^ [X9: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [X5: $i,X7: $i,X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,X4: $i > ( $i > $i ) > $i > $i > $i] :
( ( X3
@ ^ [X8: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [X9: ( $i > $i ) > $i,X10: $i > $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X8: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X8 ) )
@ ^ [X8: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [X6: $i > ( $i > $i > $i ) > $i,X7: ( $i > $i > $i > $i ) > $i,X5: ( ( $i > $i > $i ) > $i ) > $i,X4: $i > $i > $i] :
( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X12 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [X8: $i > $i,X9: $i] :
( c_setsum @ X9
@ ( X7
@ ^ [X10: $i,X11: $i,X12: $i] : c_Empty ) ) )
=> ( ! [X4: ( $i > ( $i > $i ) > $i > $i ) > $i,X6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X7: $i,X5: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X7 ) )
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty ) )
=> ( ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty )
@ c_Empty )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj1 @ c_Empty ) )
=> ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X7: $i > $i,X6: ( $i > $i > $i > $i ) > $i,X4: $i,X5: ( $i > $i > $i ) > $i > $i] :
( ( c_In
@ ( X6
@ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ X9 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X0
@ ^ [X8: $i] : X8
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( X1
@ ^ [X8: $i,X9: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X9 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X7 @ ( X7 @ c_Empty ) ) ) )
@ ^ [X8: $i > $i] : c_Empty ) ) )
=> ( ! [X7: $i,X6: $i > $i,X5: $i,X4: $i] :
( ( X1
@ ^ [X8: $i,X9: $i] : X8
@ ^ [X8: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ! [X6: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,X5: $i,X4: $i,X7: $i > $i] :
( X0
@ ^ [X8: $i] : X8
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i,X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( X0
@ ^ [X8: $i] : X8
@ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X4
@ ^ [X8: $i] : c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_setsum @ X9 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X4
@ ^ [X8: $i] : X8
@ ^ [X8: $i > $i,X9: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
thf(f109,conjecture,
! [X2: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o,X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i] :
( X3
@ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
@ ^ [X8: $i] : X5
@ ^ [X8: $i] :
( X6 @ c_Empty
@ ^ [X9: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [X5: $i,X7: $i,X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,X4: $i > ( $i > $i ) > $i > $i > $i] :
( ( X3
@ ^ [X8: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( X6
@ ^ [X9: ( $i > $i ) > $i,X10: $i > $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X8: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X8 ) )
@ ^ [X8: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [X6: $i > ( $i > $i > $i ) > $i,X7: ( $i > $i > $i > $i ) > $i,X5: ( ( $i > $i > $i ) > $i ) > $i,X4: $i > $i > $i] :
( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X12 ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [X8: $i > $i,X9: $i] :
( c_setsum @ X9
@ ( X7
@ ^ [X10: $i,X11: $i,X12: $i] : c_Empty ) ) )
=> ( ! [X4: ( $i > ( $i > $i ) > $i > $i ) > $i,X6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X7: $i,X5: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X7 ) )
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty ) )
=> ( ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( X4
@ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty )
@ c_Empty )
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj1 @ c_Empty ) )
=> ( X2
@ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [X7: $i > $i,X6: ( $i > $i > $i > $i ) > $i,X4: $i,X5: ( $i > $i > $i ) > $i > $i] :
( ( c_In
@ ( X6
@ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ X9 ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( X0
@ ^ [X8: $i] : X8
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( X1
@ ^ [X8: $i,X9: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X9 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X7 @ ( X7 @ c_Empty ) ) ) )
@ ^ [X8: $i > $i] : c_Empty ) ) )
=> ( ! [X7: $i,X6: $i > $i,X5: $i,X4: $i] :
( ( X1
@ ^ [X8: $i,X9: $i] : X8
@ ^ [X8: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ! [X6: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,X5: $i,X4: $i,X7: $i > $i] :
( X0
@ ^ [X8: $i] : X8
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i,X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( X0
@ ^ [X8: $i] : X8
@ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X4
@ ^ [X8: $i] : c_Empty
@ ^ [X8: $i > $i,X9: $i] : ( c_setsum @ X9 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X4
@ ^ [X8: $i] : X8
@ ^ [X8: $i > $i,X9: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kXY3Epcmh7/DTF2THF_29311.p',conj) ).
thf(f316,plain,
! [X11: $i > $i > $i,X12: $i > $i > $i > $i,X13: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( $true
!= ( sK2
@ ^ [Y0: $i] : Y0
@ ( X12 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X11 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X12 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( X13
@ ^ [Y0: $i] : c_Empty
@ ^ [Y0: $i > $i,Y1: $i] : ( c_setsum @ Y1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) ) )
| ( $true
= ( c_In @ ( c_Inj0 @ c_Empty )
@ ( X13
@ ^ [Y0: $i] : Y0
@ ^ [Y0: $i > $i,Y1: $i] : c_Empty ) ) ) ),
inference(cnf_transformation,[status(thm)],[f298]) ).
thf(f877,plain,
( ! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
= $false )
| spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f876]) ).
thf(f876,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty )
@ X1 )
= $false )
| spl6_2 ),
inference(pi_clausification,[status(thm)],[f875]) ).
thf(f875,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
= $false )
| spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f869]) ).
thf(f869,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) )
= $false )
| ( $true = $false )
| spl6_2 ),
inference(superposition,[status(thm)],[f306,f824]) ).
thf(f824,plain,
( ! [X1: $o] :
( ( ( c_not @ X1 )
= $false )
| ( $false = X1 ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f817,f335]) ).
thf(f335,plain,
( ( c_False != $true )
| spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f334]) ).
thf(f334,definition,
( spl6_2
<=> ( c_False = $true ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f817,plain,
! [X1: $o] :
( ( $false = X1 )
| ( ( c_not @ X1 )
= $false )
| ( c_False = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f816]) ).
thf(f816,plain,
! [X1: $o] :
( ( $true
= ( X1
=> c_False ) )
| ( ( c_not @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f814]) ).
thf(f814,plain,
! [X1: $o] :
( ( c_not @ X1 )
= ( X1
=> c_False ) ),
inference(beta_eta_normalization,[status(thm)],[f813]) ).
thf(f813,plain,
! [X1: $o] :
( ( c_not @ X1 )
= ( ^ [Y0: $o] :
( Y0
=> c_False )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f310]) ).
thf(f310,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
thf(f209,plain,
( c_not
= ( ^ [Y0: $o] :
( Y0
=> c_False ) ) ),
inference(fool_elimination,[status(thm)],[f208]) ).
thf(f208,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.kXY3Epcmh7/DTF2THF_29311.p',ax13) ).
thf(f306,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
thf(f169,plain,
( $true
= ( c_not
@ ( ?? @ $i
@ ^ [Y0: $i] : ( c_In @ Y0 @ c_Empty ) ) ) ),
inference(fool_elimination,[status(thm)],[f168]) ).
thf(f168,plain,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( c_not
@ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ),
file('/export/starexec/sandbox/tmp/tmp.kXY3Epcmh7/DTF2THF_29311.p',ax5) ).
thf(f354,plain,
~ spl6_2,
inference(avatar_split_clause,[status(thm)],[f312,f334]) ).
thf(f312,plain,
c_False != $true,
inference(cnf_transformation,[status(thm)],[f298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV529^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:49:12 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : SEV529^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.49 % Domain : Set Theory
% 0.29/0.49 % Problem : ProofGold problem HOSetConstr_188_pos_th0
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English :
% 0.29/0.49
% 0.29/0.49 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.29/0.49 % Source : [Urb20]
% 0.29/0.49 % Names : HOSetConstr_188_pos_th0.p [Urb20]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.78 v9.1.0, 0.75 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0
% 0.29/0.49 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.29/0.49 % Number of atoms : 485 ( 135 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 6 ( 4 avg)
% 0.29/0.49 % Number of connectives : 1300 ( 0 ~; 0 |; 0 &;1196 @)
% 0.29/0.49 % ( 0 <=>; 104 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 27 ( 2 avg)
% 0.29/0.49 % Number of types : 2 ( 0 usr)
% 0.29/0.49 % Number of type conns : 690 ( 690 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.29/0.49 % Number of variables : 499 ( 333 ^; 129 !; 37 ?; 499 :)
% 0.29/0.49 % SPC : TH0_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : See https://proofgold.org
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(c_Eps_i_tp,type,
% 0.29/0.49 c_Eps_i: ( $i > $o ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_False_tp,type,
% 0.29/0.49 c_False: $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_True_tp,type,
% 0.29/0.49 c_True: $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_not_tp,type,
% 0.29/0.49 c_not: $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_and_tp,type,
% 0.29/0.49 c_and: $o > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_or_tp,type,
% 0.29/0.49 c_or: $o > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_iff_tp,type,
% 0.29/0.49 c_iff: $o > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_In_tp,type,
% 0.29/0.49 c_In: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_Subq_tp,type,
% 0.29/0.49 c_Subq: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_Empty_tp,type,
% 0.29/0.49 c_Empty: $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Union_tp,type,
% 0.29/0.49 c_Union: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Power_tp,type,
% 0.29/0.49 c_Power: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Repl_tp,type,
% 0.29/0.49 c_Repl: $i > ( $i > $i ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_TransSet_tp,type,
% 0.29/0.49 c_TransSet: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_atleast2_tp,type,
% 0.29/0.49 c_atleast2: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_atleast3_tp,type,
% 0.29/0.49 c_atleast3: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_atleast4_tp,type,
% 0.29/0.49 c_atleast4: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_atleast5_tp,type,
% 0.29/0.49 c_atleast5: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_atleast6_tp,type,
% 0.29/0.49 c_atleast6: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_exactly2_tp,type,
% 0.29/0.49 c_exactly2: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_exactly3_tp,type,
% 0.29/0.49 c_exactly3: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_exactly4_tp,type,
% 0.29/0.49 c_exactly4: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_exactly5_tp,type,
% 0.29/0.49 c_exactly5: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_exu_i_tp,type,
% 0.29/0.49 c_exu_i: ( $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_reflexive_i_tp,type,
% 0.29/0.49 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_irreflexive_i_tp,type,
% 0.29/0.49 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_symmetric_i_tp,type,
% 0.29/0.49 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_antisymmetric_i_tp,type,
% 0.29/0.49 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_transitive_i_tp,type,
% 0.29/0.49 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_eqreln_i_tp,type,
% 0.29/0.49 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_per_i_tp,type,
% 0.29/0.49 c_per_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_linear_i_tp,type,
% 0.29/0.49 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_trichotomous_or_i_tp,type,
% 0.29/0.49 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_partialorder_i_tp,type,
% 0.29/0.49 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_totalorder_i_tp,type,
% 0.29/0.49 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_strictpartialorder_i_tp,type,
% 0.29/0.49 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_stricttotalorder_i_tp,type,
% 0.29/0.49 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_If_i_tp,type,
% 0.29/0.49 c_If_i: $o > $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_exactly1of2_tp,type,
% 0.29/0.49 c_exactly1of2: $o > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_exactly1of3_tp,type,
% 0.29/0.49 c_exactly1of3: $o > $o > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_nIn_tp,type,
% 0.29/0.49 c_nIn: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_nSubq_tp,type,
% 0.29/0.49 c_nSubq: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_UPair_tp,type,
% 0.29/0.49 c_UPair: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Sing_tp,type,
% 0.29/0.49 c_Sing: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_binunion_tp,type,
% 0.29/0.49 c_binunion: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_SetAdjoin_tp,type,
% 0.29/0.49 c_SetAdjoin: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_famunion_tp,type,
% 0.29/0.49 c_famunion: $i > ( $i > $i ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Sep_tp,type,
% 0.29/0.49 c_Sep: $i > ( $i > $o ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_ReplSep_tp,type,
% 0.29/0.49 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_binintersect_tp,type,
% 0.29/0.49 c_binintersect: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_setminus_tp,type,
% 0.29/0.49 c_setminus: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_inj_tp,type,
% 0.29/0.49 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_bij_tp,type,
% 0.29/0.49 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_atleastp_tp,type,
% 0.29/0.49 c_atleastp: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_equip_tp,type,
% 0.29/0.49 c_equip: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_In_rec_poly_G_i_tp,type,
% 0.29/0.49 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_In_rec_poly_i_tp,type,
% 0.29/0.49 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_ordsucc_tp,type,
% 0.29/0.49 c_ordsucc: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_nat_p_tp,type,
% 0.29/0.49 c_nat_p: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_nat_primrec_tp,type,
% 0.29/0.49 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_add_nat_tp,type,
% 0.29/0.49 c_add_nat: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_mul_nat_tp,type,
% 0.29/0.49 c_mul_nat: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_ordinal_tp,type,
% 0.29/0.49 c_ordinal: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_V__tp,type,
% 0.29/0.49 c_V_: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Inj1_tp,type,
% 0.29/0.49 c_Inj1: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Inj0_tp,type,
% 0.29/0.49 c_Inj0: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Unj_tp,type,
% 0.29/0.49 c_Unj: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_combine_funcs_tp,type,
% 0.29/0.49 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_setsum_tp,type,
% 0.29/0.49 c_setsum: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_proj0_tp,type,
% 0.29/0.49 c_proj0: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_proj1_tp,type,
% 0.29/0.49 c_proj1: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_binrep_tp,type,
% 0.29/0.49 c_binrep: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_lam_tp,type,
% 0.29/0.49 c_lam: $i > ( $i > $i ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_setprod_tp,type,
% 0.29/0.49 c_setprod: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_ap_tp,type,
% 0.29/0.49 c_ap: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_setsum_p_tp,type,
% 0.29/0.49 c_setsum_p: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_tuple_p_tp,type,
% 0.29/0.49 c_tuple_p: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_Pi_tp,type,
% 0.29/0.49 c_Pi: $i > ( $i > $i ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_setexp_tp,type,
% 0.29/0.49 c_setexp: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_Sep2_tp,type,
% 0.29/0.49 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_set_of_pairs_tp,type,
% 0.29/0.49 c_set_of_pairs: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_lam2_tp,type,
% 0.29/0.49 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_PNoEq__tp,type,
% 0.29/0.49 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_PNoLt__tp,type,
% 0.29/0.49 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_PNoLt_tp,type,
% 0.29/0.49 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_PNoLe_tp,type,
% 0.29/0.49 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_PNo_downc_tp,type,
% 0.29/0.49 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_PNo_upc_tp,type,
% 0.29/0.49 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_SNoElts__tp,type,
% 0.29/0.49 c_SNoElts_: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_SNo__tp,type,
% 0.29/0.49 c_SNo_: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_PSNo_tp,type,
% 0.29/0.49 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_SNo_tp,type,
% 0.29/0.49 c_SNo: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_SNoLev_tp,type,
% 0.29/0.49 c_SNoLev: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(c_SNoEq__tp,type,
% 0.29/0.49 c_SNoEq_: $i > $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_SNoLt_tp,type,
% 0.29/0.49 c_SNoLt: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_SNoLe_tp,type,
% 0.29/0.49 c_SNoLe: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_binop_on_tp,type,
% 0.29/0.49 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_Loop_tp,type,
% 0.29/0.49 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_Loop_with_defs_tp,type,
% 0.29/0.49 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 ).
% 0.29/0.49
% 0.29/0.49 thf(c_Loop_with_defs_cex1_tp,type,
% 0.29/0.49 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 ).
% 0.29/0.49
% 0.29/0.49 thf(c_Loop_with_defs_cex2_tp,type,
% 0.29/0.49 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 ).
% 0.29/0.49
% 0.29/0.49 thf(c_combinator_tp,type,
% 0.29/0.49 c_combinator: $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_combinator_equiv_tp,type,
% 0.29/0.49 c_combinator_equiv: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(c_equip_mod_tp,type,
% 0.29/0.49 c_equip_mod: $i > $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(ax1,axiom,
% 0.29/0.49 ! [X0: $i > $o,X1: $i] :
% 0.29/0.49 ( ( X0 @ X1 )
% 0.29/0.49 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax2,axiom,
% 0.29/0.49 ! [X0: $o] :
% 0.29/0.49 ( ( c_not @ ( c_not @ X0 ) )
% 0.29/0.49 => X0 ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax3,axiom,
% 0.29/0.49 ! [X0: $o,X1: $o] :
% 0.29/0.49 ( ( c_iff @ X0 @ X1 )
% 0.29/0.49 => ( X0 = X1 ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax4,axiom,
% 0.29/0.49 ! [X0: $i,X1: $i] :
% 0.29/0.49 ( ( c_Subq @ X0 @ X1 )
% 0.29/0.49 => ( ( c_Subq @ X1 @ X0 )
% 0.29/0.49 => ( X0 = X1 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax5,axiom,
% 0.29/0.49 ( c_not
% 0.29/0.49 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax6,axiom,
% 0.29/0.49 ! [X0: $i,X1: $i] :
% 0.29/0.49 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.29/0.49 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax7,axiom,
% 0.29/0.49 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax8,axiom,
% 0.29/0.49 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.29/0.49 ( c_iff
% 0.29/0.49 @ ( c_In @ X2
% 0.29/0.49 @ ( c_Repl @ X0
% 0.29/0.49 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.29/0.49 @ ? [X3: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X3 @ X0 )
% 0.29/0.49 @ ( X2
% 0.29/0.49 = ( X1 @ X3 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax9,axiom,
% 0.29/0.49 ! [X0: $i > $o] :
% 0.29/0.49 ( ! [X1: $i] :
% 0.29/0.49 ( ( X0 @ X1 )
% 0.29/0.49 => ! [X2: $i] :
% 0.29/0.49 ( ( c_In @ X2 @ X1 )
% 0.29/0.49 => ( X0 @ X2 ) ) )
% 0.29/0.49 => ( ( X0 @ c_Empty )
% 0.29/0.49 => ( ! [X1: $i] :
% 0.29/0.49 ( ( X0 @ X1 )
% 0.29/0.49 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.29/0.49 => ( ! [X1: $i] :
% 0.29/0.49 ( ( X0 @ X1 )
% 0.29/0.49 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.29/0.49 => ( ! [X1: $i] :
% 0.29/0.49 ( ( X0 @ X1 )
% 0.29/0.49 => ! [X2: $i > $i] :
% 0.29/0.49 ( ! [X3: $i] :
% 0.29/0.49 ( ( c_In @ X3 @ X1 )
% 0.29/0.49 => ( X0 @ ( X2 @ X3 ) ) )
% 0.29/0.49 => ( X0
% 0.29/0.49 @ ( c_Repl @ X1
% 0.29/0.49 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.29/0.49 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax10,axiom,
% 0.29/0.49 ! [X0: $i > $o] :
% 0.29/0.49 ( ! [X1: $i] :
% 0.29/0.49 ( ! [X2: $i] :
% 0.29/0.49 ( ( c_In @ X2 @ X1 )
% 0.29/0.49 => ( X0 @ X2 ) )
% 0.29/0.49 => ( X0 @ X1 ) )
% 0.29/0.49 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax11,axiom,
% 0.29/0.49 ( c_False
% 0.29/0.49 = ( ! [X0: $o] : X0 ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax12,axiom,
% 0.29/0.49 ( c_True
% 0.29/0.49 = ( ! [X0: $o] :
% 0.29/0.49 ( X0
% 0.29/0.49 => X0 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax13,axiom,
% 0.29/0.49 ( c_not
% 0.29/0.49 = ( ^ [X0: $o] :
% 0.29/0.49 ( X0
% 0.29/0.49 => c_False ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax14,axiom,
% 0.29/0.49 ( c_and
% 0.29/0.49 = ( ^ [X0: $o,X1: $o] :
% 0.29/0.49 ! [X2: $o] :
% 0.29/0.49 ( ( X0
% 0.29/0.49 => ( X1
% 0.29/0.49 => X2 ) )
% 0.29/0.49 => X2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax15,axiom,
% 0.29/0.49 ( c_or
% 0.29/0.49 = ( ^ [X0: $o,X1: $o] :
% 0.29/0.49 ! [X2: $o] :
% 0.29/0.49 ( ( X0
% 0.29/0.49 => X2 )
% 0.29/0.49 => ( ( X1
% 0.29/0.49 => X2 )
% 0.29/0.49 => X2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax16,axiom,
% 0.29/0.49 ( c_iff
% 0.29/0.49 = ( ^ [X0: $o,X1: $o] :
% 0.29/0.49 ( c_and
% 0.29/0.49 @ ( X0
% 0.29/0.49 => X1 )
% 0.29/0.49 @ ( X1
% 0.29/0.49 => X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax17,axiom,
% 0.29/0.49 ( c_Subq
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ! [X2: $i] :
% 0.29/0.49 ( ( c_In @ X2 @ X0 )
% 0.29/0.49 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax18,axiom,
% 0.29/0.49 ( c_TransSet
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ! [X1: $i] :
% 0.29/0.49 ( ( c_In @ X1 @ X0 )
% 0.29/0.49 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax19,axiom,
% 0.29/0.49 ( c_atleast2
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax20,axiom,
% 0.29/0.49 ( c_atleast3
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax21,axiom,
% 0.29/0.49 ( c_atleast4
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax22,axiom,
% 0.29/0.49 ( c_atleast5
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax23,axiom,
% 0.29/0.49 ( c_atleast6
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax24,axiom,
% 0.29/0.49 ( c_exactly2
% 0.29/0.49 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax25,axiom,
% 0.29/0.49 ( c_exactly3
% 0.29/0.49 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax26,axiom,
% 0.29/0.49 ( c_exactly4
% 0.29/0.49 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax27,axiom,
% 0.29/0.49 ( c_exactly5
% 0.29/0.49 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax28,axiom,
% 0.29/0.49 ( c_exu_i
% 0.29/0.49 = ( ^ [X0: $i > $o] :
% 0.29/0.49 ( c_and
% 0.29/0.49 @ ? [X1: $i] : ( X0 @ X1 )
% 0.29/0.49 @ ! [X1: $i,X2: $i] :
% 0.29/0.49 ( ( X0 @ X1 )
% 0.29/0.49 => ( ( X0 @ X2 )
% 0.29/0.49 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax29,axiom,
% 0.29/0.49 ( c_reflexive_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.49 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax30,axiom,
% 0.29/0.49 ( c_irreflexive_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.49 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax31,axiom,
% 0.29/0.49 ( c_symmetric_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.49 ! [X1: $i,X2: $i] :
% 0.29/0.49 ( ( X0 @ X1 @ X2 )
% 0.29/0.49 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax32,axiom,
% 0.29/0.49 ( c_antisymmetric_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.49 ! [X1: $i,X2: $i] :
% 0.29/0.49 ( ( X0 @ X1 @ X2 )
% 0.29/0.49 => ( ( X0 @ X2 @ X1 )
% 0.29/0.49 => ( X1 = X2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax33,axiom,
% 0.29/0.49 ( c_transitive_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.49 ! [X1: $i,X2: $i,X3: $i] :
% 0.29/0.49 ( ( X0 @ X1 @ X2 )
% 0.29/0.49 => ( ( X0 @ X2 @ X3 )
% 0.29/0.49 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax34,axiom,
% 0.29/0.49 ( c_eqreln_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax35,axiom,
% 0.29/0.49 ( c_per_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax36,axiom,
% 0.29/0.49 ( c_linear_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.49 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax37,axiom,
% 0.29/0.49 ( c_trichotomous_or_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.49 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax38,axiom,
% 0.29/0.49 ( c_partialorder_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax39,axiom,
% 0.29/0.49 ( c_totalorder_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax40,axiom,
% 0.29/0.49 ( c_strictpartialorder_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax41,axiom,
% 0.29/0.49 ( c_stricttotalorder_i
% 0.29/0.49 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax42,axiom,
% 0.29/0.49 ( c_If_i
% 0.29/0.49 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.29/0.49 ( c_Eps_i
% 0.29/0.49 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax43,axiom,
% 0.29/0.49 ( c_exactly1of2
% 0.29/0.49 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax44,axiom,
% 0.29/0.49 ( c_exactly1of3
% 0.29/0.49 = ( ^ [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 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax45,axiom,
% 0.29/0.49 ( c_nIn
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax46,axiom,
% 0.29/0.49 ( c_nSubq
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax47,axiom,
% 0.29/0.49 ( c_UPair
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.29/0.49 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax48,axiom,
% 0.29/0.49 ( c_Sing
% 0.29/0.49 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax49,axiom,
% 0.29/0.49 ( c_binunion
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax50,axiom,
% 0.29/0.49 ( c_SetAdjoin
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax51,axiom,
% 0.29/0.49 ( c_famunion
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i] :
% 0.29/0.49 ( c_Union
% 0.29/0.49 @ ( c_Repl @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax52,axiom,
% 0.29/0.49 ( c_Sep
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $o] :
% 0.29/0.49 ( c_If_i
% 0.29/0.49 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.29/0.49 @ ( c_Repl @ X0
% 0.29/0.49 @ ^ [X2: $i] :
% 0.29/0.49 ( ^ [X3: $i] :
% 0.29/0.49 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.29/0.49 @ ( c_Eps_i
% 0.29/0.49 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.29/0.49 @ X2 ) )
% 0.29/0.49 @ c_Empty ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax53,axiom,
% 0.29/0.49 ( c_ReplSep
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.29/0.49 ( c_Repl
% 0.29/0.49 @ ( c_Sep @ X0
% 0.29/0.49 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.29/0.49 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax54,axiom,
% 0.29/0.49 ( c_binintersect
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_Sep @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax55,axiom,
% 0.29/0.49 ( c_setminus
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_Sep @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax56,axiom,
% 0.29/0.49 ( c_inj
% 0.29/0.49 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.29/0.49 ( c_and
% 0.29/0.49 @ ! [X3: $i] :
% 0.29/0.49 ( ( c_In @ X3 @ X0 )
% 0.29/0.49 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.29/0.49 @ ! [X3: $i] :
% 0.29/0.49 ( ( c_In @ X3 @ X0 )
% 0.29/0.49 => ! [X4: $i] :
% 0.29/0.49 ( ( c_In @ X4 @ X0 )
% 0.29/0.49 => ( ( ( X2 @ X3 )
% 0.29/0.49 = ( X2 @ X4 ) )
% 0.29/0.49 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax57,axiom,
% 0.29/0.49 ( c_bij
% 0.29/0.49 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.29/0.49 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.29/0.49 @ ! [X3: $i] :
% 0.29/0.49 ( ( c_In @ X3 @ X1 )
% 0.29/0.49 => ? [X4: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X4 @ X0 )
% 0.29/0.49 @ ( ( X2 @ X4 )
% 0.29/0.49 = X3 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax58,axiom,
% 0.29/0.49 ( c_atleastp
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax59,axiom,
% 0.29/0.49 ( c_equip
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax60,axiom,
% 0.29/0.49 ( c_In_rec_poly_G_i
% 0.29/0.49 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.29/0.49 ! [X3: $i > $i > $o] :
% 0.29/0.49 ( ! [X4: $i,X5: $i > $i] :
% 0.29/0.49 ( ! [X6: $i] :
% 0.29/0.49 ( ( c_In @ X6 @ X4 )
% 0.29/0.49 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.29/0.49 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.29/0.49 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax61,axiom,
% 0.29/0.49 ( c_In_rec_poly_i
% 0.29/0.49 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.29/0.49 ( c_Eps_i
% 0.29/0.49 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax62,axiom,
% 0.29/0.49 ( c_ordsucc
% 0.29/0.49 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax63,axiom,
% 0.29/0.49 ( c_nat_p
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ! [X1: $i > $o] :
% 0.29/0.49 ( ( X1 @ c_Empty )
% 0.29/0.49 => ( ! [X2: $i] :
% 0.29/0.49 ( ( X1 @ X2 )
% 0.29/0.49 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.29/0.49 => ( X1 @ X0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax64,axiom,
% 0.29/0.49 ( c_nat_primrec
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.29/0.49 ( c_In_rec_poly_i
% 0.29/0.49 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax65,axiom,
% 0.29/0.49 ( c_add_nat
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_nat_primrec @ X0
% 0.29/0.49 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.29/0.49 @ X1 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax66,axiom,
% 0.29/0.49 ( c_mul_nat
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_nat_primrec @ c_Empty
% 0.29/0.49 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.29/0.49 @ X1 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax67,axiom,
% 0.29/0.49 ( c_ordinal
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ( c_and @ ( c_TransSet @ X0 )
% 0.29/0.49 @ ! [X1: $i] :
% 0.29/0.49 ( ( c_In @ X1 @ X0 )
% 0.29/0.49 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax68,axiom,
% 0.29/0.49 ( c_V_
% 0.29/0.49 = ( c_In_rec_poly_i
% 0.29/0.49 @ ^ [X0: $i,X1: $i > $i] :
% 0.29/0.49 ( c_famunion @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax69,axiom,
% 0.29/0.49 ( c_Inj1
% 0.29/0.49 = ( c_In_rec_poly_i
% 0.29/0.49 @ ^ [X0: $i,X1: $i > $i] :
% 0.29/0.49 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.29/0.49 @ ( c_Repl @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax70,axiom,
% 0.29/0.49 ( c_Inj0
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ( c_Repl @ X0
% 0.29/0.49 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax71,axiom,
% 0.29/0.49 ( c_Unj
% 0.29/0.49 = ( c_In_rec_poly_i
% 0.29/0.49 @ ^ [X0: $i,X1: $i > $i] :
% 0.29/0.49 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.29/0.49 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax72,axiom,
% 0.29/0.49 ( c_combine_funcs
% 0.29/0.49 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.29/0.49 ( c_If_i
% 0.29/0.49 @ ( X4
% 0.29/0.49 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.29/0.49 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.29/0.49 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax73,axiom,
% 0.29/0.49 ( c_setsum
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_binunion
% 0.29/0.49 @ ( c_Repl @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.29/0.49 @ ( c_Repl @ X1
% 0.29/0.49 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax74,axiom,
% 0.29/0.49 ( c_proj0
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ( c_ReplSep @ X0
% 0.29/0.49 @ ^ [X1: $i] :
% 0.29/0.49 ? [X2: $i] :
% 0.29/0.49 ( ( c_Inj0 @ X2 )
% 0.29/0.49 = X1 )
% 0.29/0.49 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax75,axiom,
% 0.29/0.49 ( c_proj1
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ( c_ReplSep @ X0
% 0.29/0.49 @ ^ [X1: $i] :
% 0.29/0.49 ? [X2: $i] :
% 0.29/0.49 ( ( c_Inj1 @ X2 )
% 0.29/0.49 = X1 )
% 0.29/0.49 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax76,axiom,
% 0.29/0.49 ( c_binrep
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax77,axiom,
% 0.29/0.49 ( c_lam
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i] :
% 0.29/0.49 ( c_famunion @ X0
% 0.29/0.49 @ ^ [X2: $i] :
% 0.29/0.49 ( c_Repl @ ( X1 @ X2 )
% 0.29/0.49 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax78,axiom,
% 0.29/0.49 ( c_setprod
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_lam @ X0
% 0.29/0.49 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax79,axiom,
% 0.29/0.49 ( c_ap
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_ReplSep @ X0
% 0.29/0.49 @ ^ [X2: $i] :
% 0.29/0.49 ? [X3: $i] :
% 0.29/0.49 ( X2
% 0.29/0.49 = ( c_setsum @ X1 @ X3 ) )
% 0.29/0.49 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax80,axiom,
% 0.29/0.49 ( c_setsum_p
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.49 = X0 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax81,axiom,
% 0.29/0.49 ( c_tuple_p
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ! [X2: $i] :
% 0.29/0.49 ( ( c_In @ X2 @ X1 )
% 0.29/0.49 => ? [X3: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X3 @ X0 )
% 0.29/0.49 @ ? [X4: $i] :
% 0.29/0.49 ( X2
% 0.29/0.49 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax82,axiom,
% 0.29/0.49 ( c_Pi
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i] :
% 0.29/0.49 ( c_Sep
% 0.29/0.49 @ ( c_Power
% 0.29/0.49 @ ( c_lam @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.29/0.49 @ ^ [X2: $i] :
% 0.29/0.49 ! [X3: $i] :
% 0.29/0.49 ( ( c_In @ X3 @ X0 )
% 0.29/0.49 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax83,axiom,
% 0.29/0.49 ( c_setexp
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_Pi @ X1
% 0.29/0.49 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax84,axiom,
% 0.29/0.49 ( c_Sep2
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.29/0.49 ( c_Sep
% 0.29/0.49 @ ( c_lam @ X0
% 0.29/0.49 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.29/0.49 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax85,axiom,
% 0.29/0.49 ( c_set_of_pairs
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ! [X1: $i] :
% 0.29/0.49 ( ( c_In @ X1 @ X0 )
% 0.29/0.49 => ? [X2: $i,X3: $i] :
% 0.29/0.49 ( X1
% 0.29/0.49 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.29/0.49 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax86,axiom,
% 0.29/0.49 ( c_lam2
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.29/0.49 ( c_lam @ X0
% 0.29/0.49 @ ^ [X3: $i] :
% 0.29/0.49 ( c_lam @ ( X1 @ X3 )
% 0.29/0.49 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax87,axiom,
% 0.29/0.49 ( c_PNoEq_
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.29/0.49 ! [X3: $i] :
% 0.29/0.49 ( ( c_In @ X3 @ X0 )
% 0.29/0.49 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax88,axiom,
% 0.29/0.49 ( c_PNoLt_
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.29/0.49 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax89,axiom,
% 0.29/0.49 ( c_PNoLt
% 0.29/0.49 = ( ^ [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 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax90,axiom,
% 0.29/0.49 ( c_PNoLe
% 0.29/0.49 = ( ^ [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 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax91,axiom,
% 0.29/0.49 ( c_PNo_downc
% 0.29/0.49 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.29/0.49 ? [X3: $i] :
% 0.29/0.49 ( c_and @ ( c_ordinal @ X3 )
% 0.29/0.49 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax92,axiom,
% 0.29/0.49 ( c_PNo_upc
% 0.29/0.49 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.29/0.49 ? [X3: $i] :
% 0.29/0.49 ( c_and @ ( c_ordinal @ X3 )
% 0.29/0.49 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax93,axiom,
% 0.29/0.49 ( c_SNoElts_
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ( c_binunion @ X0
% 0.29/0.49 @ ( c_Repl @ X0
% 0.29/0.49 @ ^ [X1: $i] :
% 0.29/0.49 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.49 @ X1 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax94,axiom,
% 0.29/0.49 ( c_SNo_
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.29/0.49 @ ! [X2: $i] :
% 0.29/0.49 ( ( c_In @ X2 @ X0 )
% 0.29/0.49 => ( c_exactly1of2
% 0.29/0.49 @ ( c_In
% 0.29/0.49 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.49 @ X2 )
% 0.29/0.49 @ X1 )
% 0.29/0.49 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax95,axiom,
% 0.29/0.49 ( c_PSNo
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $o] :
% 0.29/0.49 ( c_binunion
% 0.29/0.49 @ ( c_Sep @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.29/0.49 @ ( c_ReplSep @ X0
% 0.29/0.49 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.29/0.49 @ ^ [X2: $i] :
% 0.29/0.49 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.49 @ X2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax96,axiom,
% 0.29/0.49 ( c_SNo
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax97,axiom,
% 0.29/0.49 ( c_SNoLev
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ( c_Eps_i
% 0.29/0.49 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax98,axiom,
% 0.29/0.49 ( c_SNoEq_
% 0.29/0.49 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.29/0.49 ( c_PNoEq_ @ X0
% 0.29/0.49 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.29/0.49 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax99,axiom,
% 0.29/0.49 ( c_SNoLt
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.29/0.49 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.29/0.49 @ ( c_SNoLev @ X1 )
% 0.29/0.49 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax100,axiom,
% 0.29/0.49 ( c_SNoLe
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.29/0.49 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.29/0.49 @ ( c_SNoLev @ X1 )
% 0.29/0.49 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax101,axiom,
% 0.29/0.49 ( c_binop_on
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.29/0.49 ! [X2: $i] :
% 0.29/0.49 ( ( c_In @ X2 @ X0 )
% 0.29/0.49 => ! [X3: $i] :
% 0.29/0.49 ( ( c_In @ X3 @ X0 )
% 0.29/0.49 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax102,axiom,
% 0.29/0.49 ( c_Loop
% 0.29/0.49 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.29/0.49 ( c_and
% 0.29/0.49 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.29/0.49 @ ! [X5: $i] :
% 0.29/0.49 ( ( c_In @ X5 @ X0 )
% 0.29/0.49 => ( c_and
% 0.29/0.49 @ ( ( X1 @ X4 @ X5 )
% 0.29/0.49 = X5 )
% 0.29/0.49 @ ( ( X1 @ X5 @ X4 )
% 0.29/0.49 = X5 ) ) ) )
% 0.29/0.49 @ ! [X5: $i] :
% 0.29/0.49 ( ( c_In @ X5 @ X0 )
% 0.29/0.49 => ! [X6: $i] :
% 0.29/0.49 ( ( c_In @ X6 @ X0 )
% 0.29/0.49 => ( c_and
% 0.29/0.49 @ ( c_and
% 0.29/0.49 @ ( c_and
% 0.29/0.49 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.29/0.49 = X6 )
% 0.29/0.49 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.29/0.49 = X6 ) )
% 0.29/0.49 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.29/0.49 = X5 ) )
% 0.29/0.49 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.29/0.49 = X5 ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax103,axiom,
% 0.29/0.49 ( c_Loop_with_defs
% 0.29/0.49 = ( ^ [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] :
% 0.29/0.49 ( c_and
% 0.29/0.49 @ ( c_and
% 0.29/0.49 @ ( c_and
% 0.29/0.49 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.29/0.49 @ ! [X14: $i] :
% 0.29/0.49 ( ( c_In @ X14 @ X0 )
% 0.29/0.49 => ! [X15: $i] :
% 0.29/0.49 ( ( c_In @ X15 @ X0 )
% 0.29/0.49 => ( ( X5 @ X14 @ X15 )
% 0.29/0.49 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.29/0.49 @ ! [X14: $i] :
% 0.29/0.49 ( ( c_In @ X14 @ X0 )
% 0.29/0.49 => ! [X15: $i] :
% 0.29/0.49 ( ( c_In @ X15 @ X0 )
% 0.29/0.49 => ! [X16: $i] :
% 0.29/0.49 ( ( c_In @ X16 @ X0 )
% 0.29/0.49 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.29/0.49 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.29/0.49 @ ! [X14: $i] :
% 0.29/0.49 ( ( c_In @ X14 @ X0 )
% 0.29/0.49 => ! [X15: $i] :
% 0.29/0.49 ( ( c_In @ X15 @ X0 )
% 0.29/0.49 => ( c_and
% 0.29/0.49 @ ( c_and
% 0.29/0.49 @ ( c_and
% 0.29/0.49 @ ( c_and
% 0.29/0.49 @ ( ( X7 @ X14 @ X15 )
% 0.29/0.49 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.29/0.49 @ ( ( X10 @ X14 @ X15 )
% 0.29/0.49 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.29/0.49 @ ( ( X11 @ X14 @ X15 )
% 0.29/0.49 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.29/0.49 @ ( ( X12 @ X14 @ X15 )
% 0.29/0.49 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.29/0.49 @ ( ( X13 @ X14 @ X15 )
% 0.29/0.49 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.29/0.49 @ ! [X14: $i] :
% 0.29/0.49 ( ( c_In @ X14 @ X0 )
% 0.29/0.49 => ! [X15: $i] :
% 0.29/0.49 ( ( c_In @ X15 @ X0 )
% 0.29/0.49 => ! [X16: $i] :
% 0.29/0.49 ( ( c_In @ X16 @ X0 )
% 0.29/0.49 => ( c_and
% 0.29/0.49 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.29/0.49 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.29/0.49 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.29/0.49 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax104,axiom,
% 0.29/0.49 ( c_Loop_with_defs_cex1
% 0.29/0.49 = ( ^ [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] :
% 0.29/0.49 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.29/0.49 @ ? [X14: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X14 @ X0 )
% 0.29/0.49 @ ? [X15: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X15 @ X0 )
% 0.29/0.49 @ ? [X16: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X16 @ X0 )
% 0.29/0.49 @ ? [X17: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X17 @ X0 )
% 0.29/0.49 @ ( c_not
% 0.29/0.49 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.29/0.49 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax105,axiom,
% 0.29/0.49 ( c_Loop_with_defs_cex2
% 0.29/0.49 = ( ^ [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] :
% 0.29/0.49 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.29/0.49 @ ? [X14: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X14 @ X0 )
% 0.29/0.49 @ ? [X15: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X15 @ X0 )
% 0.29/0.49 @ ? [X16: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X16 @ X0 )
% 0.29/0.49 @ ? [X17: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X17 @ X0 )
% 0.29/0.49 @ ? [X18: $i] :
% 0.29/0.49 ( c_and @ ( c_In @ X18 @ X0 )
% 0.29/0.49 @ ( c_not
% 0.29/0.49 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.29/0.49 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax106,axiom,
% 0.29/0.49 ( c_combinator
% 0.29/0.49 = ( ^ [X0: $i] :
% 0.29/0.49 ! [X1: $i > $o] :
% 0.29/0.49 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.29/0.49 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.29/0.49 => ( ! [X2: $i,X3: $i] :
% 0.29/0.49 ( ( X1 @ X2 )
% 0.29/0.49 => ( ( X1 @ X3 )
% 0.29/0.49 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.29/0.49 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax107,axiom,
% 0.29/0.49 ( c_combinator_equiv
% 0.29/0.49 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.49 ! [X2: $i > $i > $o] :
% 0.29/0.49 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.29/0.49 ( ( c_per_i @ X2 )
% 0.29/0.49 => ( ! [X6: $i] :
% 0.29/0.49 ( ( c_combinator @ X6 )
% 0.29/0.49 => ( X2 @ X6 @ X6 ) )
% 0.29/0.49 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.29/0.49 ( ( c_combinator @ X6 )
% 0.29/0.49 => ( ( c_combinator @ X7 )
% 0.29/0.49 => ( ( c_combinator @ X8 )
% 0.29/0.49 => ( ( c_combinator @ X9 )
% 0.29/0.49 => ( ( X2 @ X6 @ X8 )
% 0.29/0.49 => ( ( X2 @ X7 @ X9 )
% 0.29/0.49 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.29/0.49 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.29/0.49 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.29/0.49 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.29/0.49 @ ( c_Inj0 @ c_Empty )
% 0.29/0.49 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.29/0.49 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax108,axiom,
% 0.29/0.49 ( c_equip_mod
% 0.29/0.49 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.29/0.49 ? [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 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(conj,conjecture,
% 0.29/0.49 ! [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o] :
% 0.29/0.49 ( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i] :
% 0.29/0.49 ( X3
% 0.29/0.49 @ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
% 0.29/0.49 @ ^ [X8: $i] : X5
% 0.29/0.49 @ ^ [X8: $i] :
% 0.29/0.49 ( X6 @ c_Empty
% 0.29/0.49 @ ^ [X9: $i] : c_Empty )
% 0.29/0.49 @ ( c_Inj1 @ c_Empty ) )
% 0.29/0.49 => ( ! [X4: $i > ( $i > $i ) > $i > $i > $i,X5: $i,X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,X7: $i] :
% 0.29/0.49 ( ( X3
% 0.29/0.49 @ ^ [X8: $i > $i] :
% 0.29/0.49 ( c_Inj1
% 0.29/0.49 @ ( c_Inj1
% 0.29/0.49 @ ( X6
% 0.29/0.49 @ ^ [X9: ( $i > $i ) > $i,X10: $i > $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 0.29/0.49 @ ^ [X8: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X8 ) )
% 0.29/0.49 @ ^ [X8: $i] : c_Empty
% 0.29/0.49 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
% 0.29/0.49 => ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
% 0.29/0.49 => ( ! [X4: $i > $i > $i,X5: ( ( $i > $i > $i ) > $i ) > $i,X6: $i > ( $i > $i > $i ) > $i,X7: ( $i > $i > $i > $i ) > $i] :
% 0.29/0.49 ( X2
% 0.29/0.49 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X12 ) )
% 0.29/0.49 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
% 0.29/0.49 @ ^ [X8: $i > $i,X9: $i] :
% 0.29/0.49 ( c_setsum @ X9
% 0.29/0.49 @ ( X7
% 0.29/0.49 @ ^ [X10: $i,X11: $i,X12: $i] : c_Empty ) ) )
% 0.29/0.49 => ( ! [X4: ( $i > ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X7: $i] :
% 0.29/0.49 ( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X7 ) )
% 0.29/0.49 @ ( X4
% 0.29/0.49 @ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty ) )
% 0.29/0.49 => ( ( X2
% 0.29/0.49 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
% 0.29/0.49 @ ( c_setsum
% 0.29/0.49 @ ( X4
% 0.29/0.49 @ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty )
% 0.29/0.49 @ c_Empty )
% 0.29/0.49 @ ^ [X8: $i > $i,X9: $i] : ( c_Inj1 @ c_Empty ) )
% 0.29/0.49 => ( X2
% 0.29/0.49 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
% 0.29/0.49 @ c_Empty
% 0.29/0.49 @ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
% 0.29/0.49 => ( ! [X4: $i,X5: ( $i > $i > $i ) > $i > $i,X6: ( $i > $i > $i > $i ) > $i,X7: $i > $i] :
% 0.29/0.49 ( ( c_In
% 0.29/0.49 @ ( X6
% 0.29/0.49 @ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ X9 ) )
% 0.29/0.49 @ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 0.29/0.49 => ( ( X0
% 0.29/0.49 @ ^ [X8: $i] : X8
% 0.29/0.49 @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
% 0.29/0.49 => ( X1
% 0.29/0.49 @ ^ [X8: $i,X9: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X9 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X7 @ ( X7 @ c_Empty ) ) ) )
% 0.29/0.49 @ ^ [X8: $i > $i] : c_Empty ) ) )
% 0.29/0.49 => ( ! [X4: $i,X5: $i,X6: $i > $i,X7: $i] :
% 0.29/0.49 ( ( X1
% 0.29/0.49 @ ^ [X8: $i,X9: $i] : X8
% 0.29/0.49 @ ^ [X8: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
% 0.29/0.49 => c_False )
% 0.29/0.49 => ( ! [X4: $i,X5: $i,X6: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,X7: $i > $i] :
% 0.29/0.49 ( X0
% 0.29/0.49 @ ^ [X8: $i] : X8
% 0.29/0.49 @ ( c_Inj0 @ c_Empty ) )
% 0.29/0.49 => ( ! [X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i] :
% 0.29/0.49 ( ( X0
% 0.29/0.49 @ ^ [X8: $i] : X8
% 0.29/0.49 @ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
% 0.29/0.49 @ ( X4
% 0.29/0.49 @ ^ [X8: $i] : c_Empty
% 0.29/0.49 @ ^ [X8: $i > $i,X9: $i] : ( c_setsum @ X9 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 0.29/0.49 => ( c_In @ ( c_Inj0 @ c_Empty )
% 0.29/0.49 @ ( X4
% 0.29/0.49 @ ^ [X8: $i] : X8
% 0.29/0.49 @ ^ [X8: $i > $i,X9: $i] : c_Empty ) ) )
% 0.29/0.49 => c_False ) ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 2.68/1.78 ---- Embedded in THF ---
% 2.68/1.78 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.68/1.78 %%% Generated on Tue Feb 24 12:49:13 EST 2026
% 2.68/1.78 %%% using '$$dhol' embedding, version 1.3.0.
% 2.68/1.78 %%% Logic specification used:
% 2.68/1.78 %%% thf(spec, logic, $$dhol).
% 2.68/1.78
% 2.68/1.78 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kXY3Epcmh7/DTF2DTF29311.p
% See solution above
% 2.68/1.78 ------------------------
% 2.91/1.81 ---- Cleaned THF ---
% 2.91/1.81 thf(c_Eps_i_tp,type,
% 2.91/1.81 c_Eps_i: ( $i > $o ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_False_tp,type,
% 2.91/1.81 c_False: $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_True_tp,type,
% 2.91/1.81 c_True: $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_not_tp,type,
% 2.91/1.81 c_not: $o > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_and_tp,type,
% 2.91/1.81 c_and: $o > $o > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_or_tp,type,
% 2.91/1.81 c_or: $o > $o > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_iff_tp,type,
% 2.91/1.81 c_iff: $o > $o > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_In_tp,type,
% 2.91/1.81 c_In: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_Subq_tp,type,
% 2.91/1.81 c_Subq: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_Empty_tp,type,
% 2.91/1.81 c_Empty: $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Union_tp,type,
% 2.91/1.81 c_Union: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Power_tp,type,
% 2.91/1.81 c_Power: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Repl_tp,type,
% 2.91/1.81 c_Repl: $i > ( $i > $i ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_TransSet_tp,type,
% 2.91/1.81 c_TransSet: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_atleast2_tp,type,
% 2.91/1.81 c_atleast2: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_atleast3_tp,type,
% 2.91/1.81 c_atleast3: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_atleast4_tp,type,
% 2.91/1.81 c_atleast4: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_atleast5_tp,type,
% 2.91/1.81 c_atleast5: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_atleast6_tp,type,
% 2.91/1.81 c_atleast6: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_exactly2_tp,type,
% 2.91/1.81 c_exactly2: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_exactly3_tp,type,
% 2.91/1.81 c_exactly3: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_exactly4_tp,type,
% 2.91/1.81 c_exactly4: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_exactly5_tp,type,
% 2.91/1.81 c_exactly5: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_exu_i_tp,type,
% 2.91/1.81 c_exu_i: ( $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_reflexive_i_tp,type,
% 2.91/1.81 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_irreflexive_i_tp,type,
% 2.91/1.81 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_symmetric_i_tp,type,
% 2.91/1.81 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_antisymmetric_i_tp,type,
% 2.91/1.81 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_transitive_i_tp,type,
% 2.91/1.81 c_transitive_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_eqreln_i_tp,type,
% 2.91/1.81 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_per_i_tp,type,
% 2.91/1.81 c_per_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_linear_i_tp,type,
% 2.91/1.81 c_linear_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_trichotomous_or_i_tp,type,
% 2.91/1.81 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_partialorder_i_tp,type,
% 2.91/1.81 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_totalorder_i_tp,type,
% 2.91/1.81 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_strictpartialorder_i_tp,type,
% 2.91/1.81 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_stricttotalorder_i_tp,type,
% 2.91/1.81 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_If_i_tp,type,
% 2.91/1.81 c_If_i: $o > $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_exactly1of2_tp,type,
% 2.91/1.81 c_exactly1of2: $o > $o > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_exactly1of3_tp,type,
% 2.91/1.81 c_exactly1of3: $o > $o > $o > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_nIn_tp,type,
% 2.91/1.81 c_nIn: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_nSubq_tp,type,
% 2.91/1.81 c_nSubq: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_UPair_tp,type,
% 2.91/1.81 c_UPair: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Sing_tp,type,
% 2.91/1.81 c_Sing: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_binunion_tp,type,
% 2.91/1.81 c_binunion: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_SetAdjoin_tp,type,
% 2.91/1.81 c_SetAdjoin: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_famunion_tp,type,
% 2.91/1.81 c_famunion: $i > ( $i > $i ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Sep_tp,type,
% 2.91/1.81 c_Sep: $i > ( $i > $o ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_ReplSep_tp,type,
% 2.91/1.81 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_binintersect_tp,type,
% 2.91/1.81 c_binintersect: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_setminus_tp,type,
% 2.91/1.81 c_setminus: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_inj_tp,type,
% 2.91/1.81 c_inj: $i > $i > ( $i > $i ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_bij_tp,type,
% 2.91/1.81 c_bij: $i > $i > ( $i > $i ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_atleastp_tp,type,
% 2.91/1.81 c_atleastp: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_equip_tp,type,
% 2.91/1.81 c_equip: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_In_rec_poly_G_i_tp,type,
% 2.91/1.81 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_In_rec_poly_i_tp,type,
% 2.91/1.81 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_ordsucc_tp,type,
% 2.91/1.81 c_ordsucc: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_nat_p_tp,type,
% 2.91/1.81 c_nat_p: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_nat_primrec_tp,type,
% 2.91/1.81 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_add_nat_tp,type,
% 2.91/1.81 c_add_nat: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_mul_nat_tp,type,
% 2.91/1.81 c_mul_nat: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_ordinal_tp,type,
% 2.91/1.81 c_ordinal: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_V__tp,type,
% 2.91/1.81 c_V_: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Inj1_tp,type,
% 2.91/1.81 c_Inj1: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Inj0_tp,type,
% 2.91/1.81 c_Inj0: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Unj_tp,type,
% 2.91/1.81 c_Unj: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_combine_funcs_tp,type,
% 2.91/1.81 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_setsum_tp,type,
% 2.91/1.81 c_setsum: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_proj0_tp,type,
% 2.91/1.81 c_proj0: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_proj1_tp,type,
% 2.91/1.81 c_proj1: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_binrep_tp,type,
% 2.91/1.81 c_binrep: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_lam_tp,type,
% 2.91/1.81 c_lam: $i > ( $i > $i ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_setprod_tp,type,
% 2.91/1.81 c_setprod: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_ap_tp,type,
% 2.91/1.81 c_ap: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_setsum_p_tp,type,
% 2.91/1.81 c_setsum_p: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_tuple_p_tp,type,
% 2.91/1.81 c_tuple_p: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_Pi_tp,type,
% 2.91/1.81 c_Pi: $i > ( $i > $i ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_setexp_tp,type,
% 2.91/1.81 c_setexp: $i > $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_Sep2_tp,type,
% 2.91/1.81 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_set_of_pairs_tp,type,
% 2.91/1.81 c_set_of_pairs: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_lam2_tp,type,
% 2.91/1.81 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_PNoEq__tp,type,
% 2.91/1.81 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_PNoLt__tp,type,
% 2.91/1.81 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_PNoLt_tp,type,
% 2.91/1.81 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_PNoLe_tp,type,
% 2.91/1.81 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_PNo_downc_tp,type,
% 2.91/1.81 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_PNo_upc_tp,type,
% 2.91/1.81 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_SNoElts__tp,type,
% 2.91/1.81 c_SNoElts_: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_SNo__tp,type,
% 2.91/1.81 c_SNo_: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_PSNo_tp,type,
% 2.91/1.81 c_PSNo: $i > ( $i > $o ) > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_SNo_tp,type,
% 2.91/1.81 c_SNo: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_SNoLev_tp,type,
% 2.91/1.81 c_SNoLev: $i > $i ).
% 2.91/1.81
% 2.91/1.81 thf(c_SNoEq__tp,type,
% 2.91/1.81 c_SNoEq_: $i > $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_SNoLt_tp,type,
% 2.91/1.81 c_SNoLt: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_SNoLe_tp,type,
% 2.91/1.81 c_SNoLe: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_binop_on_tp,type,
% 2.91/1.81 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_Loop_tp,type,
% 2.91/1.81 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_Loop_with_defs_tp,type,
% 2.91/1.81 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 ).
% 2.91/1.81
% 2.91/1.81 thf(c_Loop_with_defs_cex1_tp,type,
% 2.91/1.81 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 ).
% 2.91/1.81
% 2.91/1.81 thf(c_Loop_with_defs_cex2_tp,type,
% 2.91/1.81 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 ).
% 2.91/1.81
% 2.91/1.81 thf(c_combinator_tp,type,
% 2.91/1.81 c_combinator: $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_combinator_equiv_tp,type,
% 2.91/1.81 c_combinator_equiv: $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(c_equip_mod_tp,type,
% 2.91/1.81 c_equip_mod: $i > $i > $i > $o ).
% 2.91/1.81
% 2.91/1.81 thf(ax1,axiom,
% 2.91/1.81 ! [X0: $i > $o,X1: $i] :
% 2.91/1.81 ( ( X0 @ X1 )
% 2.91/1.81 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax2,axiom,
% 2.91/1.81 ! [X0: $o] :
% 2.91/1.81 ( ( c_not @ ( c_not @ X0 ) )
% 2.91/1.81 => X0 ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax3,axiom,
% 2.91/1.81 ! [X0: $o,X1: $o] :
% 2.91/1.81 ( ( c_iff @ X0 @ X1 )
% 2.91/1.81 => ( X0 = X1 ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax4,axiom,
% 2.91/1.81 ! [X0: $i,X1: $i] :
% 2.91/1.81 ( ( c_Subq @ X0 @ X1 )
% 2.91/1.81 => ( ( c_Subq @ X1 @ X0 )
% 2.91/1.81 => ( X0 = X1 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax5,axiom,
% 2.91/1.81 ( c_not
% 2.91/1.81 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax6,axiom,
% 2.91/1.81 ! [X0: $i,X1: $i] :
% 2.91/1.81 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 2.91/1.81 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax7,axiom,
% 2.91/1.81 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax8,axiom,
% 2.91/1.81 ! [X0: $i,X1: $i > $i,X2: $i] :
% 2.91/1.81 ( c_iff
% 2.91/1.81 @ ( c_In @ X2
% 2.91/1.81 @ ( c_Repl @ X0
% 2.91/1.81 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 2.91/1.81 @ ? [X3: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X3 @ X0 )
% 2.91/1.81 @ ( X2
% 2.91/1.81 = ( X1 @ X3 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax9,axiom,
% 2.91/1.81 ! [X0: $i > $o] :
% 2.91/1.81 ( ! [X1: $i] :
% 2.91/1.81 ( ( X0 @ X1 )
% 2.91/1.81 => ! [X2: $i] :
% 2.91/1.81 ( ( c_In @ X2 @ X1 )
% 2.91/1.81 => ( X0 @ X2 ) ) )
% 2.91/1.81 => ( ( X0 @ c_Empty )
% 2.91/1.81 => ( ! [X1: $i] :
% 2.91/1.81 ( ( X0 @ X1 )
% 2.91/1.81 => ( X0 @ ( c_Union @ X1 ) ) )
% 2.91/1.81 => ( ! [X1: $i] :
% 2.91/1.81 ( ( X0 @ X1 )
% 2.91/1.81 => ( X0 @ ( c_Power @ X1 ) ) )
% 2.91/1.81 => ( ! [X1: $i] :
% 2.91/1.81 ( ( X0 @ X1 )
% 2.91/1.81 => ! [X2: $i > $i] :
% 2.91/1.81 ( ! [X3: $i] :
% 2.91/1.81 ( ( c_In @ X3 @ X1 )
% 2.91/1.81 => ( X0 @ ( X2 @ X3 ) ) )
% 2.91/1.81 => ( X0
% 2.91/1.81 @ ( c_Repl @ X1
% 2.91/1.81 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 2.91/1.81 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax10,axiom,
% 2.91/1.81 ! [X0: $i > $o] :
% 2.91/1.81 ( ! [X1: $i] :
% 2.91/1.81 ( ! [X2: $i] :
% 2.91/1.81 ( ( c_In @ X2 @ X1 )
% 2.91/1.81 => ( X0 @ X2 ) )
% 2.91/1.81 => ( X0 @ X1 ) )
% 2.91/1.81 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax11,axiom,
% 2.91/1.81 ( c_False
% 2.91/1.81 = ( ! [X0: $o] : X0 ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax12,axiom,
% 2.91/1.81 ( c_True
% 2.91/1.81 = ( ! [X0: $o] :
% 2.91/1.81 ( X0
% 2.91/1.81 => X0 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax13,axiom,
% 2.91/1.81 ( c_not
% 2.91/1.81 = ( ^ [X0: $o] :
% 2.91/1.81 ( X0
% 2.91/1.81 => c_False ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax14,axiom,
% 2.91/1.81 ( c_and
% 2.91/1.81 = ( ^ [X0: $o,X1: $o] :
% 2.91/1.81 ! [X2: $o] :
% 2.91/1.81 ( ( X0
% 2.91/1.81 => ( X1
% 2.91/1.81 => X2 ) )
% 2.91/1.81 => X2 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax15,axiom,
% 2.91/1.81 ( c_or
% 2.91/1.81 = ( ^ [X0: $o,X1: $o] :
% 2.91/1.81 ! [X2: $o] :
% 2.91/1.81 ( ( X0
% 2.91/1.81 => X2 )
% 2.91/1.81 => ( ( X1
% 2.91/1.81 => X2 )
% 2.91/1.81 => X2 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax16,axiom,
% 2.91/1.81 ( c_iff
% 2.91/1.81 = ( ^ [X0: $o,X1: $o] :
% 2.91/1.81 ( c_and
% 2.91/1.81 @ ( X0
% 2.91/1.81 => X1 )
% 2.91/1.81 @ ( X1
% 2.91/1.81 => X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax17,axiom,
% 2.91/1.81 ( c_Subq
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ! [X2: $i] :
% 2.91/1.81 ( ( c_In @ X2 @ X0 )
% 2.91/1.81 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax18,axiom,
% 2.91/1.81 ( c_TransSet
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ! [X1: $i] :
% 2.91/1.81 ( ( c_In @ X1 @ X0 )
% 2.91/1.81 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax19,axiom,
% 2.91/1.81 ( c_atleast2
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax20,axiom,
% 2.91/1.81 ( c_atleast3
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax21,axiom,
% 2.91/1.81 ( c_atleast4
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax22,axiom,
% 2.91/1.81 ( c_atleast5
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax23,axiom,
% 2.91/1.81 ( c_atleast6
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax24,axiom,
% 2.91/1.81 ( c_exactly2
% 2.91/1.81 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax25,axiom,
% 2.91/1.81 ( c_exactly3
% 2.91/1.81 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax26,axiom,
% 2.91/1.81 ( c_exactly4
% 2.91/1.81 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax27,axiom,
% 2.91/1.81 ( c_exactly5
% 2.91/1.81 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax28,axiom,
% 2.91/1.81 ( c_exu_i
% 2.91/1.81 = ( ^ [X0: $i > $o] :
% 2.91/1.81 ( c_and
% 2.91/1.81 @ ? [X1: $i] : ( X0 @ X1 )
% 2.91/1.81 @ ! [X1: $i,X2: $i] :
% 2.91/1.81 ( ( X0 @ X1 )
% 2.91/1.81 => ( ( X0 @ X2 )
% 2.91/1.81 => ( X1 = X2 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax29,axiom,
% 2.91/1.81 ( c_reflexive_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] :
% 2.91/1.81 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax30,axiom,
% 2.91/1.81 ( c_irreflexive_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] :
% 2.91/1.81 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax31,axiom,
% 2.91/1.81 ( c_symmetric_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] :
% 2.91/1.81 ! [X1: $i,X2: $i] :
% 2.91/1.81 ( ( X0 @ X1 @ X2 )
% 2.91/1.81 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax32,axiom,
% 2.91/1.81 ( c_antisymmetric_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] :
% 2.91/1.81 ! [X1: $i,X2: $i] :
% 2.91/1.81 ( ( X0 @ X1 @ X2 )
% 2.91/1.81 => ( ( X0 @ X2 @ X1 )
% 2.91/1.81 => ( X1 = X2 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax33,axiom,
% 2.91/1.81 ( c_transitive_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] :
% 2.91/1.81 ! [X1: $i,X2: $i,X3: $i] :
% 2.91/1.81 ( ( X0 @ X1 @ X2 )
% 2.91/1.81 => ( ( X0 @ X2 @ X3 )
% 2.91/1.81 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax34,axiom,
% 2.91/1.81 ( c_eqreln_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax35,axiom,
% 2.91/1.81 ( c_per_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax36,axiom,
% 2.91/1.81 ( c_linear_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] :
% 2.91/1.81 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax37,axiom,
% 2.91/1.81 ( c_trichotomous_or_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] :
% 2.91/1.81 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax38,axiom,
% 2.91/1.81 ( c_partialorder_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax39,axiom,
% 2.91/1.81 ( c_totalorder_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax40,axiom,
% 2.91/1.81 ( c_strictpartialorder_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax41,axiom,
% 2.91/1.81 ( c_stricttotalorder_i
% 2.91/1.81 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax42,axiom,
% 2.91/1.81 ( c_If_i
% 2.91/1.81 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 2.91/1.81 ( c_Eps_i
% 2.91/1.81 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax43,axiom,
% 2.91/1.81 ( c_exactly1of2
% 2.91/1.81 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax44,axiom,
% 2.91/1.81 ( c_exactly1of3
% 2.91/1.81 = ( ^ [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 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax45,axiom,
% 2.91/1.81 ( c_nIn
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax46,axiom,
% 2.91/1.81 ( c_nSubq
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax47,axiom,
% 2.91/1.81 ( c_UPair
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 2.91/1.81 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax48,axiom,
% 2.91/1.81 ( c_Sing
% 2.91/1.81 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax49,axiom,
% 2.91/1.81 ( c_binunion
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax50,axiom,
% 2.91/1.81 ( c_SetAdjoin
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax51,axiom,
% 2.91/1.81 ( c_famunion
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i] :
% 2.91/1.81 ( c_Union
% 2.91/1.81 @ ( c_Repl @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax52,axiom,
% 2.91/1.81 ( c_Sep
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $o] :
% 2.91/1.81 ( c_If_i
% 2.91/1.81 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 2.91/1.81 @ ( c_Repl @ X0
% 2.91/1.81 @ ^ [X2: $i] :
% 2.91/1.81 ( ^ [X3: $i] :
% 2.91/1.81 ( c_If_i @ ( X1 @ X3 ) @ X3
% 2.91/1.81 @ ( c_Eps_i
% 2.91/1.81 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 2.91/1.81 @ X2 ) )
% 2.91/1.81 @ c_Empty ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax53,axiom,
% 2.91/1.81 ( c_ReplSep
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 2.91/1.81 ( c_Repl
% 2.91/1.81 @ ( c_Sep @ X0
% 2.91/1.81 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.91/1.81 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax54,axiom,
% 2.91/1.81 ( c_binintersect
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_Sep @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax55,axiom,
% 2.91/1.81 ( c_setminus
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_Sep @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax56,axiom,
% 2.91/1.81 ( c_inj
% 2.91/1.81 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.91/1.81 ( c_and
% 2.91/1.81 @ ! [X3: $i] :
% 2.91/1.81 ( ( c_In @ X3 @ X0 )
% 2.91/1.81 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 2.91/1.81 @ ! [X3: $i] :
% 2.91/1.81 ( ( c_In @ X3 @ X0 )
% 2.91/1.81 => ! [X4: $i] :
% 2.91/1.81 ( ( c_In @ X4 @ X0 )
% 2.91/1.81 => ( ( ( X2 @ X3 )
% 2.91/1.81 = ( X2 @ X4 ) )
% 2.91/1.81 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax57,axiom,
% 2.91/1.81 ( c_bij
% 2.91/1.81 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.91/1.81 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 2.91/1.81 @ ! [X3: $i] :
% 2.91/1.81 ( ( c_In @ X3 @ X1 )
% 2.91/1.81 => ? [X4: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X4 @ X0 )
% 2.91/1.81 @ ( ( X2 @ X4 )
% 2.91/1.81 = X3 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax58,axiom,
% 2.91/1.81 ( c_atleastp
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax59,axiom,
% 2.91/1.81 ( c_equip
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax60,axiom,
% 2.91/1.81 ( c_In_rec_poly_G_i
% 2.91/1.81 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 2.91/1.81 ! [X3: $i > $i > $o] :
% 2.91/1.81 ( ! [X4: $i,X5: $i > $i] :
% 2.91/1.81 ( ! [X6: $i] :
% 2.91/1.81 ( ( c_In @ X6 @ X4 )
% 2.91/1.81 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 2.91/1.81 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 2.91/1.81 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax61,axiom,
% 2.91/1.81 ( c_In_rec_poly_i
% 2.91/1.81 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 2.91/1.81 ( c_Eps_i
% 2.91/1.81 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax62,axiom,
% 2.91/1.81 ( c_ordsucc
% 2.91/1.81 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax63,axiom,
% 2.91/1.81 ( c_nat_p
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ! [X1: $i > $o] :
% 2.91/1.81 ( ( X1 @ c_Empty )
% 2.91/1.81 => ( ! [X2: $i] :
% 2.91/1.81 ( ( X1 @ X2 )
% 2.91/1.81 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 2.91/1.81 => ( X1 @ X0 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax64,axiom,
% 2.91/1.81 ( c_nat_primrec
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.91/1.81 ( c_In_rec_poly_i
% 2.91/1.81 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax65,axiom,
% 2.91/1.81 ( c_add_nat
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_nat_primrec @ X0
% 2.91/1.81 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 2.91/1.81 @ X1 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax66,axiom,
% 2.91/1.81 ( c_mul_nat
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_nat_primrec @ c_Empty
% 2.91/1.81 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 2.91/1.81 @ X1 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax67,axiom,
% 2.91/1.81 ( c_ordinal
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ( c_and @ ( c_TransSet @ X0 )
% 2.91/1.81 @ ! [X1: $i] :
% 2.91/1.81 ( ( c_In @ X1 @ X0 )
% 2.91/1.81 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax68,axiom,
% 2.91/1.81 ( c_V_
% 2.91/1.81 = ( c_In_rec_poly_i
% 2.91/1.81 @ ^ [X0: $i,X1: $i > $i] :
% 2.91/1.81 ( c_famunion @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax69,axiom,
% 2.91/1.81 ( c_Inj1
% 2.91/1.81 = ( c_In_rec_poly_i
% 2.91/1.81 @ ^ [X0: $i,X1: $i > $i] :
% 2.91/1.81 ( c_binunion @ ( c_Sing @ c_Empty )
% 2.91/1.81 @ ( c_Repl @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax70,axiom,
% 2.91/1.81 ( c_Inj0
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ( c_Repl @ X0
% 2.91/1.81 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax71,axiom,
% 2.91/1.81 ( c_Unj
% 2.91/1.81 = ( c_In_rec_poly_i
% 2.91/1.81 @ ^ [X0: $i,X1: $i > $i] :
% 2.91/1.81 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 2.91/1.81 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax72,axiom,
% 2.91/1.81 ( c_combine_funcs
% 2.91/1.81 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 2.91/1.81 ( c_If_i
% 2.91/1.81 @ ( X4
% 2.91/1.81 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 2.91/1.81 @ ( X2 @ ( c_Unj @ X4 ) )
% 2.91/1.81 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax73,axiom,
% 2.91/1.81 ( c_setsum
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_binunion
% 2.91/1.81 @ ( c_Repl @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 2.91/1.81 @ ( c_Repl @ X1
% 2.91/1.81 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax74,axiom,
% 2.91/1.81 ( c_proj0
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ( c_ReplSep @ X0
% 2.91/1.81 @ ^ [X1: $i] :
% 2.91/1.81 ? [X2: $i] :
% 2.91/1.81 ( ( c_Inj0 @ X2 )
% 2.91/1.81 = X1 )
% 2.91/1.81 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax75,axiom,
% 2.91/1.81 ( c_proj1
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ( c_ReplSep @ X0
% 2.91/1.81 @ ^ [X1: $i] :
% 2.91/1.81 ? [X2: $i] :
% 2.91/1.81 ( ( c_Inj1 @ X2 )
% 2.91/1.81 = X1 )
% 2.91/1.81 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax76,axiom,
% 2.91/1.81 ( c_binrep
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax77,axiom,
% 2.91/1.81 ( c_lam
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i] :
% 2.91/1.81 ( c_famunion @ X0
% 2.91/1.81 @ ^ [X2: $i] :
% 2.91/1.81 ( c_Repl @ ( X1 @ X2 )
% 2.91/1.81 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax78,axiom,
% 2.91/1.81 ( c_setprod
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_lam @ X0
% 2.91/1.81 @ ^ [X2: $i] : X1 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax79,axiom,
% 2.91/1.81 ( c_ap
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_ReplSep @ X0
% 2.91/1.81 @ ^ [X2: $i] :
% 2.91/1.81 ? [X3: $i] :
% 2.91/1.81 ( X2
% 2.91/1.81 = ( c_setsum @ X1 @ X3 ) )
% 2.91/1.81 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax80,axiom,
% 2.91/1.81 ( c_setsum_p
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 2.91/1.81 = X0 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax81,axiom,
% 2.91/1.81 ( c_tuple_p
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ! [X2: $i] :
% 2.91/1.81 ( ( c_In @ X2 @ X1 )
% 2.91/1.81 => ? [X3: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X3 @ X0 )
% 2.91/1.81 @ ? [X4: $i] :
% 2.91/1.81 ( X2
% 2.91/1.81 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax82,axiom,
% 2.91/1.81 ( c_Pi
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i] :
% 2.91/1.81 ( c_Sep
% 2.91/1.81 @ ( c_Power
% 2.91/1.81 @ ( c_lam @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 2.91/1.81 @ ^ [X2: $i] :
% 2.91/1.81 ! [X3: $i] :
% 2.91/1.81 ( ( c_In @ X3 @ X0 )
% 2.91/1.81 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax83,axiom,
% 2.91/1.81 ( c_setexp
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_Pi @ X1
% 2.91/1.81 @ ^ [X2: $i] : X0 ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax84,axiom,
% 2.91/1.81 ( c_Sep2
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 2.91/1.81 ( c_Sep
% 2.91/1.81 @ ( c_lam @ X0
% 2.91/1.81 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.91/1.81 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax85,axiom,
% 2.91/1.81 ( c_set_of_pairs
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ! [X1: $i] :
% 2.91/1.81 ( ( c_In @ X1 @ X0 )
% 2.91/1.81 => ? [X2: $i,X3: $i] :
% 2.91/1.81 ( X1
% 2.91/1.81 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 2.91/1.81 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax86,axiom,
% 2.91/1.81 ( c_lam2
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 2.91/1.81 ( c_lam @ X0
% 2.91/1.81 @ ^ [X3: $i] :
% 2.91/1.81 ( c_lam @ ( X1 @ X3 )
% 2.91/1.81 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax87,axiom,
% 2.91/1.81 ( c_PNoEq_
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.91/1.81 ! [X3: $i] :
% 2.91/1.81 ( ( c_In @ X3 @ X0 )
% 2.91/1.81 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax88,axiom,
% 2.91/1.81 ( c_PNoLt_
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.91/1.81 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax89,axiom,
% 2.91/1.81 ( c_PNoLt
% 2.91/1.81 = ( ^ [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 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax90,axiom,
% 2.91/1.81 ( c_PNoLe
% 2.91/1.81 = ( ^ [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 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax91,axiom,
% 2.91/1.81 ( c_PNo_downc
% 2.91/1.81 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.91/1.81 ? [X3: $i] :
% 2.91/1.81 ( c_and @ ( c_ordinal @ X3 )
% 2.91/1.81 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax92,axiom,
% 2.91/1.81 ( c_PNo_upc
% 2.91/1.81 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.91/1.81 ? [X3: $i] :
% 2.91/1.81 ( c_and @ ( c_ordinal @ X3 )
% 2.91/1.81 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax93,axiom,
% 2.91/1.81 ( c_SNoElts_
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ( c_binunion @ X0
% 2.91/1.81 @ ( c_Repl @ X0
% 2.91/1.81 @ ^ [X1: $i] :
% 2.91/1.81 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.91/1.81 @ X1 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax94,axiom,
% 2.91/1.81 ( c_SNo_
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 2.91/1.81 @ ! [X2: $i] :
% 2.91/1.81 ( ( c_In @ X2 @ X0 )
% 2.91/1.81 => ( c_exactly1of2
% 2.91/1.81 @ ( c_In
% 2.91/1.81 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.91/1.81 @ X2 )
% 2.91/1.81 @ X1 )
% 2.91/1.81 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax95,axiom,
% 2.91/1.81 ( c_PSNo
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $o] :
% 2.91/1.81 ( c_binunion
% 2.91/1.81 @ ( c_Sep @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 2.91/1.81 @ ( c_ReplSep @ X0
% 2.91/1.81 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 2.91/1.81 @ ^ [X2: $i] :
% 2.91/1.81 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.91/1.81 @ X2 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax96,axiom,
% 2.91/1.81 ( c_SNo
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax97,axiom,
% 2.91/1.81 ( c_SNoLev
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ( c_Eps_i
% 2.91/1.81 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax98,axiom,
% 2.91/1.81 ( c_SNoEq_
% 2.91/1.81 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.91/1.81 ( c_PNoEq_ @ X0
% 2.91/1.81 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 2.91/1.81 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax99,axiom,
% 2.91/1.81 ( c_SNoLt
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 2.91/1.81 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.91/1.81 @ ( c_SNoLev @ X1 )
% 2.91/1.81 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax100,axiom,
% 2.91/1.81 ( c_SNoLe
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 2.91/1.81 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.91/1.81 @ ( c_SNoLev @ X1 )
% 2.91/1.81 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax101,axiom,
% 2.91/1.81 ( c_binop_on
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.91/1.81 ! [X2: $i] :
% 2.91/1.81 ( ( c_In @ X2 @ X0 )
% 2.91/1.81 => ! [X3: $i] :
% 2.91/1.81 ( ( c_In @ X3 @ X0 )
% 2.91/1.81 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax102,axiom,
% 2.91/1.81 ( c_Loop
% 2.91/1.81 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 2.91/1.81 ( c_and
% 2.91/1.81 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 2.91/1.81 @ ! [X5: $i] :
% 2.91/1.81 ( ( c_In @ X5 @ X0 )
% 2.91/1.81 => ( c_and
% 2.91/1.81 @ ( ( X1 @ X4 @ X5 )
% 2.91/1.81 = X5 )
% 2.91/1.81 @ ( ( X1 @ X5 @ X4 )
% 2.91/1.81 = X5 ) ) ) )
% 2.91/1.81 @ ! [X5: $i] :
% 2.91/1.81 ( ( c_In @ X5 @ X0 )
% 2.91/1.81 => ! [X6: $i] :
% 2.91/1.81 ( ( c_In @ X6 @ X0 )
% 2.91/1.81 => ( c_and
% 2.91/1.81 @ ( c_and
% 2.91/1.81 @ ( c_and
% 2.91/1.81 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 2.91/1.81 = X6 )
% 2.91/1.81 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 2.91/1.81 = X6 ) )
% 2.91/1.81 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 2.91/1.81 = X5 ) )
% 2.91/1.81 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 2.91/1.81 = X5 ) ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax103,axiom,
% 2.91/1.81 ( c_Loop_with_defs
% 2.91/1.81 = ( ^ [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] :
% 2.91/1.81 ( c_and
% 2.91/1.81 @ ( c_and
% 2.91/1.81 @ ( c_and
% 2.91/1.81 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 2.91/1.81 @ ! [X14: $i] :
% 2.91/1.81 ( ( c_In @ X14 @ X0 )
% 2.91/1.81 => ! [X15: $i] :
% 2.91/1.81 ( ( c_In @ X15 @ X0 )
% 2.91/1.81 => ( ( X5 @ X14 @ X15 )
% 2.91/1.81 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 2.91/1.81 @ ! [X14: $i] :
% 2.91/1.81 ( ( c_In @ X14 @ X0 )
% 2.91/1.81 => ! [X15: $i] :
% 2.91/1.81 ( ( c_In @ X15 @ X0 )
% 2.91/1.81 => ! [X16: $i] :
% 2.91/1.81 ( ( c_In @ X16 @ X0 )
% 2.91/1.81 => ( ( X6 @ X14 @ X15 @ X16 )
% 2.91/1.81 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 2.91/1.81 @ ! [X14: $i] :
% 2.91/1.81 ( ( c_In @ X14 @ X0 )
% 2.91/1.81 => ! [X15: $i] :
% 2.91/1.81 ( ( c_In @ X15 @ X0 )
% 2.91/1.81 => ( c_and
% 2.91/1.81 @ ( c_and
% 2.91/1.81 @ ( c_and
% 2.91/1.81 @ ( c_and
% 2.91/1.81 @ ( ( X7 @ X14 @ X15 )
% 2.91/1.81 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 2.91/1.81 @ ( ( X10 @ X14 @ X15 )
% 2.91/1.81 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 2.91/1.81 @ ( ( X11 @ X14 @ X15 )
% 2.91/1.81 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 2.91/1.81 @ ( ( X12 @ X14 @ X15 )
% 2.91/1.81 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 2.91/1.81 @ ( ( X13 @ X14 @ X15 )
% 2.91/1.81 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 2.91/1.81 @ ! [X14: $i] :
% 2.91/1.81 ( ( c_In @ X14 @ X0 )
% 2.91/1.81 => ! [X15: $i] :
% 2.91/1.81 ( ( c_In @ X15 @ X0 )
% 2.91/1.81 => ! [X16: $i] :
% 2.91/1.81 ( ( c_In @ X16 @ X0 )
% 2.91/1.81 => ( c_and
% 2.91/1.81 @ ( ( X8 @ X14 @ X15 @ X16 )
% 2.91/1.81 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 2.91/1.81 @ ( ( X9 @ X14 @ X15 @ X16 )
% 2.91/1.81 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax104,axiom,
% 2.91/1.81 ( c_Loop_with_defs_cex1
% 2.91/1.81 = ( ^ [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] :
% 2.91/1.81 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.91/1.81 @ ? [X14: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X14 @ X0 )
% 2.91/1.81 @ ? [X15: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X15 @ X0 )
% 2.91/1.81 @ ? [X16: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X16 @ X0 )
% 2.91/1.81 @ ? [X17: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X17 @ X0 )
% 2.91/1.81 @ ( c_not
% 2.91/1.81 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 2.91/1.81 = X4 ) ) ) ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax105,axiom,
% 2.91/1.81 ( c_Loop_with_defs_cex2
% 2.91/1.81 = ( ^ [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] :
% 2.91/1.81 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.91/1.81 @ ? [X14: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X14 @ X0 )
% 2.91/1.81 @ ? [X15: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X15 @ X0 )
% 2.91/1.81 @ ? [X16: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X16 @ X0 )
% 2.91/1.81 @ ? [X17: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X17 @ X0 )
% 2.91/1.81 @ ? [X18: $i] :
% 2.91/1.81 ( c_and @ ( c_In @ X18 @ X0 )
% 2.91/1.81 @ ( c_not
% 2.91/1.81 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 2.91/1.81 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax106,axiom,
% 2.91/1.81 ( c_combinator
% 2.91/1.81 = ( ^ [X0: $i] :
% 2.91/1.81 ! [X1: $i > $o] :
% 2.91/1.81 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 2.91/1.81 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 2.91/1.81 => ( ! [X2: $i,X3: $i] :
% 2.91/1.81 ( ( X1 @ X2 )
% 2.91/1.81 => ( ( X1 @ X3 )
% 2.91/1.81 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 2.91/1.81 => ( X1 @ X0 ) ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax107,axiom,
% 2.91/1.81 ( c_combinator_equiv
% 2.91/1.81 = ( ^ [X0: $i,X1: $i] :
% 2.91/1.81 ! [X2: $i > $i > $o] :
% 2.91/1.81 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 2.91/1.81 ( ( c_per_i @ X2 )
% 2.91/1.81 => ( ! [X6: $i] :
% 2.91/1.81 ( ( c_combinator @ X6 )
% 2.91/1.81 => ( X2 @ X6 @ X6 ) )
% 2.91/1.81 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.91/1.81 ( ( c_combinator @ X6 )
% 2.91/1.81 => ( ( c_combinator @ X7 )
% 2.91/1.81 => ( ( c_combinator @ X8 )
% 2.91/1.81 => ( ( c_combinator @ X9 )
% 2.91/1.81 => ( ( X2 @ X6 @ X8 )
% 2.91/1.81 => ( ( X2 @ X7 @ X9 )
% 2.91/1.81 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 2.91/1.81 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 2.91/1.81 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 2.91/1.81 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 2.91/1.81 @ ( c_Inj0 @ c_Empty )
% 2.91/1.81 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 2.91/1.81 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(ax108,axiom,
% 2.91/1.81 ( c_equip_mod
% 2.91/1.81 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.91/1.81 ? [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 ) ) ) ) ) ).
% 2.91/1.81
% 2.91/1.81 thf(conj,conjecture,
% 2.91/1.81 ! [X0: ( $i > $i ) > $i > $o,X1: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,X2: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,X3: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o] :
% 2.91/1.81 ( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i] :
% 2.91/1.81 ( X3
% 2.91/1.81 @ ^ [X8: $i > $i] : ( c_Inj0 @ ( X8 @ c_Empty ) )
% 2.91/1.81 @ ^ [X8: $i] : X5
% 2.91/1.81 @ ^ [X8: $i] :
% 2.91/1.81 ( X6 @ c_Empty
% 2.91/1.81 @ ^ [X9: $i] : c_Empty )
% 2.91/1.81 @ ( c_Inj1 @ c_Empty ) )
% 2.91/1.81 => ( ! [X4: $i > ( $i > $i ) > $i > $i > $i,X5: $i,X6: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,X7: $i] :
% 2.91/1.81 ( ( X3
% 2.91/1.81 @ ^ [X8: $i > $i] :
% 2.91/1.81 ( c_Inj1
% 2.91/1.81 @ ( c_Inj1
% 2.91/1.81 @ ( X6
% 2.91/1.81 @ ^ [X9: ( $i > $i ) > $i,X10: $i > $i,X11: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 2.91/1.81 @ ^ [X8: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ X8 ) )
% 2.91/1.81 @ ^ [X8: $i] : c_Empty
% 2.91/1.81 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
% 2.91/1.81 => ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
% 2.91/1.81 => ( ! [X4: $i > $i > $i,X5: ( ( $i > $i > $i ) > $i ) > $i,X6: $i > ( $i > $i > $i ) > $i,X7: ( $i > $i > $i > $i ) > $i] :
% 2.91/1.81 ( X2
% 2.91/1.81 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ X12 ) )
% 2.91/1.81 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
% 2.91/1.81 @ ^ [X8: $i > $i,X9: $i] :
% 2.91/1.81 ( c_setsum @ X9
% 2.91/1.81 @ ( X7
% 2.91/1.81 @ ^ [X10: $i,X11: $i,X12: $i] : c_Empty ) ) )
% 2.91/1.81 => ( ! [X4: ( $i > ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X7: $i] :
% 2.91/1.81 ( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ X7 ) )
% 2.91/1.81 @ ( X4
% 2.91/1.81 @ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty ) )
% 2.91/1.81 => ( ( X2
% 2.91/1.81 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
% 2.91/1.81 @ ( c_setsum
% 2.91/1.81 @ ( X4
% 2.91/1.81 @ ^ [X8: $i,X9: $i > $i,X10: $i] : c_Empty )
% 2.91/1.81 @ c_Empty )
% 2.91/1.81 @ ^ [X8: $i > $i,X9: $i] : ( c_Inj1 @ c_Empty ) )
% 2.91/1.81 => ( X2
% 2.91/1.81 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i,X9: $i,X10: $i,X11: $i > $i,X12: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
% 2.91/1.81 @ c_Empty
% 2.91/1.81 @ ^ [X8: $i > $i,X9: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
% 2.91/1.81 => ( ! [X4: $i,X5: ( $i > $i > $i ) > $i > $i,X6: ( $i > $i > $i > $i ) > $i,X7: $i > $i] :
% 2.91/1.81 ( ( c_In
% 2.91/1.81 @ ( X6
% 2.91/1.81 @ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ X9 ) )
% 2.91/1.81 @ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 2.91/1.81 => ( ( X0
% 2.91/1.81 @ ^ [X8: $i] : X8
% 2.91/1.81 @ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
% 2.91/1.81 => ( X1
% 2.91/1.81 @ ^ [X8: $i,X9: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ X9 ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( X7 @ ( X7 @ c_Empty ) ) ) )
% 2.91/1.81 @ ^ [X8: $i > $i] : c_Empty ) ) )
% 2.91/1.81 => ( ! [X4: $i,X5: $i,X6: $i > $i,X7: $i] :
% 2.91/1.81 ( ( X1
% 2.91/1.81 @ ^ [X8: $i,X9: $i] : X8
% 2.91/1.81 @ ^ [X8: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
% 2.91/1.81 => c_False )
% 2.91/1.81 => ( ! [X4: $i,X5: $i,X6: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,X7: $i > $i] :
% 2.91/1.81 ( X0
% 2.91/1.81 @ ^ [X8: $i] : X8
% 2.91/1.81 @ ( c_Inj0 @ c_Empty ) )
% 2.91/1.81 => ( ! [X4: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i] :
% 2.91/1.81 ( ( X0
% 2.91/1.81 @ ^ [X8: $i] : X8
% 2.91/1.81 @ ( X6 @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X5 @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( X6 @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
% 2.91/1.81 @ ( X4
% 2.91/1.81 @ ^ [X8: $i] : c_Empty
% 2.91/1.81 @ ^ [X8: $i > $i,X9: $i] : ( c_setsum @ X9 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 2.91/1.81 => ( c_In @ ( c_Inj0 @ c_Empty )
% 2.91/1.81 @ ( X4
% 2.91/1.81 @ ^ [X8: $i] : X8
% 2.91/1.81 @ ^ [X8: $i > $i,X9: $i] : c_Empty ) ) )
% 2.91/1.81 => c_False ) ) ) ) ) ) ) ) ).
% 2.91/1.81 ------------------------
% 2.91/1.84 % (29421)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_29311 for (2999ds/2Mi)
% 2.91/1.84 % (29422)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_29311 for (2999ds/275Mi)
% 2.91/1.84 % (29418)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_29311 for (2999ds/4Mi)
% 2.91/1.84 % (29417)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/183Mi)
% 2.91/1.84 % (29419)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_29311 for (2999ds/27Mi)
% 2.91/1.84 % (29423)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/18Mi)
% 2.91/1.84 % (29420)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/2Mi)
% 2.91/1.84 % (29420)Instruction limit reached!
% 2.91/1.84 % (29420)------------------------------
% 2.91/1.84 % (29420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.84 % (29420)Termination reason: Unknown
% 2.91/1.84 % (29420)Termination phase: shuffling
% 2.91/1.84
% 2.91/1.84 % (29420)Memory used [KB]: 1151
% 2.91/1.84 % (29420)Time elapsed: 0.002 s
% 2.91/1.84 % (29420)Instructions burned: 2 (million)
% 2.91/1.84 % (29420)------------------------------
% 2.91/1.84 % (29420)------------------------------
% 2.91/1.84 % (29421)Instruction limit reached!
% 2.91/1.84 % (29421)------------------------------
% 2.91/1.84 % (29421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.84 % (29421)Termination reason: Unknown
% 2.91/1.84 % (29421)Termination phase: shuffling
% 2.91/1.84
% 2.91/1.84 % (29421)Memory used [KB]: 1279
% 2.91/1.84 % (29421)Time elapsed: 0.003 s
% 2.91/1.84 % (29421)Instructions burned: 2 (million)
% 2.91/1.84 % (29421)------------------------------
% 2.91/1.84 % (29421)------------------------------
% 2.91/1.84 % (29418)Instruction limit reached!
% 2.91/1.84 % (29418)------------------------------
% 2.91/1.84 % (29418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.84 % (29418)Termination reason: Unknown
% 2.91/1.84 % (29418)Termination phase: shuffling
% 2.91/1.84
% 2.91/1.84 % (29418)Memory used [KB]: 1279
% 2.91/1.84 % (29418)Time elapsed: 0.004 s
% 2.91/1.84 % (29418)Instructions burned: 4 (million)
% 2.91/1.84 % (29418)------------------------------
% 2.91/1.84 % (29418)------------------------------
% 2.91/1.85 % (29423)Instruction limit reached!
% 2.91/1.85 % (29423)------------------------------
% 2.91/1.85 % (29423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.85 % (29423)Termination reason: Unknown
% 2.91/1.85 % (29423)Termination phase: shuffling
% 2.91/1.85
% 2.91/1.85 % (29423)Memory used [KB]: 1535
% 2.91/1.85 % (29423)Time elapsed: 0.011 s
% 2.91/1.85 % (29423)Instructions burned: 19 (million)
% 2.91/1.85 % (29423)------------------------------
% 2.91/1.85 % (29423)------------------------------
% 2.91/1.85 % (29419)Instruction limit reached!
% 2.91/1.85 % (29419)------------------------------
% 2.91/1.85 % (29419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.85 % (29419)Termination reason: Unknown
% 2.91/1.85 % (29419)Termination phase: Property scanning
% 2.91/1.85
% 2.91/1.85 % (29419)Memory used [KB]: 1535
% 2.91/1.85 % (29419)Time elapsed: 0.015 s
% 2.91/1.85 % (29419)Instructions burned: 29 (million)
% 2.91/1.85 % (29419)------------------------------
% 2.91/1.85 % (29419)------------------------------
% 2.91/1.86 % (29425)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_29311 for (2999ds/37Mi)
% 2.91/1.86 % (29426)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_29311 for (2999ds/15Mi)
% 2.91/1.86 % (29424)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/3Mi)
% 2.91/1.86 % (29424)Instruction limit reached!
% 2.91/1.86 % (29424)------------------------------
% 2.91/1.86 % (29424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.86 % (29424)Termination reason: Unknown
% 2.91/1.86 % (29424)Termination phase: shuffling
% 2.91/1.86
% 2.91/1.86 % (29424)Memory used [KB]: 1279
% 2.91/1.86 % (29424)Time elapsed: 0.003 s
% 2.91/1.86 % (29424)Instructions burned: 3 (million)
% 2.91/1.86 % (29424)------------------------------
% 2.91/1.86 % (29424)------------------------------
% 2.91/1.87 % (29426)Instruction limit reached!
% 2.91/1.87 % (29426)------------------------------
% 2.91/1.87 % (29426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.87 % (29426)Termination reason: Unknown
% 2.91/1.87 % (29426)Termination phase: shuffling
% 2.91/1.87
% 2.91/1.87 % (29426)Memory used [KB]: 1535
% 2.91/1.87 % (29426)Time elapsed: 0.009 s
% 2.91/1.87 % (29426)Instructions burned: 16 (million)
% 2.91/1.87 % (29426)------------------------------
% 2.91/1.87 % (29426)------------------------------
% 2.91/1.87 % (29427)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_29311 for (2999ds/3Mi)
% 2.91/1.87 % (29422)Refutation not found, incomplete strategy
% 2.91/1.87 % (29422)------------------------------
% 2.91/1.87 % (29422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.87 % (29422)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.87
% 2.91/1.87
% 2.91/1.87 % (29422)Memory used [KB]: 6396
% 2.91/1.87 % (29422)Time elapsed: 0.030 s
% 2.91/1.87 % (29422)Instructions burned: 60 (million)
% 2.91/1.87 % (29422)------------------------------
% 2.91/1.87 % (29422)------------------------------
% 2.91/1.87 % (29427)Instruction limit reached!
% 2.91/1.87 % (29427)------------------------------
% 2.91/1.87 % (29427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.87 % (29427)Termination reason: Unknown
% 2.91/1.87 % (29427)Termination phase: shuffling
% 2.91/1.87
% 2.91/1.87 % (29427)Memory used [KB]: 1279
% 2.91/1.87 % (29427)Time elapsed: 0.004 s
% 2.91/1.87 % (29427)Instructions burned: 3 (million)
% 2.91/1.87 % (29427)------------------------------
% 2.91/1.87 % (29427)------------------------------
% 2.91/1.87 % (29428)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_29311 for (2999ds/1041Mi)
% 2.91/1.88 % (29425)Instruction limit reached!
% 2.91/1.88 % (29425)------------------------------
% 2.91/1.88 % (29425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.88 % (29425)Termination reason: Unknown
% 2.91/1.88 % (29425)Termination phase: Property scanning
% 2.91/1.88
% 2.91/1.88 % (29425)Memory used [KB]: 1535
% 2.91/1.88 % (29425)Time elapsed: 0.019 s
% 2.91/1.88 % (29425)Instructions burned: 37 (million)
% 2.91/1.88 % (29425)------------------------------
% 2.91/1.88 % (29425)------------------------------
% 2.91/1.88 % (29429)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/7Mi)
% 2.91/1.88 % (29429)Instruction limit reached!
% 2.91/1.88 % (29429)------------------------------
% 2.91/1.88 % (29429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.88 % (29429)Termination reason: Unknown
% 2.91/1.88 % (29429)Termination phase: shuffling
% 2.91/1.88
% 2.91/1.88 % (29429)Memory used [KB]: 1279
% 2.91/1.88 % (29429)Time elapsed: 0.006 s
% 2.91/1.88 % (29429)Instructions burned: 8 (million)
% 2.91/1.88 % (29429)------------------------------
% 2.91/1.88 % (29429)------------------------------
% 2.91/1.88 % (29430)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/16Mi)
% 2.91/1.89 % (29431)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_29311 for (2999ds/3Mi)
% 2.91/1.89 % (29432)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_29311 for (2999ds/3Mi)
% 2.91/1.89 % (29431)Instruction limit reached!
% 2.91/1.89 % (29431)------------------------------
% 2.91/1.89 % (29431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.89 % (29431)Termination reason: Unknown
% 2.91/1.89 % (29432)Instruction limit reached!
% 2.91/1.89 % (29432)------------------------------
% 2.91/1.89 % (29432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.89 % (29431)Termination phase: shuffling
% 2.91/1.89
% 2.91/1.89 % (29431)Memory used [KB]: 1279
% 2.91/1.89 % (29431)Time elapsed: 0.003 s
% 2.91/1.89 % (29431)Instructions burned: 3 (million)
% 2.91/1.89 % (29431)------------------------------
% 2.91/1.89 % (29431)------------------------------
% 2.91/1.89 % (29432)Termination reason: Unknown
% 2.91/1.89 % (29432)Termination phase: shuffling
% 2.91/1.89
% 2.91/1.89 % (29432)Memory used [KB]: 1279
% 2.91/1.89 % (29432)Time elapsed: 0.003 s
% 2.91/1.89 % (29432)Instructions burned: 3 (million)
% 2.91/1.89 % (29432)------------------------------
% 2.91/1.89 % (29432)------------------------------
% 2.91/1.89 % (29430)Instruction limit reached!
% 2.91/1.89 % (29430)------------------------------
% 2.91/1.89 % (29430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.89 % (29430)Termination reason: Unknown
% 2.91/1.89 % (29430)Termination phase: shuffling
% 2.91/1.89
% 2.91/1.89 % (29430)Memory used [KB]: 1535
% 2.91/1.89 % (29430)Time elapsed: 0.010 s
% 2.91/1.89 % (29430)Instructions burned: 16 (million)
% 2.91/1.89 % (29430)------------------------------
% 2.91/1.89 % (29430)------------------------------
% 2.91/1.89 % (29433)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/7Mi)
% 2.91/1.90 % (29433)Instruction limit reached!
% 2.91/1.90 % (29433)------------------------------
% 2.91/1.90 % (29433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.90 % (29433)Termination reason: Unknown
% 2.91/1.90 % (29433)Termination phase: shuffling
% 2.91/1.90
% 2.91/1.90 % (29433)Memory used [KB]: 1279
% 2.91/1.90 % (29433)Time elapsed: 0.005 s
% 2.91/1.90 % (29433)Instructions burned: 7 (million)
% 2.91/1.90 % (29433)------------------------------
% 2.91/1.90 % (29433)------------------------------
% 2.93/1.90 % (29434)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/3Mi)
% 2.93/1.90 % (29434)Instruction limit reached!
% 2.93/1.90 % (29434)------------------------------
% 2.93/1.90 % (29434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.90 % (29434)Termination reason: Unknown
% 2.93/1.90 % (29434)Termination phase: shuffling
% 2.93/1.90
% 2.93/1.90 % (29434)Memory used [KB]: 1279
% 2.93/1.90 % (29434)Time elapsed: 0.004 s
% 2.93/1.90 % (29434)Instructions burned: 4 (million)
% 2.93/1.90 % (29434)------------------------------
% 2.93/1.90 % (29434)------------------------------
% 2.93/1.91 % (29435)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/4Mi)
% 2.93/1.91 % (29437)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/710Mi)
% 2.93/1.91 % (29436)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/18Mi)
% 2.93/1.91 % (29435)Instruction limit reached!
% 2.93/1.91 % (29435)------------------------------
% 2.93/1.91 % (29435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.91 % (29435)Termination reason: Unknown
% 2.93/1.91 % (29435)Termination phase: shuffling
% 2.93/1.91
% 2.93/1.91 % (29435)Memory used [KB]: 1279
% 2.93/1.91 % (29435)Time elapsed: 0.004 s
% 2.93/1.91 % (29435)Instructions burned: 4 (million)
% 2.93/1.91 % (29435)------------------------------
% 2.93/1.91 % (29435)------------------------------
% 2.93/1.91 % (29438)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/6Mi)
% 2.93/1.92 % (29438)Instruction limit reached!
% 2.93/1.92 % (29438)------------------------------
% 2.93/1.92 % (29438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.92 % (29438)Termination reason: Unknown
% 2.93/1.92 % (29438)Termination phase: shuffling
% 2.93/1.92
% 2.93/1.92 % (29438)Memory used [KB]: 1279
% 2.93/1.92 % (29438)Time elapsed: 0.005 s
% 2.93/1.92 % (29438)Instructions burned: 7 (million)
% 2.93/1.92 % (29438)------------------------------
% 2.93/1.92 % (29438)------------------------------
% 2.93/1.92 % (29436)Instruction limit reached!
% 2.93/1.92 % (29436)------------------------------
% 2.93/1.92 % (29436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.92 % (29436)Termination reason: Unknown
% 2.93/1.92 % (29436)Termination phase: shuffling
% 2.93/1.92
% 2.93/1.92 % (29436)Memory used [KB]: 1535
% 2.93/1.92 % (29436)Time elapsed: 0.011 s
% 2.93/1.92 % (29436)Instructions burned: 18 (million)
% 2.93/1.92 % (29436)------------------------------
% 2.93/1.92 % (29436)------------------------------
% 2.93/1.92 % (29439)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/902Mi)
% 2.93/1.92 % (29417)Instruction limit reached!
% 2.93/1.92 % (29417)------------------------------
% 2.93/1.92 % (29417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.92 % (29417)Termination reason: Unknown
% 2.93/1.92 % (29417)Termination phase: Saturation
% 2.93/1.92
% 2.93/1.92 % (29417)Memory used [KB]: 1918
% 2.93/1.92 % (29417)Time elapsed: 0.082 s
% 2.93/1.92 % (29417)Instructions burned: 184 (million)
% 2.93/1.92 % (29417)------------------------------
% 2.93/1.92 % (29417)------------------------------
% 2.93/1.92 % (29440)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/21Mi)
% 2.93/1.93 % (29441)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/5Mi)
% 2.93/1.93 % (29440)Instruction limit reached!
% 2.93/1.93 % (29440)------------------------------
% 2.93/1.93 % (29440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (29440)Termination reason: Unknown
% 2.93/1.93 % (29440)Termination phase: Property scanning
% 2.93/1.93
% 2.93/1.93 % (29440)Memory used [KB]: 1535
% 2.93/1.93 % (29440)Time elapsed: 0.012 s
% 2.93/1.93 % (29440)Instructions burned: 23 (million)
% 2.93/1.93 % (29440)------------------------------
% 2.93/1.93 % (29440)------------------------------
% 2.93/1.93 % (29441)Instruction limit reached!
% 2.93/1.93 % (29441)------------------------------
% 2.93/1.93 % (29441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (29441)Termination reason: Unknown
% 2.93/1.93 % (29441)Termination phase: shuffling
% 2.93/1.93
% 2.93/1.93 % (29441)Memory used [KB]: 1279
% 2.93/1.93 % (29441)Time elapsed: 0.005 s
% 2.93/1.93 % (29441)Instructions burned: 7 (million)
% 2.93/1.93 % (29441)------------------------------
% 2.93/1.93 % (29441)------------------------------
% 2.93/1.94 % (29442)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/6Mi)
% 2.93/1.94 % (29443)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29311 for (2999ds/377Mi)
% 2.93/1.94 % (29442)Instruction limit reached!
% 2.93/1.94 % (29442)------------------------------
% 2.93/1.94 % (29442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.94 % (29442)Termination reason: Unknown
% 2.93/1.94 % (29442)Termination phase: shuffling
% 2.93/1.94
% 2.93/1.94 % (29442)Memory used [KB]: 1279
% 2.93/1.94 % (29442)Time elapsed: 0.005 s
% 2.93/1.94 % (29442)Instructions burned: 7 (million)
% 2.93/1.94 % (29442)------------------------------
% 2.93/1.94 % (29442)------------------------------
% 2.93/1.95 % (29444)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/779Mi)
% 2.93/1.95 % (29445)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/19Mi)
% 2.93/1.95 % (29439)Refutation not found, incomplete strategy
% 2.93/1.95 % (29439)------------------------------
% 2.93/1.95 % (29439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (29439)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.95
% 2.93/1.95
% 2.93/1.95 % (29439)Memory used [KB]: 6396
% 2.93/1.95 % (29439)Time elapsed: 0.037 s
% 2.93/1.95 % (29439)Instructions burned: 73 (million)
% 2.93/1.95 % (29439)------------------------------
% 2.93/1.95 % (29439)------------------------------
% 2.93/1.96 % (29446)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/879Mi)
% 2.93/1.96 % (29445)Instruction limit reached!
% 2.93/1.96 % (29445)------------------------------
% 2.93/1.96 % (29445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.96 % (29445)Termination reason: Unknown
% 2.93/1.96 % (29445)Termination phase: Property scanning
% 2.93/1.96
% 2.93/1.96 % (29445)Memory used [KB]: 1535
% 2.93/1.96 % (29445)Time elapsed: 0.011 s
% 2.93/1.96 % (29445)Instructions burned: 20 (million)
% 2.93/1.96 % (29445)------------------------------
% 2.93/1.96 % (29445)------------------------------
% 2.93/1.97 % (29447)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/17Mi)
% 2.93/1.98 % (29448)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/3Mi)
% 2.93/1.98 % (29448)Instruction limit reached!
% 2.93/1.98 % (29448)------------------------------
% 2.93/1.98 % (29448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.98 % (29448)Termination reason: Unknown
% 2.93/1.98 % (29448)Termination phase: shuffling
% 2.93/1.98
% 2.93/1.98 % (29448)Memory used [KB]: 1279
% 2.93/1.98 % (29448)Time elapsed: 0.003 s
% 2.93/1.98 % (29448)Instructions burned: 3 (million)
% 2.93/1.98 % (29448)------------------------------
% 2.93/1.98 % (29448)------------------------------
% 2.93/1.98 % (29447)Instruction limit reached!
% 2.93/1.98 % (29447)------------------------------
% 2.93/1.98 % (29447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.98 % (29447)Termination reason: Unknown
% 2.93/1.98 % (29447)Termination phase: shuffling
% 2.93/1.98
% 2.93/1.98 % (29447)Memory used [KB]: 1535
% 2.93/1.98 % (29447)Time elapsed: 0.010 s
% 2.93/1.98 % (29447)Instructions burned: 17 (million)
% 2.93/1.98 % (29447)------------------------------
% 2.93/1.98 % (29447)------------------------------
% 2.93/2.00 % (29449)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/30Mi)
% 2.93/2.00 % (29450)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/127Mi)
% 2.93/2.01 % (29449)Instruction limit reached!
% 2.93/2.01 % (29449)------------------------------
% 2.93/2.01 % (29449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.01 % (29449)Termination reason: Unknown
% 2.93/2.01 % (29449)Termination phase: Preprocessing 3
% 2.93/2.01
% 2.93/2.01 % (29449)Memory used [KB]: 1535
% 2.93/2.01 % (29449)Time elapsed: 0.016 s
% 2.93/2.01 % (29449)Instructions burned: 31 (million)
% 2.93/2.01 % (29449)------------------------------
% 2.93/2.01 % (29449)------------------------------
% 4.27/2.03 % (29451)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29311 for (2998ds/100Mi)
% 4.27/2.05 % (29450)Instruction limit reached!
% 4.27/2.05 % (29450)------------------------------
% 4.27/2.05 % (29450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.05 % (29450)Termination reason: Unknown
% 4.27/2.05 % (29450)Termination phase: Property scanning
% 4.27/2.05
% 4.27/2.05 % (29450)Memory used [KB]: 1918
% 4.27/2.05 % (29450)Time elapsed: 0.061 s
% 4.27/2.05 % (29450)Instructions burned: 129 (million)
% 4.27/2.05 % (29450)------------------------------
% 4.27/2.05 % (29450)------------------------------
% 4.27/2.07 % (29451)Instruction limit reached!
% 4.27/2.07 % (29451)------------------------------
% 4.27/2.07 % (29451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.07 % (29451)Termination reason: Unknown
% 4.27/2.07 % (29451)Termination phase: Property scanning
% 4.27/2.07
% 4.27/2.07 % (29451)Memory used [KB]: 1918
% 4.27/2.07 % (29451)Time elapsed: 0.043 s
% 4.27/2.07 % (29451)Instructions burned: 102 (million)
% 4.27/2.07 % (29451)------------------------------
% 4.27/2.07 % (29451)------------------------------
% 4.27/2.07 % (29452)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_29311 for (2997ds/3Mi)
% 4.27/2.07 % (29452)Instruction limit reached!
% 4.27/2.07 % (29452)------------------------------
% 4.27/2.07 % (29452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.07 % (29452)Termination reason: Unknown
% 4.27/2.07 % (29452)Termination phase: shuffling
% 4.27/2.07
% 4.27/2.07 % (29452)Memory used [KB]: 1279
% 4.27/2.07 % (29452)Time elapsed: 0.004 s
% 4.27/2.07 % (29452)Instructions burned: 4 (million)
% 4.27/2.07 % (29452)------------------------------
% 4.27/2.07 % (29452)------------------------------
% 4.27/2.09 % (29453)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_29311 for (2997ds/20Mi)
% 4.27/2.09 % (29443)Instruction limit reached!
% 4.27/2.09 % (29443)------------------------------
% 4.27/2.09 % (29443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.09 % (29443)Termination reason: Unknown
% 4.27/2.09 % (29443)Termination phase: Saturation
% 4.27/2.09
% 4.27/2.09 % (29443)Memory used [KB]: 6524
% 4.27/2.09 % (29443)Time elapsed: 0.157 s
% 4.27/2.09 % (29443)Instructions burned: 377 (million)
% 4.27/2.09 % (29443)------------------------------
% 4.27/2.09 % (29443)------------------------------
% 4.27/2.09 % (29454)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_29311 for (2997ds/86Mi)
% 4.27/2.10 % (29453)Instruction limit reached!
% 4.27/2.10 % (29453)------------------------------
% 4.27/2.10 % (29453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.10 % (29453)Termination reason: Unknown
% 4.27/2.10 % (29453)Termination phase: Property scanning
% 4.27/2.10
% 4.27/2.10 % (29453)Memory used [KB]: 1535
% 4.27/2.10 % (29453)Time elapsed: 0.012 s
% 4.27/2.10 % (29453)Instructions burned: 21 (million)
% 4.27/2.10 % (29453)------------------------------
% 4.27/2.10 % (29453)------------------------------
% 4.27/2.11 % (29455)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_29311 for (2997ds/107Mi)
% 4.27/2.11 % (29456)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_29311 for (2997ds/39Mi)
% 4.88/2.13 % (29454)Instruction limit reached!
% 4.88/2.13 % (29454)------------------------------
% 4.88/2.13 % (29454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.88/2.13 % (29454)Termination reason: Unknown
% 4.88/2.13 % (29454)Termination phase: Property scanning
% 4.88/2.13
% 4.88/2.13 % (29454)Memory used [KB]: 1918
% 4.88/2.13 % (29454)Time elapsed: 0.038 s
% 4.88/2.13 % (29454)Instructions burned: 87 (million)
% 4.88/2.13 % (29454)------------------------------
% 4.88/2.13 % (29454)------------------------------
% 4.88/2.13 % (29456)Instruction limit reached!
% 4.88/2.13 % (29456)------------------------------
% 4.88/2.13 % (29456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.88/2.13 % (29456)Termination reason: Unknown
% 4.88/2.13 % (29456)Termination phase: Property scanning
% 4.88/2.13
% 4.88/2.13 % (29456)Memory used [KB]: 1535
% 4.88/2.13 % (29456)Time elapsed: 0.019 s
% 4.88/2.13 % (29456)Instructions burned: 39 (million)
% 4.88/2.13 % (29456)------------------------------
% 4.88/2.13 % (29456)------------------------------
% 4.88/2.14 % (29457)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_29311 for (2996ds/448Mi)
% 4.88/2.15 % (29458)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_29311 for (2996ds/46Mi)
% 4.88/2.15 % (29455)Instruction limit reached!
% 4.88/2.15 % (29455)------------------------------
% 4.88/2.15 % (29455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.88/2.15 % (29455)Termination reason: Unknown
% 4.88/2.15 % (29455)Termination phase: Property scanning
% 4.88/2.15
% 4.88/2.15 % (29455)Memory used [KB]: 1663
% 4.88/2.15 % (29455)Time elapsed: 0.048 s
% 4.88/2.15 % (29455)Instructions burned: 108 (million)
% 4.88/2.15 % (29455)------------------------------
% 4.88/2.15 % (29455)------------------------------
% 4.88/2.17 % (29458)Instruction limit reached!
% 4.88/2.17 % (29458)------------------------------
% 4.88/2.17 % (29458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.88/2.17 % (29458)Termination reason: Unknown
% 4.88/2.17 % (29458)Termination phase: Property scanning
% 4.88/2.17
% 4.88/2.17 % (29458)Memory used [KB]: 1663
% 4.88/2.17 % (29458)Time elapsed: 0.023 s
% 4.88/2.17 % (29458)Instructions burned: 46 (million)
% 4.88/2.17 % (29458)------------------------------
% 4.88/2.17 % (29458)------------------------------
% 4.88/2.17 % (29459)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_29311 for (2996ds/98Mi)
% 4.88/2.19 % (29460)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_29311 for (2996ds/507Mi)
% 5.36/2.21 % (29459)Instruction limit reached!
% 5.36/2.21 % (29459)------------------------------
% 5.36/2.21 % (29459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.36/2.21 % (29459)Termination reason: Unknown
% 5.36/2.21 % (29459)Termination phase: Property scanning
% 5.36/2.21
% 5.36/2.21 % (29459)Memory used [KB]: 1791
% 5.36/2.21 % (29459)Time elapsed: 0.043 s
% 5.36/2.21 % (29459)Instructions burned: 99 (million)
% 5.36/2.21 % (29459)------------------------------
% 5.36/2.21 % (29459)------------------------------
% 5.36/2.23 % (29437)Instruction limit reached!
% 5.36/2.23 % (29437)------------------------------
% 5.36/2.23 % (29437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.36/2.23 % (29437)Termination reason: Unknown
% 5.36/2.23 % (29437)Termination phase: Saturation
% 5.36/2.23
% 5.36/2.23 % (29437)Memory used [KB]: 7803
% 5.36/2.23 % (29437)Time elapsed: 0.325 s
% 5.36/2.23 % (29437)Instructions burned: 710 (million)
% 5.36/2.23 % (29437)------------------------------
% 5.36/2.23 % (29437)------------------------------
% 5.36/2.23 % (29461)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_29311 for (2996ds/149Mi)
% 5.36/2.25 % (29462)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_29311 for (2995ds/39Mi)
% 5.36/2.26 % (29462)Instruction limit reached!
% 5.36/2.26 % (29462)------------------------------
% 5.36/2.26 % (29462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.36/2.26 % (29462)Termination reason: Unknown
% 5.36/2.26 % (29462)Termination phase: Property scanning
% 5.36/2.26
% 5.36/2.26 % (29462)Memory used [KB]: 1663
% 5.36/2.26 % (29462)Time elapsed: 0.020 s
% 5.36/2.26 % (29462)Instructions burned: 39 (million)
% 5.36/2.26 % (29462)------------------------------
% 5.36/2.26 % (29462)------------------------------
% 5.36/2.28 % (29463)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29311 for (2995ds/6Mi)
% 5.36/2.29 % (29463)Instruction limit reached!
% 5.36/2.29 % (29463)------------------------------
% 5.36/2.29 % (29463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.36/2.29 % (29463)Termination reason: Unknown
% 5.36/2.29 % (29463)Termination phase: shuffling
% 5.36/2.29
% 5.36/2.29 % (29463)Memory used [KB]: 1279
% 5.36/2.29 % (29463)Time elapsed: 0.005 s
% 5.36/2.29 % (29463)Instructions burned: 6 (million)
% 5.36/2.29 % (29463)------------------------------
% 5.36/2.29 % (29463)------------------------------
% 5.36/2.29 % (29428)Instruction limit reached!
% 5.36/2.29 % (29428)------------------------------
% 5.36/2.29 % (29428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.36/2.29 % (29428)Termination reason: Unknown
% 5.36/2.29 % (29428)Termination phase: Saturation
% 5.36/2.29
% 5.36/2.29 % (29428)Memory used [KB]: 7291
% 5.36/2.29 % (29428)Time elapsed: 0.421 s
% 5.36/2.29 % (29428)Instructions burned: 1041 (million)
% 5.36/2.29 % (29428)------------------------------
% 5.36/2.29 % (29428)------------------------------
% 5.36/2.29 % (29444)Instruction limit reached!
% 5.36/2.29 % (29444)------------------------------
% 5.36/2.29 % (29444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.36/2.29 % (29444)Termination reason: Unknown
% 5.36/2.29 % (29444)Termination phase: Saturation
% 5.36/2.29
% 5.36/2.29 % (29444)Memory used [KB]: 7164
% 5.36/2.29 % (29444)Time elapsed: 0.344 s
% 5.36/2.29 % (29444)Instructions burned: 780 (million)
% 5.36/2.29 % (29444)------------------------------
% 5.36/2.29 % (29444)------------------------------
% 5.82/2.30 % (29461)Instruction limit reached!
% 5.82/2.30 % (29461)------------------------------
% 5.82/2.30 % (29461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.30 % (29461)Termination reason: Unknown
% 5.82/2.30 % (29461)Termination phase: Twee Goal Transformation
% 5.82/2.30
% 5.82/2.30 % (29461)Memory used [KB]: 2046
% 5.82/2.30 % (29461)Time elapsed: 0.068 s
% 5.82/2.30 % (29461)Instructions burned: 149 (million)
% 5.82/2.30 % (29461)------------------------------
% 5.82/2.30 % (29461)------------------------------
% 5.82/2.30 % (29464)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_29311 for (2995ds/1087Mi)
% 5.82/2.31 % (29465)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_29311 for (2995ds/47Mi)
% 5.82/2.31 % (29466)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_29311 for (2995ds/44Mi)
% 5.82/2.32 % (29467)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_29311 for (2995ds/432Mi)
% 5.82/2.33 % (29466)Instruction limit reached!
% 5.82/2.33 % (29466)------------------------------
% 5.82/2.33 % (29466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.33 % (29466)Termination reason: Unknown
% 5.82/2.33 % (29466)Termination phase: Property scanning
% 5.82/2.33
% 5.82/2.33 % (29466)Memory used [KB]: 1535
% 5.82/2.33 % (29466)Time elapsed: 0.022 s
% 5.82/2.33 % (29466)Instructions burned: 46 (million)
% 5.82/2.33 % (29466)------------------------------
% 5.82/2.33 % (29466)------------------------------
% 5.82/2.33 % (29465)Instruction limit reached!
% 5.82/2.33 % (29465)------------------------------
% 5.82/2.33 % (29465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.33 % (29465)Termination reason: Unknown
% 5.82/2.33 % (29465)Termination phase: Function definition elimination
% 5.82/2.33
% 5.82/2.33 % (29465)Memory used [KB]: 1663
% 5.82/2.33 % (29465)Time elapsed: 0.025 s
% 5.82/2.33 % (29465)Instructions burned: 47 (million)
% 5.82/2.33 % (29465)------------------------------
% 5.82/2.33 % (29465)------------------------------
% 5.82/2.35 % (29468)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/62Mi)
% 5.82/2.35 % (29469)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/31Mi)
% 5.82/2.36 % (29457)Instruction limit reached!
% 5.82/2.36 % (29457)------------------------------
% 5.82/2.36 % (29457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.36 % (29457)Termination reason: Unknown
% 5.82/2.36 % (29457)Termination phase: Saturation
% 5.82/2.36
% 5.82/2.36 % (29457)Memory used [KB]: 7291
% 5.82/2.36 % (29457)Time elapsed: 0.214 s
% 5.82/2.36 % (29457)Instructions burned: 449 (million)
% 5.82/2.36 % (29457)------------------------------
% 5.82/2.36 % (29457)------------------------------
% 5.82/2.36 % (29469)Instruction limit reached!
% 5.82/2.36 % (29469)------------------------------
% 5.82/2.36 % (29469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.36 % (29469)Termination reason: Unknown
% 5.82/2.36 % (29469)Termination phase: Preprocessing 3
% 5.82/2.36
% 5.82/2.36 % (29469)Memory used [KB]: 1535
% 5.82/2.36 % (29469)Time elapsed: 0.016 s
% 5.82/2.36 % (29469)Instructions burned: 31 (million)
% 5.82/2.36 % (29469)------------------------------
% 5.82/2.36 % (29469)------------------------------
% 5.82/2.37 % (29470)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/96Mi)
% 5.82/2.38 % (29468)Instruction limit reached!
% 5.82/2.38 % (29468)------------------------------
% 5.82/2.38 % (29468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.38 % (29468)Termination reason: Unknown
% 5.82/2.38 % (29468)Termination phase: Function definition elimination
% 5.82/2.38
% 5.82/2.38 % (29468)Memory used [KB]: 1791
% 5.82/2.38 % (29468)Time elapsed: 0.030 s
% 5.82/2.38 % (29468)Instructions burned: 62 (million)
% 5.82/2.38 % (29468)------------------------------
% 5.82/2.38 % (29468)------------------------------
% 5.82/2.38 % (29471)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/453Mi)
% 5.82/2.38 % (29460)Instruction limit reached!
% 5.82/2.38 % (29460)------------------------------
% 5.82/2.38 % (29460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.38 % (29460)Termination reason: Unknown
% 5.82/2.38 % (29460)Termination phase: Saturation
% 5.82/2.38
% 5.82/2.38 % (29460)Memory used [KB]: 6908
% 5.82/2.38 % (29460)Time elapsed: 0.197 s
% 5.82/2.38 % (29460)Instructions burned: 509 (million)
% 5.82/2.38 % (29460)------------------------------
% 5.82/2.38 % (29460)------------------------------
% 5.82/2.39 % (29472)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/71Mi)
% 6.60/2.40 % (29473)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/83Mi)
% 6.60/2.41 % (29470)Instruction limit reached!
% 6.60/2.41 % (29470)------------------------------
% 6.60/2.41 % (29470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.41 % (29470)Termination reason: Unknown
% 6.60/2.41 % (29470)Termination phase: Property scanning
% 6.60/2.41
% 6.60/2.41 % (29470)Memory used [KB]: 1918
% 6.60/2.41 % (29470)Time elapsed: 0.042 s
% 6.60/2.41 % (29470)Instructions burned: 98 (million)
% 6.60/2.41 % (29470)------------------------------
% 6.60/2.41 % (29470)------------------------------
% 6.60/2.42 % (29446)Instruction limit reached!
% 6.60/2.42 % (29446)------------------------------
% 6.60/2.42 % (29446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.42 % (29446)Termination reason: Unknown
% 6.60/2.42 % (29446)Termination phase: Saturation
% 6.60/2.42
% 6.60/2.42 % (29446)Memory used [KB]: 8315
% 6.60/2.42 % (29446)Time elapsed: 0.466 s
% 6.60/2.42 % (29446)Instructions burned: 879 (million)
% 6.60/2.42 % (29446)------------------------------
% 6.60/2.42 % (29446)------------------------------
% 6.60/2.42 % (29472)Instruction limit reached!
% 6.60/2.42 % (29472)------------------------------
% 6.60/2.42 % (29472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.42 % (29472)Termination reason: Unknown
% 6.60/2.42 % (29472)Termination phase: Function definition elimination
% 6.60/2.42
% 6.60/2.42 % (29472)Memory used [KB]: 1791
% 6.60/2.42 % (29472)Time elapsed: 0.033 s
% 6.60/2.42 % (29472)Instructions burned: 73 (million)
% 6.60/2.42 % (29472)------------------------------
% 6.60/2.42 % (29472)------------------------------
% 6.60/2.43 % (29474)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/11Mi)
% 6.60/2.44 % (29474)Instruction limit reached!
% 6.60/2.44 % (29474)------------------------------
% 6.60/2.44 % (29474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.44 % (29474)Termination reason: Unknown
% 6.60/2.44 % (29474)Termination phase: shuffling
% 6.60/2.44
% 6.60/2.44 % (29474)Memory used [KB]: 1407
% 6.60/2.44 % (29474)Time elapsed: 0.007 s
% 6.60/2.44 % (29474)Instructions burned: 11 (million)
% 6.60/2.44 % (29474)------------------------------
% 6.60/2.44 % (29474)------------------------------
% 6.60/2.44 % (29475)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_29311 for (2994ds/41Mi)
% 6.60/2.44 % (29473)Instruction limit reached!
% 6.60/2.44 % (29473)------------------------------
% 6.60/2.44 % (29473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.44 % (29473)Termination reason: Unknown
% 6.60/2.44 % (29473)Termination phase: Saturation
% 6.60/2.44
% 6.60/2.44 % (29473)Memory used [KB]: 6524
% 6.60/2.44 % (29473)Time elapsed: 0.044 s
% 6.60/2.44 % (29473)Instructions burned: 83 (million)
% 6.60/2.44 % (29473)------------------------------
% 6.60/2.44 % (29473)------------------------------
% 6.60/2.44 % (29476)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/6Mi)
% 6.60/2.45 % (29476)Instruction limit reached!
% 6.60/2.45 % (29476)------------------------------
% 6.60/2.45 % (29476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.45 % (29476)Termination reason: Unknown
% 6.60/2.45 % (29476)Termination phase: shuffling
% 6.60/2.45
% 6.60/2.45 % (29476)Memory used [KB]: 1279
% 6.60/2.45 % (29476)Time elapsed: 0.006 s
% 6.60/2.45 % (29476)Instructions burned: 7 (million)
% 6.60/2.45 % (29476)------------------------------
% 6.60/2.45 % (29476)------------------------------
% 6.60/2.45 % (29477)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/150Mi)
% 6.60/2.46 % (29475)Instruction limit reached!
% 6.60/2.46 % (29475)------------------------------
% 6.60/2.46 % (29475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.46 % (29475)Termination reason: Unknown
% 6.60/2.46 % (29475)Termination phase: Property scanning
% 6.60/2.46
% 6.60/2.46 % (29475)Memory used [KB]: 1535
% 6.60/2.46 % (29475)Time elapsed: 0.021 s
% 6.60/2.46 % (29475)Instructions burned: 41 (million)
% 6.60/2.46 % (29475)------------------------------
% 6.60/2.46 % (29475)------------------------------
% 6.60/2.46 % (29478)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/343Mi)
% 6.60/2.47 % (29479)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/109Mi)
% 6.60/2.48 % (29480)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/253Mi)
% 6.60/2.49 % (29467)Instruction limit reached!
% 6.60/2.49 % (29467)------------------------------
% 6.60/2.49 % (29467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.49 % (29467)Termination reason: Unknown
% 6.60/2.49 % (29467)Termination phase: Saturation
% 6.60/2.49
% 6.60/2.49 % (29467)Memory used [KB]: 2302
% 6.60/2.49 % (29467)Time elapsed: 0.175 s
% 6.60/2.49 % (29467)Instructions burned: 432 (million)
% 6.60/2.49 % (29467)------------------------------
% 6.60/2.49 % (29467)------------------------------
% 7.08/2.51 % (29481)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/140Mi)
% 7.08/2.51 % (29479)Instruction limit reached!
% 7.08/2.51 % (29479)------------------------------
% 7.08/2.51 % (29479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.51 % (29479)Termination reason: Unknown
% 7.08/2.51 % (29479)Termination phase: Property scanning
% 7.08/2.51
% 7.08/2.51 % (29479)Memory used [KB]: 1918
% 7.08/2.51 % (29479)Time elapsed: 0.050 s
% 7.08/2.51 % (29479)Instructions burned: 110 (million)
% 7.08/2.51 % (29479)------------------------------
% 7.08/2.51 % (29479)------------------------------
% 7.08/2.52 % (29477)Instruction limit reached!
% 7.08/2.52 % (29477)------------------------------
% 7.08/2.52 % (29477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.52 % (29477)Termination reason: Unknown
% 7.08/2.52 % (29477)Termination phase: Property scanning
% 7.08/2.52
% 7.08/2.52 % (29477)Memory used [KB]: 1918
% 7.08/2.52 % (29477)Time elapsed: 0.072 s
% 7.08/2.52 % (29477)Instructions burned: 151 (million)
% 7.08/2.52 % (29477)------------------------------
% 7.08/2.52 % (29477)------------------------------
% 7.08/2.53 % (29482)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/614Mi)
% 7.08/2.55 % (29483)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_29311 for (2993ds/202Mi)
% 7.08/2.56 % (29471)Instruction limit reached!
% 7.08/2.56 % (29471)------------------------------
% 7.08/2.56 % (29471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.56 % (29471)Termination reason: Unknown
% 7.08/2.56 % (29471)Termination phase: Saturation
% 7.08/2.56
% 7.08/2.56 % (29471)Memory used [KB]: 6780
% 7.08/2.56 % (29471)Time elapsed: 0.185 s
% 7.08/2.56 % (29471)Instructions burned: 454 (million)
% 7.08/2.56 % (29471)------------------------------
% 7.08/2.56 % (29471)------------------------------
% 7.08/2.57 % (29481)Refutation not found, incomplete strategy
% 7.08/2.57 % (29481)------------------------------
% 7.08/2.57 % (29481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.57 % (29481)Termination reason: Refutation not found, incomplete strategy
% 7.08/2.57
% 7.08/2.57
% 7.08/2.57 % (29481)Memory used [KB]: 6652
% 7.08/2.57 % (29481)Time elapsed: 0.063 s
% 7.08/2.57 % (29481)Instructions burned: 126 (million)
% 7.08/2.57 % (29481)------------------------------
% 7.08/2.57 % (29481)------------------------------
% 7.08/2.58 % (29484)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_29311 for (2992ds/339Mi)
% 7.08/2.59 % (29485)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_29311 for (2992ds/283Mi)
% 7.52/2.61 % (29480)Instruction limit reached!
% 7.52/2.61 % (29480)------------------------------
% 7.52/2.61 % (29480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.61 % (29480)Termination reason: Unknown
% 7.52/2.61 % (29480)Termination phase: Saturation
% 7.52/2.61
% 7.52/2.61 % (29480)Memory used [KB]: 6780
% 7.52/2.61 % (29480)Time elapsed: 0.134 s
% 7.52/2.61 % (29480)Instructions burned: 254 (million)
% 7.52/2.61 % (29480)------------------------------
% 7.52/2.61 % (29480)------------------------------
% 7.52/2.63 % (29478)Refutation not found, incomplete strategy
% 7.52/2.63 % (29478)------------------------------
% 7.52/2.63 % (29478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.63 % (29478)Termination reason: Refutation not found, incomplete strategy
% 7.52/2.63
% 7.52/2.63
% 7.52/2.63 % (29478)Memory used [KB]: 6908
% 7.52/2.63 % (29478)Time elapsed: 0.171 s
% 7.52/2.63 % (29478)Instructions burned: 314 (million)
% 7.52/2.63 % (29478)------------------------------
% 7.52/2.63 % (29478)------------------------------
% 7.52/2.63 % (29486)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_29311 for (2991ds/134Mi)
% 7.52/2.64 % (29483)First to succeed.
% 7.52/2.65 % (29487)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_29311 for (2991ds/298Mi)
% 7.52/2.65 % (29483)Refutation found. Thanks to Tanya!
% 7.52/2.65 % SZS status Theorem for DTF2THF_29311
% 7.52/2.65 % SZS output start Proof for DTF2THF_29311
% 7.52/2.65 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i).
% 7.52/2.65 thf(func_def_3, type, c_not: $o > $o).
% 7.52/2.65 thf(func_def_4, type, c_and: $o > $o > $o).
% 7.52/2.65 thf(func_def_5, type, c_or: $o > $o > $o).
% 7.52/2.65 thf(func_def_6, type, c_iff: $o > $o > $o).
% 7.52/2.65 thf(func_def_7, type, c_In: $i > $i > $o).
% 7.52/2.65 thf(func_def_8, type, c_Subq: $i > $i > $o).
% 7.52/2.65 thf(func_def_10, type, c_Union: $i > $i).
% 7.52/2.65 thf(func_def_11, type, c_Power: $i > $i).
% 7.52/2.65 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i).
% 7.52/2.65 thf(func_def_13, type, c_TransSet: $i > $o).
% 7.52/2.65 thf(func_def_14, type, c_atleast2: $i > $o).
% 7.52/2.65 thf(func_def_15, type, c_atleast3: $i > $o).
% 7.52/2.65 thf(func_def_16, type, c_atleast4: $i > $o).
% 7.52/2.65 thf(func_def_17, type, c_atleast5: $i > $o).
% 7.52/2.65 thf(func_def_18, type, c_atleast6: $i > $o).
% 7.52/2.65 thf(func_def_19, type, c_exactly2: $i > $o).
% 7.52/2.65 thf(func_def_20, type, c_exactly3: $i > $o).
% 7.52/2.65 thf(func_def_21, type, c_exactly4: $i > $o).
% 7.52/2.65 thf(func_def_22, type, c_exactly5: $i > $o).
% 7.52/2.65 thf(func_def_23, type, c_exu_i: ($i > $o) > $o).
% 7.52/2.65 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o).
% 7.52/2.65 thf(func_def_37, type, c_If_i: $o > $i > $i > $i).
% 7.52/2.65 thf(func_def_38, type, c_exactly1of2: $o > $o > $o).
% 7.52/2.65 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o).
% 7.52/2.65 thf(func_def_40, type, c_nIn: $i > $i > $o).
% 7.52/2.65 thf(func_def_41, type, c_nSubq: $i > $i > $o).
% 7.52/2.65 thf(func_def_42, type, c_UPair: $i > $i > $i).
% 7.52/2.65 thf(func_def_43, type, c_Sing: $i > $i).
% 7.52/2.65 thf(func_def_44, type, c_binunion: $i > $i > $i).
% 7.52/2.65 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i).
% 7.52/2.65 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i).
% 7.52/2.65 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i).
% 7.52/2.65 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i).
% 7.52/2.65 thf(func_def_49, type, c_binintersect: $i > $i > $i).
% 7.52/2.65 thf(func_def_50, type, c_setminus: $i > $i > $i).
% 7.52/2.65 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o).
% 7.52/2.65 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o).
% 7.52/2.65 thf(func_def_53, type, c_atleastp: $i > $i > $o).
% 7.52/2.65 thf(func_def_54, type, c_equip: $i > $i > $o).
% 7.52/2.65 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o).
% 7.52/2.65 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i).
% 7.52/2.65 thf(func_def_57, type, c_ordsucc: $i > $i).
% 7.52/2.65 thf(func_def_58, type, c_nat_p: $i > $o).
% 7.52/2.65 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i).
% 7.52/2.65 thf(func_def_60, type, c_add_nat: $i > $i > $i).
% 7.52/2.65 thf(func_def_61, type, c_mul_nat: $i > $i > $i).
% 7.52/2.65 thf(func_def_62, type, c_ordinal: $i > $o).
% 7.52/2.65 thf(func_def_63, type, c_V_: $i > $i).
% 7.52/2.65 thf(func_def_64, type, c_Inj1: $i > $i).
% 7.52/2.65 thf(func_def_65, type, c_Inj0: $i > $i).
% 7.52/2.65 thf(func_def_66, type, c_Unj: $i > $i).
% 7.52/2.65 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i).
% 7.52/2.65 thf(func_def_68, type, c_setsum: $i > $i > $i).
% 7.52/2.65 thf(func_def_69, type, c_proj0: $i > $i).
% 7.52/2.65 thf(func_def_70, type, c_proj1: $i > $i).
% 7.52/2.65 thf(func_def_71, type, c_binrep: $i > $i > $i).
% 7.52/2.65 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i).
% 7.52/2.65 thf(func_def_73, type, c_setprod: $i > $i > $i).
% 7.52/2.65 thf(func_def_74, type, c_ap: $i > $i > $i).
% 7.52/2.65 thf(func_def_75, type, c_setsum_p: $i > $o).
% 7.52/2.65 thf(func_def_76, type, c_tuple_p: $i > $i > $o).
% 7.52/2.65 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i).
% 7.52/2.65 thf(func_def_78, type, c_setexp: $i > $i > $i).
% 7.52/2.65 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i).
% 7.52/2.65 thf(func_def_80, type, c_set_of_pairs: $i > $o).
% 7.52/2.65 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i).
% 7.52/2.65 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o).
% 7.52/2.65 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o).
% 7.52/2.65 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o).
% 7.52/2.65 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o).
% 7.52/2.65 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 7.52/2.65 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 7.52/2.65 thf(func_def_88, type, c_SNoElts_: $i > $i).
% 7.52/2.65 thf(func_def_89, type, c_SNo_: $i > $i > $o).
% 7.52/2.65 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i).
% 7.52/2.65 thf(func_def_91, type, c_SNo: $i > $o).
% 7.52/2.65 thf(func_def_92, type, c_SNoLev: $i > $i).
% 7.52/2.65 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o).
% 7.52/2.65 thf(func_def_94, type, c_SNoLt: $i > $i > $o).
% 7.52/2.65 thf(func_def_95, type, c_SNoLe: $i > $i > $o).
% 7.52/2.65 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o).
% 7.52/2.65 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o).
% 7.52/2.65 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).
% 7.52/2.65 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).
% 7.52/2.65 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).
% 7.52/2.65 thf(func_def_101, type, c_combinator: $i > $o).
% 7.52/2.65 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o).
% 7.52/2.65 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o).
% 7.52/2.65 thf(func_def_131, type, diff: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 7.52/2.65 thf(func_def_132, type, sK0: (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o).
% 7.52/2.65 thf(func_def_133, type, sK1: (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o).
% 7.52/2.65 thf(func_def_134, type, sK2: ($i > $i) > $i > $o).
% 7.52/2.65 thf(func_def_135, type, sK3: ($i > $i > $i) > (($i > $i) > $i) > $o).
% 7.52/2.65 thf(func_def_136, type, sK4: ($i > $o) > $i).
% 7.52/2.65 thf(func_def_139, type, ph7: !>[X0: $tType]:(X0)).
% 7.52/2.65 thf(f1250,plain,(
% 7.52/2.65 $false),
% 7.52/2.65 inference(avatar_sat_refutation,[status(thm)],[f354,f1249])).
% 7.52/2.65 thf(f1249,plain,(
% 7.52/2.65 spl6_2),
% 7.52/2.65 inference(avatar_contradiction_clause,[status(thm)],[f1248])).
% 7.52/2.65 thf(f1248,plain,(
% 7.52/2.65 $false | spl6_2),
% 7.52/2.65 inference(trivial_inequality_removal,[status(thm)],[f1225])).
% 7.52/2.65 thf(f1225,plain,(
% 7.52/2.65 ($true = $false) | spl6_2),
% 7.52/2.65 inference(superposition,[status(thm)],[f877,f382])).
% 7.52/2.65 thf(f382,plain,(
% 7.52/2.65 ( ! [X1 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true = (c_In @ (c_Inj0 @ c_Empty) @ (X1 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) )),
% 7.52/2.65 inference(trivial_inequality_removal,[status(thm)],[f380])).
% 7.52/2.65 thf(f380,plain,(
% 7.52/2.65 ( ! [X1 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true != $true) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X1 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) )),
% 7.52/2.65 inference(superposition,[status(thm)],[f316,f314])).
% 7.52/2.65 thf(f314,plain,(
% 7.52/2.65 ($true = (sK2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty)))),
% 7.52/2.65 inference(cnf_transformation,[status(thm)],[f298])).
% 7.52/2.65 thf(f298,plain,(
% 7.52/2.65 ! [X4 : ($i > $i > $i > $i) > $i] : ($true = (sK0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X4 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty))))))))))))) & ! [X5 : $i > $i,X6 : ($i > $i > $i > $i) > $i] : (($true != (c_In @ (X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))) | ($true = (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X5 @ (X5 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))) | ($true != (sK2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))))) & ! [X7 : $i,X8 : $i > ($i > $i) > $i] : ($true = (sK1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i]: (X8 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))) & ! [X9 : ($i > ($i > $i) > $i > $i) > $i,X10 : $i] : (($true != (sK0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty)))))) | ($true != (c_In @ (c_Inj0 @ (c_Inj1 @ X10)) @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))) | ($true = (sK0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))))) & ! [X11 : $i > $i > $i,X12 : $i > $i > $i > $i,X13 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true != (sK2 @ (^[Y0 : $i]: (Y0)) @ (X12 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X11 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X12 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X13 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X13 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) & ((c_False = $true) | ($true != (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))))) & ($true = (sK2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty))) & ! [X14 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true) | ($true != (sK1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X14 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))))) & (c_False != $true)),
% 7.52/2.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f296,f297])).
% 7.52/2.65 thf(f297,plain,(
% 7.52/2.65 ? [X0 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X1 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X2 : ($i > $i) > $i > $o,X3 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X4 : ($i > $i > $i > $i) > $i] : ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X4 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty))))))))))))) & ! [X5 : $i > $i,X6 : ($i > $i > $i > $i) > $i] : (($true != (c_In @ (X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))) | ($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X5 @ (X5 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))) | ($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))))) & ! [X7 : $i,X8 : $i > ($i > $i) > $i] : ($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i]: (X8 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))) & ! [X9 : ($i > ($i > $i) > $i > $i) > $i,X10 : $i] : (($true != (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty)))))) | ($true != (c_In @ (c_Inj0 @ (c_Inj1 @ X10)) @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))) | ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))))) & ! [X11 : $i > $i > $i,X12 : $i > $i > $i > $i,X13 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (X12 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X11 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X12 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X13 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X13 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) & ((c_False = $true) | ($true != (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))))) & ($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty))) & ! [X14 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true) | ($true != (X1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X14 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))))) & (c_False != $true)) => (! [X4 : ($i > $i > $i > $i) > $i] : ($true = (sK0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X4 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty))))))))))))) & ! [X6 : ($i > $i > $i > $i) > $i,X5 : $i > $i] : (($true != (c_In @ (X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))) | ($true = (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X5 @ (X5 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))) | ($true != (sK2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))))) & ! [X8 : $i > ($i > $i) > $i,X7 : $i] : ($true = (sK1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i]: (X8 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))) & ! [X10 : $i,X9 : ($i > ($i > $i) > $i > $i) > $i] : (($true != (sK0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty)))))) | ($true != (c_In @ (c_Inj0 @ (c_Inj1 @ X10)) @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))) | ($true = (sK0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))))) & ! [X13 : ($i > $i) > (($i > $i) > $i > $i) > $i,X12 : $i > $i > $i > $i,X11 : $i > $i > $i] : (($true != (sK2 @ (^[Y0 : $i]: (Y0)) @ (X12 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X11 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X12 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X13 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X13 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) & ((c_False = $true) | ($true != (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))))) & ($true = (sK2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty))) & ! [X14 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true) | ($true != (sK1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X14 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))))) & (c_False != $true))),
% 7.52/2.65 introduced(definition,[],[choice_axiom])).
% 7.52/2.65 thf(f296,plain,(
% 7.52/2.65 ? [X0 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X1 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X2 : ($i > $i) > $i > $o,X3 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X4 : ($i > $i > $i > $i) > $i] : ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X4 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty))))))))))))) & ! [X5 : $i > $i,X6 : ($i > $i > $i > $i) > $i] : (($true != (c_In @ (X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))) | ($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X5 @ (X5 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))) | ($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))))) & ! [X7 : $i,X8 : $i > ($i > $i) > $i] : ($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i]: (X8 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))) & ! [X9 : ($i > ($i > $i) > $i > $i) > $i,X10 : $i] : (($true != (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty)))))) | ($true != (c_In @ (c_Inj0 @ (c_Inj1 @ X10)) @ (X9 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))) | ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))))) & ! [X11 : $i > $i > $i,X12 : $i > $i > $i > $i,X13 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (X12 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X11 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X12 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X13 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X13 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) & ((c_False = $true) | ($true != (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))))) & ($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty))) & ! [X14 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true) | ($true != (X1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X14 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))))) & (c_False != $true))),
% 7.52/2.65 inference(rectify,[status(thm)],[f293])).
% 7.52/2.65 thf(f293,plain,(
% 7.52/2.65 ? [X0 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X1 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X2 : ($i > $i) > $i > $o,X3 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X7 : ($i > $i > $i > $i) > $i] : ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X7 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty))))))))))))) & ! [X10 : $i > $i,X11 : ($i > $i > $i > $i) > $i] : (($true != (c_In @ (X11 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))) | ($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X10 @ (X10 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))) | ($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))))) & ! [X4 : $i,X5 : $i > ($i > $i) > $i] : ($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X4)) @ (^[Y0 : $i]: (X5 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))) & ! [X8 : ($i > ($i > $i) > $i > $i) > $i,X9 : $i] : (($true != (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X8 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty)))))) | ($true != (c_In @ (c_Inj0 @ (c_Inj1 @ X9)) @ (X8 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))) | ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))))) & ! [X12 : $i > $i > $i,X13 : $i > $i > $i > $i,X14 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (X13 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X12 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X13 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X14 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X14 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) & ((c_False = $true) | ($true != (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))))) & ($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty))) & ! [X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true) | ($true != (X1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X6 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))))) & (c_False != $true))),
% 7.52/2.65 inference(flattening,[status(thm)],[f292])).
% 7.52/2.65 thf(f292,plain,(
% 7.52/2.65 ? [X0 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X1 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X2 : ($i > $i) > $i > $o,X3 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (((((((((c_False != $true) & ! [X12 : $i > $i > $i,X13 : $i > $i > $i > $i,X14 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (X13 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X12 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X13 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X14 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X14 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty))))))))) & ($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty)))) & ((c_False = $true) | ($true != (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty))))))))) & ! [X10 : $i > $i,X11 : ($i > $i > $i > $i) > $i] : ((($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X10 @ (X10 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))) | ($true != (X2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))))) | ($true != (c_In @ (X11 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))))) & ! [X8 : ($i > ($i > $i) > $i > $i) > $i,X9 : $i] : ((($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty)))))))) | ($true != (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X8 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty))))))) | ($true != (c_In @ (c_Inj0 @ (c_Inj1 @ X9)) @ (X8 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))))) & ! [X7 : ($i > $i > $i > $i) > $i] : ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X7 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))))))))))) & ! [X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true) | ($true != (X1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X6 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))) & ! [X4 : $i,X5 : $i > ($i > $i) > $i] : ($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X4)) @ (^[Y0 : $i]: (X5 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))))),
% 7.52/2.65 inference(ennf_transformation,[status(thm)],[f289])).
% 7.52/2.65 thf(f289,plain,(
% 7.52/2.65 ~! [X0 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X1 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X2 : ($i > $i) > $i > $o,X3 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X4 : $i,X5 : $i > ($i > $i) > $i] : ($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X4)) @ (^[Y0 : $i]: (X5 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))) => (! [X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X6 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty)))) => ((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true)) => (! [X7 : ($i > $i > $i > $i) > $i] : ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X7 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty))))))))))))) => (! [X8 : ($i > ($i > $i) > $i > $i) > $i,X9 : $i] : (($true = (c_In @ (c_Inj0 @ (c_Inj1 @ X9)) @ (X8 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))) => (($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X8 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty)))))) => ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty)))))))))) => (! [X10 : $i > $i,X11 : ($i > $i > $i > $i) > $i] : (($true = (c_In @ (X11 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))) => (($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty))))) => ($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X10 @ (X10 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))))) => ((($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty))))))) => (c_False = $true)) => (($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty))) => (! [X12 : $i > $i > $i,X13 : $i > $i > $i > $i,X14 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (X13 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X12 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X13 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X14 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) => ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X14 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) => (c_False = $true)))))))))),
% 7.52/2.65 inference(rectify,[status(thm)],[f127])).
% 7.52/2.65 thf(f127,plain,(
% 7.52/2.65 ~! [X0 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X1 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X2 : ($i > $i) > $i > $o,X3 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X5 : $i,X6 : $i > ($i > $i) > $i] : ($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj0 @ (Y0 @ c_Empty))) @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X6 @ c_Empty @ (^[Y1 : $i]: (c_Empty)))) @ (c_Inj1 @ c_Empty))) => (! [X14 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : (($true = (X1 @ (^[Y0 : $i > $i]: (c_Inj1 @ (c_Inj1 @ (X14 @ (^[Y1 : ($i > $i) > $i]: ((^[Y2 : $i > $i]: ((^[Y3 : $i]: (c_setsum @ c_Empty @ c_Empty)))))))))) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ (c_Inj1 @ Y0))) @ (^[Y0 : $i]: (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty)))) => ((c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty)) = $true)) => (! [X23 : ($i > $i > $i > $i) > $i] : ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ Y4))))))))))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (X23 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty))))))))))))) => (! [X36 : ($i > ($i > $i) > $i > $i) > $i,X38 : $i] : (($true = (c_In @ (c_Inj0 @ (c_Inj1 @ X38)) @ (X36 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))))) => (($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))))))))))) @ (c_setsum @ (X36 @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (c_Empty))))))) @ c_Empty) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj1 @ c_Empty)))))) => ($true = (X0 @ (^[Y0 : $i > (($i > $i) > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: (c_Inj0 @ (c_Inj0 @ c_Empty))))))))))) @ c_Empty @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty)))))))))) => (! [X60 : $i > $i,X61 : ($i > $i > $i > $i) > $i] : (($true = (c_In @ (X61 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ Y1))))))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)))))) => (($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty))))) => ($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ (c_setsum @ (c_Inj1 @ Y1) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X60 @ (X60 @ c_Empty))))))) @ (^[Y0 : $i > $i]: (c_Empty)))))) => ((($true = (X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (^[Y0 : $i > $i]: (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty))))))) => (c_False = $true)) => (($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (c_Inj0 @ c_Empty))) => (! [X83 : $i > $i > $i,X84 : $i > $i > $i > $i,X86 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true = (X2 @ (^[Y0 : $i]: (Y0)) @ (X84 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X83 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X84 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X86 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) => ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X86 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) => (c_False = $true)))))))))),
% 7.52/2.65 inference(fool_elimination,[status(thm)],[f126])).
% 7.52/2.65 thf(f126,plain,(
% 7.52/2.65 ~! [X0 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X1 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X2 : ($i > $i) > $i > $o,X3 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X5 : $i,X6 : $i > ($i > $i) > $i] : (X1 @ (^[X8 : $i > $i] : (c_Inj0 @ (X8 @ c_Empty))) @ (^[X9 : $i] : (X5)) @ (^[X10 : $i] : (X6 @ c_Empty @ (^[X11 : $i] : (c_Empty)))) @ (c_Inj1 @ c_Empty)) => (! [X14 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i] : ((X1 @ (^[X16 : $i > $i] : (c_Inj1 @ (c_Inj1 @ (X14 @ (^[X17 : ($i > $i) > $i, X18 : $i > $i, X19 : $i] : (c_setsum @ c_Empty @ c_Empty)))))) @ (^[X20 : $i] : (c_setsum @ c_Empty @ (c_Inj1 @ X20))) @ (^[X21 : $i] : (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))) => (c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty))) => (! [X23 : ($i > $i > $i > $i) > $i] : (X0 @ (^[X26 : $i > (($i > $i) > $i) > $i, X27 : $i, X28 : $i, X29 : $i > $i, X30 : $i] : (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ X30))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[X31 : $i > $i, X32 : $i] : (c_setsum @ X32 @ (X23 @ (^[X33 : $i, X34 : $i, X35 : $i] : (c_Empty)))))) => (! [X36 : ($i > ($i > $i) > $i > $i) > $i,X38 : $i] : ((c_In @ (c_Inj0 @ (c_Inj1 @ X38)) @ (X36 @ (^[X40 : $i, X41 : $i > $i, X42 : $i] : (c_Empty)))) => ((X0 @ (^[X43 : $i > (($i > $i) > $i) > $i, X44 : $i, X45 : $i, X46 : $i > $i, X47 : $i] : (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))) @ (c_setsum @ (X36 @ (^[X48 : $i, X49 : $i > $i, X50 : $i] : (c_Empty))) @ c_Empty) @ (^[X51 : $i > $i, X52 : $i] : (c_Inj1 @ c_Empty))) => (X0 @ (^[X53 : $i > (($i > $i) > $i) > $i, X54 : $i, X55 : $i, X56 : $i > $i, X57 : $i] : (c_Inj0 @ (c_Inj0 @ c_Empty))) @ c_Empty @ (^[X58 : $i > $i, X59 : $i] : (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))) => (! [X60 : $i > $i,X61 : ($i > $i > $i > $i) > $i] : ((c_In @ (X61 @ (^[X64 : $i, X65 : $i, X66 : $i] : (c_Inj1 @ X65))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty))))) => ((X2 @ (^[X67 : $i] : (X67)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))) => (X3 @ (^[X68 : $i, X69 : $i] : (c_setsum @ (c_setsum @ (c_Inj1 @ X69) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X60 @ (X60 @ c_Empty))))) @ (^[X70 : $i > $i] : (c_Empty))))) => (((X3 @ (^[X75 : $i, X76 : $i] : (X75)) @ (^[X77 : $i > $i] : (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))) => c_False) => ((X2 @ (^[X82 : $i] : (X82)) @ (c_Inj0 @ c_Empty)) => (! [X83 : $i > $i > $i,X84 : $i > $i > $i > $i,X86 : ($i > $i) > (($i > $i) > $i > $i) > $i] : ((X2 @ (^[X87 : $i] : (X87)) @ (X84 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X83 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X84 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X86 @ (^[X88 : $i] : (c_Empty)) @ (^[X89 : $i > $i, X90 : $i] : (c_setsum @ X90 @ (c_setsum @ c_Empty @ c_Empty)))))) => (c_In @ (c_Inj0 @ c_Empty) @ (X86 @ (^[X91 : $i] : (X91)) @ (^[X92 : $i > $i, X93 : $i] : (c_Empty))))) => c_False))))))))),
% 7.52/2.65 inference(rectify,[status(thm)],[f110])).
% 7.52/2.65 thf(f110,negated_conjecture,(
% 7.52/2.65 ~! [X2 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X3 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X0 : ($i > $i) > $i > $o,X1 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X4 : $i,X5 : $i,X6 : $i > ($i > $i) > $i,X7 : $i] : (X3 @ (^[X8 : $i > $i] : (c_Inj0 @ (X8 @ c_Empty))) @ (^[X8 : $i] : (X5)) @ (^[X8 : $i] : (X6 @ c_Empty @ (^[X9 : $i] : (c_Empty)))) @ (c_Inj1 @ c_Empty)) => (! [X5 : $i,X7 : $i,X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i,X4 : $i > ($i > $i) > $i > $i > $i] : ((X3 @ (^[X8 : $i > $i] : (c_Inj1 @ (c_Inj1 @ (X6 @ (^[X9 : ($i > $i) > $i, X10 : $i > $i, X11 : $i] : (c_setsum @ c_Empty @ c_Empty)))))) @ (^[X8 : $i] : (c_setsum @ c_Empty @ (c_Inj1 @ X8))) @ (^[X8 : $i] : (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))) => (c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty))) => (! [X6 : $i > ($i > $i > $i) > $i,X7 : ($i > $i > $i > $i) > $i,X5 : (($i > $i > $i) > $i) > $i,X4 : $i > $i > $i] : (X2 @ (^[X8 : $i > (($i > $i) > $i) > $i, X9 : $i, X10 : $i, X11 : $i > $i, X12 : $i] : (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ X12))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[X8 : $i > $i, X9 : $i] : (c_setsum @ X9 @ (X7 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)))))) => (! [X4 : ($i > ($i > $i) > $i > $i) > $i,X6 : $i > (($i > $i) > $i > $i) > $i > $i,X7 : $i,X5 : $i] : ((c_In @ (c_Inj0 @ (c_Inj1 @ X7)) @ (X4 @ (^[X8 : $i, X9 : $i > $i, X10 : $i] : (c_Empty)))) => ((X2 @ (^[X8 : $i > (($i > $i) > $i) > $i, X9 : $i, X10 : $i, X11 : $i > $i, X12 : $i] : (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))) @ (c_setsum @ (X4 @ (^[X8 : $i, X9 : $i > $i, X10 : $i] : (c_Empty))) @ c_Empty) @ (^[X8 : $i > $i, X9 : $i] : (c_Inj1 @ c_Empty))) => (X2 @ (^[X8 : $i > (($i > $i) > $i) > $i, X9 : $i, X10 : $i, X11 : $i > $i, X12 : $i] : (c_Inj0 @ (c_Inj0 @ c_Empty))) @ c_Empty @ (^[X8 : $i > $i, X9 : $i] : (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))) => (! [X7 : $i > $i,X6 : ($i > $i > $i > $i) > $i,X4 : $i,X5 : ($i > $i > $i) > $i > $i] : ((c_In @ (X6 @ (^[X8 : $i, X9 : $i, X10 : $i] : (c_Inj1 @ X9))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty))))) => ((X0 @ (^[X8 : $i] : (X8)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))) => (X1 @ (^[X8 : $i, X9 : $i] : (c_setsum @ (c_setsum @ (c_Inj1 @ X9) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X7 @ (X7 @ c_Empty))))) @ (^[X8 : $i > $i] : (c_Empty))))) => (! [X7 : $i,X6 : $i > $i,X5 : $i,X4 : $i] : ((X1 @ (^[X8 : $i, X9 : $i] : (X8)) @ (^[X8 : $i > $i] : (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))) => c_False) => (! [X6 : ($i > ($i > $i) > $i > $i) > (($i > $i) > $i) > $i > $i,X5 : $i,X4 : $i,X7 : $i > $i] : (X0 @ (^[X8 : $i] : (X8)) @ (c_Inj0 @ c_Empty)) => (! [X5 : $i > $i > $i,X6 : $i > $i > $i > $i,X7 : $i,X4 : ($i > $i) > (($i > $i) > $i > $i) > $i] : ((X0 @ (^[X8 : $i] : (X8)) @ (X6 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X5 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X6 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X4 @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : $i > $i, X9 : $i] : (c_setsum @ X9 @ (c_setsum @ c_Empty @ c_Empty)))))) => (c_In @ (c_Inj0 @ c_Empty) @ (X4 @ (^[X8 : $i] : (X8)) @ (^[X8 : $i > $i, X9 : $i] : (c_Empty))))) => c_False))))))))),
% 7.52/2.65 inference(negated_conjecture,[status(cth)],[f109])).
% 7.52/2.65 thf(f109,conjecture,(
% 7.52/2.65 ! [X2 : (($i > (($i > $i) > $i) > $i) > $i > $i > ($i > $i) > $i > $i) > $i > (($i > $i) > $i > $i) > $o,X3 : (($i > $i) > $i) > ($i > $i) > ($i > $i) > $i > $o,X0 : ($i > $i) > $i > $o,X1 : ($i > $i > $i) > (($i > $i) > $i) > $o] : (! [X4 : $i,X5 : $i,X6 : $i > ($i > $i) > $i,X7 : $i] : (X3 @ (^[X8 : $i > $i] : (c_Inj0 @ (X8 @ c_Empty))) @ (^[X8 : $i] : (X5)) @ (^[X8 : $i] : (X6 @ c_Empty @ (^[X9 : $i] : (c_Empty)))) @ (c_Inj1 @ c_Empty)) => (! [X5 : $i,X7 : $i,X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i,X4 : $i > ($i > $i) > $i > $i > $i] : ((X3 @ (^[X8 : $i > $i] : (c_Inj1 @ (c_Inj1 @ (X6 @ (^[X9 : ($i > $i) > $i, X10 : $i > $i, X11 : $i] : (c_setsum @ c_Empty @ c_Empty)))))) @ (^[X8 : $i] : (c_setsum @ c_Empty @ (c_Inj1 @ X8))) @ (^[X8 : $i] : (c_Empty)) @ (c_Inj0 @ (c_Inj1 @ c_Empty))) => (c_In @ (c_Inj1 @ c_Empty) @ (c_setsum @ (c_setsum @ c_Empty @ c_Empty) @ c_Empty))) => (! [X6 : $i > ($i > $i > $i) > $i,X7 : ($i > $i > $i > $i) > $i,X5 : (($i > $i > $i) > $i) > $i,X4 : $i > $i > $i] : (X2 @ (^[X8 : $i > (($i > $i) > $i) > $i, X9 : $i, X10 : $i, X11 : $i > $i, X12 : $i] : (c_setsum @ (c_Inj0 @ c_Empty) @ (c_Inj0 @ X12))) @ (c_setsum @ (c_Inj1 @ (c_Inj1 @ c_Empty)) @ c_Empty) @ (^[X8 : $i > $i, X9 : $i] : (c_setsum @ X9 @ (X7 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)))))) => (! [X4 : ($i > ($i > $i) > $i > $i) > $i,X6 : $i > (($i > $i) > $i > $i) > $i > $i,X7 : $i,X5 : $i] : ((c_In @ (c_Inj0 @ (c_Inj1 @ X7)) @ (X4 @ (^[X8 : $i, X9 : $i > $i, X10 : $i] : (c_Empty)))) => ((X2 @ (^[X8 : $i > (($i > $i) > $i) > $i, X9 : $i, X10 : $i, X11 : $i > $i, X12 : $i] : (c_Inj0 @ (c_Inj0 @ (c_setsum @ c_Empty @ (c_Inj0 @ c_Empty))))) @ (c_setsum @ (X4 @ (^[X8 : $i, X9 : $i > $i, X10 : $i] : (c_Empty))) @ c_Empty) @ (^[X8 : $i > $i, X9 : $i] : (c_Inj1 @ c_Empty))) => (X2 @ (^[X8 : $i > (($i > $i) > $i) > $i, X9 : $i, X10 : $i, X11 : $i > $i, X12 : $i] : (c_Inj0 @ (c_Inj0 @ c_Empty))) @ c_Empty @ (^[X8 : $i > $i, X9 : $i] : (c_Inj0 @ (c_Inj0 @ (c_setsum @ (c_Inj0 @ c_Empty) @ c_Empty))))))) => (! [X7 : $i > $i,X6 : ($i > $i > $i > $i) > $i,X4 : $i,X5 : ($i > $i > $i) > $i > $i] : ((c_In @ (X6 @ (^[X8 : $i, X9 : $i, X10 : $i] : (c_Inj1 @ X9))) @ (c_setsum @ (c_Inj0 @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty))) @ (c_setsum @ (c_Inj1 @ (c_setsum @ c_Empty @ c_Empty)) @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty))))) => ((X0 @ (^[X8 : $i] : (X8)) @ (c_setsum @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj1 @ (c_Inj1 @ c_Empty)))) => (X1 @ (^[X8 : $i, X9 : $i] : (c_setsum @ (c_setsum @ (c_Inj1 @ X9) @ (c_Inj1 @ c_Empty)) @ (c_setsum @ c_Empty @ (X7 @ (X7 @ c_Empty))))) @ (^[X8 : $i > $i] : (c_Empty))))) => (! [X7 : $i,X6 : $i > $i,X5 : $i,X4 : $i] : ((X1 @ (^[X8 : $i, X9 : $i] : (X8)) @ (^[X8 : $i > $i] : (c_setsum @ (c_setsum @ (c_Inj0 @ (c_setsum @ c_Empty @ c_Empty)) @ c_Empty) @ (c_Inj0 @ (c_Inj0 @ (c_Inj1 @ c_Empty)))))) => c_False) => (! [X6 : ($i > ($i > $i) > $i > $i) > (($i > $i) > $i) > $i > $i,X5 : $i,X4 : $i,X7 : $i > $i] : (X0 @ (^[X8 : $i] : (X8)) @ (c_Inj0 @ c_Empty)) => (! [X5 : $i > $i > $i,X6 : $i > $i > $i > $i,X7 : $i,X4 : ($i > $i) > (($i > $i) > $i > $i) > $i] : ((X0 @ (^[X8 : $i] : (X8)) @ (X6 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X5 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X6 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X4 @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : $i > $i, X9 : $i] : (c_setsum @ X9 @ (c_setsum @ c_Empty @ c_Empty)))))) => (c_In @ (c_Inj0 @ c_Empty) @ (X4 @ (^[X8 : $i] : (X8)) @ (^[X8 : $i > $i, X9 : $i] : (c_Empty))))) => c_False))))))))),
% 7.52/2.65 file('/export/starexec/sandbox/tmp/tmp.kXY3Epcmh7/DTF2THF_29311.p',conj)).
% 7.52/2.65 thf(f316,plain,(
% 7.52/2.65 ( ! [X11 : $i > $i > $i,X12 : $i > $i > $i > $i,X13 : ($i > $i) > (($i > $i) > $i > $i) > $i] : (($true != (sK2 @ (^[Y0 : $i]: (Y0)) @ (X12 @ (c_setsum @ (c_Inj1 @ (c_Inj0 @ c_Empty)) @ (X11 @ c_Empty @ c_Empty)) @ (c_setsum @ (c_setsum @ c_Empty @ (c_setsum @ c_Empty @ c_Empty)) @ (X12 @ (c_Inj0 @ c_Empty) @ (c_Inj1 @ c_Empty) @ (c_setsum @ c_Empty @ c_Empty))) @ (X13 @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_setsum @ Y1 @ (c_setsum @ c_Empty @ c_Empty))))))))) | ($true = (c_In @ (c_Inj0 @ c_Empty) @ (X13 @ (^[Y0 : $i]: (Y0)) @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: (c_Empty)))))))) )),
% 7.52/2.65 inference(cnf_transformation,[status(thm)],[f298])).
% 7.52/2.65 thf(f877,plain,(
% 7.52/2.65 ( ! [X1 : $i] : (((c_In @ X1 @ c_Empty) = $false)) ) | spl6_2),
% 7.52/2.65 inference(beta_eta_normalization,[status(thm)],[f876])).
% 7.52/2.65 thf(f876,plain,(
% 7.52/2.65 ( ! [X1 : $i] : ((((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X1) = $false)) ) | spl6_2),
% 7.52/2.65 inference(pi_clausification,[status(thm)],[f875])).
% 7.52/2.65 thf(f875,plain,(
% 7.52/2.65 ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false) | spl6_2),
% 7.52/2.65 inference(trivial_inequality_removal,[status(thm)],[f869])).
% 7.52/2.65 thf(f869,plain,(
% 7.52/2.65 ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false) | ($true = $false) | spl6_2),
% 7.52/2.65 inference(superposition,[status(thm)],[f306,f824])).
% 7.52/2.65 thf(f824,plain,(
% 7.52/2.65 ( ! [X1 : $o] : (((c_not @ X1) = $false) | ($false = X1)) ) | spl6_2),
% 7.52/2.65 inference(subsumption_resolution,[status(thm)],[f817,f335])).
% 7.52/2.65 thf(f335,plain,(
% 7.52/2.65 (c_False != $true) | spl6_2),
% 7.52/2.65 inference(avatar_component_clause,[status(thm)],[f334])).
% 7.52/2.65 thf(f334,definition,(
% 7.52/2.65 spl6_2 <=> (c_False = $true)),
% 7.52/2.65 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 7.52/2.65 thf(f817,plain,(
% 7.52/2.65 ( ! [X1 : $o] : (($false = X1) | ((c_not @ X1) = $false) | (c_False = $true)) )),
% 7.52/2.65 inference(binary_proxy_clausification,[status(thm)],[f816])).
% 7.52/2.65 thf(f816,plain,(
% 7.52/2.65 ( ! [X1 : $o] : (($true = (X1 => c_False)) | ((c_not @ X1) = $false)) )),
% 7.52/2.65 inference(binary_proxy_clausification,[status(thm)],[f814])).
% 7.52/2.65 thf(f814,plain,(
% 7.52/2.65 ( ! [X1 : $o] : (((c_not @ X1) = (X1 => c_False))) )),
% 7.52/2.65 inference(beta_eta_normalization,[status(thm)],[f813])).
% 7.52/2.65 thf(f813,plain,(
% 7.52/2.65 ( ! [X1 : $o] : (((c_not @ X1) = ((^[Y0 : $o]: (Y0 => c_False)) @ X1))) )),
% 7.52/2.65 inference(argument_congruence,[status(thm)],[f310])).
% 7.52/2.65 thf(f310,plain,(
% 7.52/2.65 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 7.52/2.65 inference(cnf_transformation,[status(thm)],[f209])).
% 7.52/2.65 thf(f209,plain,(
% 7.52/2.65 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 7.52/2.65 inference(fool_elimination,[status(thm)],[f208])).
% 7.52/2.65 thf(f208,plain,(
% 7.52/2.65 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 7.52/2.65 inference(rectify,[status(thm)],[f13])).
% 7.52/2.65 thf(f13,axiom,(
% 7.52/2.65 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 7.52/2.65 file('/export/starexec/sandbox/tmp/tmp.kXY3Epcmh7/DTF2THF_29311.p',ax13)).
% 7.52/2.65 thf(f306,plain,(
% 7.52/2.65 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 7.52/2.65 inference(cnf_transformation,[status(thm)],[f169])).
% 7.52/2.65 thf(f169,plain,(
% 7.52/2.65 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 7.52/2.65 inference(fool_elimination,[status(thm)],[f168])).
% 7.52/2.65 thf(f168,plain,(
% 7.52/2.65 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 7.52/2.65 inference(rectify,[status(thm)],[f5])).
% 7.52/2.65 thf(f5,axiom,(
% 7.52/2.65 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 7.52/2.65 file('/export/starexec/sandbox/tmp/tmp.kXY3Epcmh7/DTF2THF_29311.p',ax5)).
% 7.52/2.65 thf(f354,plain,(
% 7.52/2.65 ~spl6_2),
% 7.52/2.65 inference(avatar_split_clause,[status(thm)],[f312,f334])).
% 7.52/2.65 thf(f312,plain,(
% 7.52/2.65 (c_False != $true)),
% 7.52/2.65 inference(cnf_transformation,[status(thm)],[f298])).
% 7.52/2.65 % SZS output end Proof for DTF2THF_29311
% 7.52/2.65 % (29483)------------------------------
% 7.52/2.65 % (29483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.65 % (29483)Termination reason: Refutation
% 7.52/2.65
% 7.52/2.65 % (29483)Memory used [KB]: 6908
% 7.52/2.65 % (29483)Time elapsed: 0.128 s
% 7.52/2.65 % (29483)Instructions burned: 172 (million)
% 7.52/2.65 % (29483)------------------------------
% 7.52/2.65 % (29483)------------------------------
% 7.52/2.65 % (29416)Success in time 0.842 s
%------------------------------------------------------------------------------