TSTP Solution File: SCT171^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT171^1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 : Thu Aug 31 14:12:22 EDT 2023
% Result : Theorem 40.88s 41.43s
% Output : Proof 40.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SCT171^1 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.15 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 16:34:16 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.19/0.48 %----Proving TH0
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SCT171^1 : TPTP v8.1.2. Released v5.3.0.
% 0.19/0.48 % Domain : Social Choice Theory
% 0.19/0.48 % Problem : Arrow's Impossibility Theorem line 309, 100 axioms selected
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.19/0.48 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Bla11]
% 0.19/0.48 % Names : arrow_100_thf_l309 [Bla11]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.23 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0
% 0.19/0.48 % Syntax : Number of formulae : 287 ( 28 unt; 85 typ; 0 def)
% 0.19/0.48 % Number of atoms : 800 ( 114 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 19 ( 3 avg)
% 0.19/0.48 % Number of connectives : 1837 ( 115 ~; 6 |; 14 &;1399 @)
% 0.19/0.48 % ( 50 <=>; 253 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 20 ( 8 avg)
% 0.19/0.48 % Number of types : 5 ( 4 usr)
% 0.19/0.48 % Number of type conns : 1176 (1176 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 84 ( 81 usr; 9 con; 0-4 aty)
% 0.19/0.48 % Number of variables : 523 ( 37 ^; 485 !; 1 ?; 523 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.48 % 2011-08-09 19:16:58
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 %----Should-be-implicit typings (4)
% 0.19/0.48 thf(ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
% 0.19/0.48 arrow_1346734812le_alt: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
% 0.19/0.48 arrow_1092341143e_indi: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_ty_tc__Nat__Onat,type,
% 0.19/0.48 nat: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_Mtc__Arrow__,type,
% 0.19/0.48 produc1832616231le_alt: $tType ).
% 0.19/0.48
% 0.19/0.48 %----Explicit typings (81)
% 0.19/0.48 thf(sy_c_All,type,
% 0.19/0.48 all: ( produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OIIA,type,
% 0.19/0.48 arrow_1724561858le_IIA: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OLin,type,
% 0.19/0.48 arrow_1751445586le_Lin: ( produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OProf,type,
% 0.19/0.48 arrow_1605628760e_Prof: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Oabove,type,
% 0.19/0.48 arrow_452340254_above: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Odictator,type,
% 0.19/0.48 arrow_1098709355ctator: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Omkbot,type,
% 0.19/0.48 arrow_1717184938_mkbot: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Omktop,type,
% 0.19/0.48 arrow_1865892024_mktop: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Ounanimity,type,
% 0.19/0.48 arrow_1889221221nimity: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
% 0.19/0.48 finite1907699781e_indi: ( arrow_1092341143e_indi > $o ) > nat ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000tc_,type,
% 0.19/0.48 inj_on945046484di_nat: ( arrow_1092341143e_indi > nat ) > ( arrow_1092341143e_indi > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O,type,
% 0.19/0.48 pi_Arr1422400881lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O_001,type,
% 0.19/0.48 pi_Arr1941314005e_indi: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M,type,
% 0.19/0.48 pi_Arr1021537730_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_002,type,
% 0.19/0.48 pi_Arr1767527177lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_003,type,
% 0.19/0.48 pi_Arr170420797e_indi: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd,type,
% 0.19/0.48 pi_Pro410810898lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > $o > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd_004,type,
% 0.19/0.48 pi_Pro1340600692e_indi: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojn,type,
% 0.19/0.48 pi_o_A1302557673_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__,type,
% 0.19/0.48 pi_o_A71242893_alt_o: ( $o > $o ) > ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sd,type,
% 0.19/0.48 pi_o_P1538584260_alt_o: ( $o > $o ) > ( $o > ( produc1832616231le_alt > $o ) > $o ) > ( $o > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk,type,
% 0.19/0.48 pi_o_P988780107le_alt: ( $o > $o ) > ( $o > produc1832616231le_alt > $o ) > ( $o > produc1832616231le_alt ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062,type,
% 0.19/0.48 pi_Arr1140519125_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062_005,type,
% 0.19/0.48 pi_Arr651234977_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062_006,type,
% 0.19/0.48 pi_Arr418143960_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000tc__,type,
% 0.19/0.48 pi_Arr1055270199le_alt: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oal,type,
% 0.19/0.48 pi_Pro539263375_alt_o: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o > $o ) > ( produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oal_007,type,
% 0.19/0.48 pi_Pro1535452471e_indi: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > arrow_1092341143e_indi > $o ) > ( produc1832616231le_alt > arrow_1092341143e_indi ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____sdiojnqkdh,type,
% 0.19/0.48 hilber564731065di_nat: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > nat ) > nat > arrow_1092341143e_indi ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_M,type,
% 0.19/0.48 if_Pro399136856_alt_o: $o > ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_I_062_Itc__Arrow____Order____Mira,type,
% 0.19/0.48 ord_le939309728lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__Arrow____Order____Mirabelle_,type,
% 0.19/0.48 ord_le972845494lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__prod_Itc__Arrow____Order____,type,
% 0.19/0.48 ord_le898419007lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____sdi,type,
% 0.19/0.48 ord_le316791758indi_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__prod_Itc__Arrow____Order____Mirabe,type,
% 0.19/0.48 ord_le1973646398_alt_o: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Oord__class_Oless_000_Eo,type,
% 0.19/0.48 ord_less_o: $o > $o > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.19/0.48 ord_less_nat: nat > nat > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_I_062_Itc__Arrow____Order____Mirab,type,
% 0.19/0.48 top_to1049332548lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__,type,
% 0.19/0.48 top_to790289938lt_o_o: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__prod_Itc__Arrow____Order____M,type,
% 0.19/0.48 top_to1830848411lt_o_o: ( produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Otop__class_Otop_000_062_I_Eo_M_Eo_J,type,
% 0.19/0.48 top_top_o_o: $o > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____sdio,type,
% 0.19/0.48 top_to527331954indi_o: arrow_1092341143e_indi > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel,type,
% 0.19/0.48 top_to679332578_alt_o: produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Orderings_Otop__class_Otop_000_Eo,type,
% 0.19/0.48 top_top_o: $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_,type,
% 0.19/0.48 produc990411159le_alt: arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__,type,
% 0.19/0.48 collec2125720304_alt_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_,type,
% 0.19/0.48 collec1718651462_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk,type,
% 0.19/0.48 collec1079683069_alt_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
% 0.19/0.48 collec1832628290e_indi: ( arrow_1092341143e_indi > $o ) > arrow_1092341143e_indi > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa,type,
% 0.19/0.48 collec1201320914le_alt: ( produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__,type,
% 0.19/0.48 member903234717lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh___008,type,
% 0.19/0.48 member986213183e_indi: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_,type,
% 0.19/0.48 member733327538_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi__009,type,
% 0.19/0.48 member1754345465lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi__010,type,
% 0.19/0.48 member1208133347e_indi: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk,type,
% 0.19/0.48 member1949484546lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( ( produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk_011,type,
% 0.19/0.48 member1255309082e_indi: ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnq,type,
% 0.19/0.48 member1710515983_alt_o: ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O,type,
% 0.19/0.48 member537117565_alt_o: ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdi,type,
% 0.19/0.48 member1099673524_alt_o: ( $o > produc1832616231le_alt > $o ) > ( ( $o > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd,type,
% 0.19/0.48 member1368218865le_alt: ( $o > produc1832616231le_alt ) > ( ( $o > produc1832616231le_alt ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062_,type,
% 0.19/0.48 member24189887_alt_o: ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062__012,type,
% 0.19/0.48 member1079651021_alt_o: ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062__013,type,
% 0.19/0.48 member1561882372_alt_o: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_Mtc__p,type,
% 0.19/0.48 member1621875105le_alt: ( arrow_1092341143e_indi > produc1832616231le_alt ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa,type,
% 0.19/0.48 member1362619835_alt_o: ( produc1832616231le_alt > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa_014,type,
% 0.19/0.48 member1486844321e_indi: ( produc1832616231le_alt > arrow_1092341143e_indi ) > ( ( produc1832616231le_alt > arrow_1092341143e_indi ) > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000_Eo,type,
% 0.19/0.48 member_o: $o > ( $o > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
% 0.19/0.48 member1714766084e_indi: arrow_1092341143e_indi > ( arrow_1092341143e_indi > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_Mtc,type,
% 0.19/0.48 member545531028le_alt: produc1832616231le_alt > ( produc1832616231le_alt > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_F,type,
% 0.19/0.48 f: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_Lab____,type,
% 0.19/0.48 lab: produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_Lba____,type,
% 0.19/0.48 lba: produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_P____,type,
% 0.19/0.48 p: arrow_1092341143e_indi > produc1832616231le_alt > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_a____,type,
% 0.19/0.48 a: arrow_1346734812le_alt ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_b____,type,
% 0.19/0.48 b: arrow_1346734812le_alt ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_c____,type,
% 0.19/0.48 c: arrow_1346734812le_alt ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_d____,type,
% 0.19/0.48 d: arrow_1346734812le_alt ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_e____,type,
% 0.19/0.48 e: arrow_1346734812le_alt ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_h____,type,
% 0.19/0.48 h: arrow_1092341143e_indi > nat ).
% 0.19/0.48
% 0.19/0.48 thf(sy_v_n____,type,
% 0.19/0.48 n: nat ).
% 0.19/0.48
% 0.19/0.48 %----Relevant facts (198)
% 0.19/0.48 thf(fact_0_assms_I3_J,axiom,
% 0.19/0.48 arrow_1724561858le_IIA @ f ).
% 0.19/0.48
% 0.19/0.48 thf(fact_1_u,axiom,
% 0.19/0.48 arrow_1889221221nimity @ f ).
% 0.19/0.48
% 0.19/0.48 thf(fact_2__096c_A_126_061_Ad_096,axiom,
% 0.19/0.48 c != d ).
% 0.19/0.48
% 0.19/0.48 thf(fact_3__096P_A_058_AProf_096,axiom,
% 0.19/0.48 member1561882372_alt_o @ p @ arrow_1605628760e_Prof ).
% 0.19/0.48
% 0.19/0.48 thf(fact_4_in__mkbot,axiom,
% 0.19/0.48 ! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o,Z_2: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ ( arrow_1717184938_mkbot @ L @ Z_2 ) )
% 0.19/0.48 <=> ( ( Y != Z_2 )
% 0.19/0.48 & ( ( X = Z_2 )
% 0.19/0.48 => ( X != Y ) )
% 0.19/0.48 & ( ( X != Z_2 )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_5_in__mktop,axiom,
% 0.19/0.48 ! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o,Z_2: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ ( arrow_1865892024_mktop @ L @ Z_2 ) )
% 0.19/0.48 <=> ( ( X != Z_2 )
% 0.19/0.48 & ( ( Y = Z_2 )
% 0.19/0.48 => ( X != Y ) )
% 0.19/0.48 & ( ( Y != Z_2 )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_6__C2_C,axiom,
% 0.19/0.48 ! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_26: arrow_1346734812le_alt,B_16: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_25 != B_15 )
% 0.19/0.48 => ( ( A_26 != B_16 )
% 0.19/0.48 => ( ( A_25 != B_16 )
% 0.19/0.48 => ( ( B_15 != A_26 )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( P_6 @ I ) ) )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_7__C1_C,axiom,
% 0.19/0.48 ! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_26: arrow_1346734812le_alt,B_16: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_25 != B_15 )
% 0.19/0.48 => ( ( A_26 != B_16 )
% 0.19/0.48 => ( ( A_25 != B_16 )
% 0.19/0.48 => ( ( B_15 != A_26 )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( P_6 @ I ) ) )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_8__C4_C,axiom,
% 0.19/0.48 ! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,C_4: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_25 != B_15 )
% 0.19/0.48 => ( ( B_15 != C_4 )
% 0.19/0.48 => ( ( A_25 != C_4 )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ C_4 ) @ ( P_6 @ I ) ) )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ C_4 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_9_pairwise__neutrality,axiom,
% 0.19/0.48 ! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_26: arrow_1346734812le_alt,B_16: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_25 != B_15 )
% 0.19/0.48 => ( ( A_26 != B_16 )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( P_6 @ I ) ) )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_10__C3_C,axiom,
% 0.19/0.48 ! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_25 != B_15 )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ A_25 ) @ ( P_6 @ I ) ) )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ A_25 ) @ ( f @ P_6 ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
% 0.19/0.48 ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( p @ I ) )
% 0.19/0.48 <=> ( ( ( ord_less_nat @ ( h @ I ) @ n )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e ) ) )
% 0.19/0.48 & ( ~ ( ord_less_nat @ ( h @ I ) @ n )
% 0.19/0.48 => ( ( ( ( h @ I )
% 0.19/0.48 = n )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( arrow_452340254_above @ ( p @ I ) @ c @ e ) ) )
% 0.19/0.48 & ( ( ( h @ I )
% 0.19/0.48 != n )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
% 0.19/0.48 member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( p @ ( hilber564731065di_nat @ top_to527331954indi_o @ h @ n ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
% 0.19/0.48 ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
% 0.19/0.48 @ ( f
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
% 0.19/0.48 @ ( if_Pro399136856_alt_o
% 0.19/0.48 @ ( ( h @ I )
% 0.19/0.48 = n )
% 0.19/0.48 @ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
% 0.19/0.48 @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_14_PW,axiom,
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
% 0.19/0.48 @ ( f
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
% 0.19/0.48 @ ( if_Pro399136856_alt_o
% 0.19/0.48 @ ( ( h @ I )
% 0.19/0.48 = n )
% 0.19/0.48 @ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
% 0.19/0.48 @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_15_split__paired__All,axiom,
% 0.19/0.48 ! [P_4: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( all @ P_4 )
% 0.19/0.48 <=> ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] : ( P_4 @ ( produc990411159le_alt @ A_5 @ B_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
% 0.19/0.48 ( member1561882372_alt_o
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
% 0.19/0.48 @ ( if_Pro399136856_alt_o
% 0.19/0.48 @ ( ( h @ I )
% 0.19/0.48 = n )
% 0.19/0.48 @ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
% 0.19/0.48 @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) )
% 0.19/0.48 @ arrow_1605628760e_Prof ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
% 0.19/0.48 ( member545531028le_alt @ ( produc990411159le_alt @ c @ e )
% 0.19/0.48 @ ( f
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
% 0.19/0.48 @ ( if_Pro399136856_alt_o
% 0.19/0.48 @ ( ( h @ I )
% 0.19/0.48 = n )
% 0.19/0.48 @ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
% 0.19/0.48 @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
% 0.19/0.48 ( member545531028le_alt @ ( produc990411159le_alt @ e @ d )
% 0.19/0.48 @ ( f
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
% 0.19/0.48 @ ( if_Pro399136856_alt_o
% 0.19/0.48 @ ( ( h @ I )
% 0.19/0.48 = n )
% 0.19/0.48 @ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
% 0.19/0.48 @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_19_n_I1_J,axiom,
% 0.19/0.48 ord_less_nat @ n @ ( finite1907699781e_indi @ top_to527331954indi_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_20_injh,axiom,
% 0.19/0.48 inj_on945046484di_nat @ h @ top_to527331954indi_o ).
% 0.19/0.48
% 0.19/0.48 thf(fact_21_Pair__inject,axiom,
% 0.19/0.48 ! [A_24: arrow_1346734812le_alt,B_14: arrow_1346734812le_alt,A_23: arrow_1346734812le_alt,B_13: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( ( produc990411159le_alt @ A_24 @ B_14 )
% 0.19/0.48 = ( produc990411159le_alt @ A_23 @ B_13 ) )
% 0.19/0.48 => ~ ( ( A_24 = A_23 )
% 0.19/0.48 => ( B_14 != B_13 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_22_Pair__eq,axiom,
% 0.19/0.48 ! [A_22: arrow_1346734812le_alt,B_12: arrow_1346734812le_alt,A_21: arrow_1346734812le_alt,B_11: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( ( produc990411159le_alt @ A_22 @ B_12 )
% 0.19/0.48 = ( produc990411159le_alt @ A_21 @ B_11 ) )
% 0.19/0.48 <=> ( ( A_22 = A_21 )
% 0.19/0.48 & ( B_12 = B_11 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_23_IIA__def,axiom,
% 0.19/0.48 ! [F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( arrow_1724561858le_IIA @ F )
% 0.19/0.48 <=> ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ! [Xa: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ Xa @ arrow_1605628760e_Prof )
% 0.19/0.48 => ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
% 0.19/0.48 ( ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( X_1 @ I ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( Xa @ I ) ) )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ X_1 ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ Xa ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_24_unanimity__def,axiom,
% 0.19/0.48 ! [F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( arrow_1889221221nimity @ F )
% 0.19/0.48 <=> ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
% 0.19/0.48 ( ! [I: arrow_1092341143e_indi] : ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( X_1 @ I ) )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ X_1 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_25_top1I,axiom,
% 0.19/0.48 ! [X_34: produc1832616231le_alt > $o] : ( top_to1830848411lt_o_o @ X_34 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_26_top1I,axiom,
% 0.19/0.48 ! [X_34: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( top_to790289938lt_o_o @ X_34 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_27_top1I,axiom,
% 0.19/0.48 ! [X_34: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( top_to1049332548lt_o_o @ X_34 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_28_top1I,axiom,
% 0.19/0.48 ! [X_34: produc1832616231le_alt] : ( top_to679332578_alt_o @ X_34 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_29_top1I,axiom,
% 0.19/0.48 ! [X_34: arrow_1092341143e_indi] : ( top_to527331954indi_o @ X_34 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_30_UNIV__I,axiom,
% 0.19/0.48 ! [X_33: $o] : ( member_o @ X_33 @ top_top_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_31_UNIV__I,axiom,
% 0.19/0.48 ! [X_33: arrow_1092341143e_indi] : ( member1714766084e_indi @ X_33 @ top_to527331954indi_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_32_UNIV__I,axiom,
% 0.19/0.48 ! [X_33: produc1832616231le_alt] : ( member545531028le_alt @ X_33 @ top_to679332578_alt_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_33_UNIV__I,axiom,
% 0.19/0.48 ! [X_33: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( member1561882372_alt_o @ X_33 @ top_to790289938lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_34_UNIV__I,axiom,
% 0.19/0.48 ! [X_33: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( member733327538_alt_o @ X_33 @ top_to1049332548lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_35_UNIV__I,axiom,
% 0.19/0.48 ! [X_33: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ X_33 @ top_to1830848411lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_36_iso__tuple__UNIV__I,axiom,
% 0.19/0.48 ! [X_32: $o] : ( member_o @ X_32 @ top_top_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_37_iso__tuple__UNIV__I,axiom,
% 0.19/0.48 ! [X_32: arrow_1092341143e_indi] : ( member1714766084e_indi @ X_32 @ top_to527331954indi_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_38_iso__tuple__UNIV__I,axiom,
% 0.19/0.48 ! [X_32: produc1832616231le_alt] : ( member545531028le_alt @ X_32 @ top_to679332578_alt_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_39_iso__tuple__UNIV__I,axiom,
% 0.19/0.48 ! [X_32: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( member1561882372_alt_o @ X_32 @ top_to790289938lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_40_iso__tuple__UNIV__I,axiom,
% 0.19/0.48 ! [X_32: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( member733327538_alt_o @ X_32 @ top_to1049332548lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_41_iso__tuple__UNIV__I,axiom,
% 0.19/0.48 ! [X_32: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ X_32 @ top_to1830848411lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_42_top__apply,axiom,
% 0.19/0.48 ! [X_31: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( top_to1830848411lt_o_o @ X_31 )
% 0.19/0.48 <=> top_top_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_43_top__apply,axiom,
% 0.19/0.48 ! [X_31: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( top_to790289938lt_o_o @ X_31 )
% 0.19/0.48 <=> top_top_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_44_top__apply,axiom,
% 0.19/0.48 ! [X_31: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( top_to1049332548lt_o_o @ X_31 )
% 0.19/0.48 <=> top_top_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_45_top__apply,axiom,
% 0.19/0.48 ! [X_31: produc1832616231le_alt] :
% 0.19/0.48 ( ( top_to679332578_alt_o @ X_31 )
% 0.19/0.48 <=> top_top_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_46_top__apply,axiom,
% 0.19/0.48 ! [X_31: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( top_to527331954indi_o @ X_31 )
% 0.19/0.48 <=> top_top_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_47_not__top__less,axiom,
% 0.19/0.48 ! [A_20: ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ~ ( ord_le898419007lt_o_o @ top_to1830848411lt_o_o @ A_20 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_48_not__top__less,axiom,
% 0.19/0.48 ! [A_20: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ~ ( ord_le972845494lt_o_o @ top_to790289938lt_o_o @ A_20 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_49_not__top__less,axiom,
% 0.19/0.48 ! [A_20: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ~ ( ord_le939309728lt_o_o @ top_to1049332548lt_o_o @ A_20 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_50_not__top__less,axiom,
% 0.19/0.48 ! [A_20: $o] :
% 0.19/0.48 ~ ( ord_less_o @ top_top_o @ A_20 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_51_not__top__less,axiom,
% 0.19/0.48 ! [A_20: produc1832616231le_alt > $o] :
% 0.19/0.48 ~ ( ord_le1973646398_alt_o @ top_to679332578_alt_o @ A_20 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_52_not__top__less,axiom,
% 0.19/0.48 ! [A_20: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ~ ( ord_le316791758indi_o @ top_to527331954indi_o @ A_20 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_53_linorder__cases,axiom,
% 0.19/0.48 ! [X_30: nat,Y_23: nat] :
% 0.19/0.48 ( ~ ( ord_less_nat @ X_30 @ Y_23 )
% 0.19/0.48 => ( ( X_30 != Y_23 )
% 0.19/0.48 => ( ord_less_nat @ Y_23 @ X_30 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_54_order__less__asym,axiom,
% 0.19/0.48 ! [X_29: arrow_1092341143e_indi > $o,Y_22: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_29 @ Y_22 )
% 0.19/0.48 => ~ ( ord_le316791758indi_o @ Y_22 @ X_29 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_55_order__less__asym,axiom,
% 0.19/0.48 ! [X_29: nat,Y_22: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_29 @ Y_22 )
% 0.19/0.48 => ~ ( ord_less_nat @ Y_22 @ X_29 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_56_xt1_I10_J,axiom,
% 0.19/0.48 ! [Z_1: arrow_1092341143e_indi > $o,Y_21: arrow_1092341143e_indi > $o,X_28: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ Y_21 @ X_28 )
% 0.19/0.48 => ( ( ord_le316791758indi_o @ Z_1 @ Y_21 )
% 0.19/0.48 => ( ord_le316791758indi_o @ Z_1 @ X_28 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_57_xt1_I10_J,axiom,
% 0.19/0.48 ! [Z_1: nat,Y_21: nat,X_28: nat] :
% 0.19/0.48 ( ( ord_less_nat @ Y_21 @ X_28 )
% 0.19/0.48 => ( ( ord_less_nat @ Z_1 @ Y_21 )
% 0.19/0.48 => ( ord_less_nat @ Z_1 @ X_28 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_58_order__less__trans,axiom,
% 0.19/0.48 ! [Z: arrow_1092341143e_indi > $o,X_27: arrow_1092341143e_indi > $o,Y_20: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_27 @ Y_20 )
% 0.19/0.48 => ( ( ord_le316791758indi_o @ Y_20 @ Z )
% 0.19/0.48 => ( ord_le316791758indi_o @ X_27 @ Z ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_59_order__less__trans,axiom,
% 0.19/0.48 ! [Z: nat,X_27: nat,Y_20: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_27 @ Y_20 )
% 0.19/0.48 => ( ( ord_less_nat @ Y_20 @ Z )
% 0.19/0.48 => ( ord_less_nat @ X_27 @ Z ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_60_xt1_I2_J,axiom,
% 0.19/0.48 ! [C_3: arrow_1092341143e_indi > $o,B_10: arrow_1092341143e_indi > $o,A_19: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ B_10 @ A_19 )
% 0.19/0.48 => ( ( B_10 = C_3 )
% 0.19/0.48 => ( ord_le316791758indi_o @ C_3 @ A_19 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_61_xt1_I2_J,axiom,
% 0.19/0.48 ! [C_3: nat,B_10: nat,A_19: nat] :
% 0.19/0.48 ( ( ord_less_nat @ B_10 @ A_19 )
% 0.19/0.48 => ( ( B_10 = C_3 )
% 0.19/0.48 => ( ord_less_nat @ C_3 @ A_19 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_62_ord__less__eq__trans,axiom,
% 0.19/0.48 ! [C_2: arrow_1092341143e_indi > $o,A_18: arrow_1092341143e_indi > $o,B_9: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ A_18 @ B_9 )
% 0.19/0.48 => ( ( B_9 = C_2 )
% 0.19/0.48 => ( ord_le316791758indi_o @ A_18 @ C_2 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_63_ord__less__eq__trans,axiom,
% 0.19/0.48 ! [C_2: nat,A_18: nat,B_9: nat] :
% 0.19/0.48 ( ( ord_less_nat @ A_18 @ B_9 )
% 0.19/0.48 => ( ( B_9 = C_2 )
% 0.19/0.48 => ( ord_less_nat @ A_18 @ C_2 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_64_xt1_I1_J,axiom,
% 0.19/0.48 ! [C_1: arrow_1092341143e_indi > $o,A_17: arrow_1092341143e_indi > $o,B_8: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( A_17 = B_8 )
% 0.19/0.48 => ( ( ord_le316791758indi_o @ C_1 @ B_8 )
% 0.19/0.48 => ( ord_le316791758indi_o @ C_1 @ A_17 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_65_xt1_I1_J,axiom,
% 0.19/0.48 ! [C_1: nat,A_17: nat,B_8: nat] :
% 0.19/0.48 ( ( A_17 = B_8 )
% 0.19/0.48 => ( ( ord_less_nat @ C_1 @ B_8 )
% 0.19/0.48 => ( ord_less_nat @ C_1 @ A_17 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_66_ord__eq__less__trans,axiom,
% 0.19/0.48 ! [C: arrow_1092341143e_indi > $o,A_16: arrow_1092341143e_indi > $o,B_7: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( A_16 = B_7 )
% 0.19/0.48 => ( ( ord_le316791758indi_o @ B_7 @ C )
% 0.19/0.48 => ( ord_le316791758indi_o @ A_16 @ C ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_67_ord__eq__less__trans,axiom,
% 0.19/0.48 ! [C: nat,A_16: nat,B_7: nat] :
% 0.19/0.48 ( ( A_16 = B_7 )
% 0.19/0.48 => ( ( ord_less_nat @ B_7 @ C )
% 0.19/0.48 => ( ord_less_nat @ A_16 @ C ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_68_xt1_I9_J,axiom,
% 0.19/0.48 ! [B_6: arrow_1092341143e_indi > $o,A_15: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ B_6 @ A_15 )
% 0.19/0.48 => ~ ( ord_le316791758indi_o @ A_15 @ B_6 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_69_xt1_I9_J,axiom,
% 0.19/0.48 ! [B_6: nat,A_15: nat] :
% 0.19/0.48 ( ( ord_less_nat @ B_6 @ A_15 )
% 0.19/0.48 => ~ ( ord_less_nat @ A_15 @ B_6 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_70_order__less__asym_H,axiom,
% 0.19/0.48 ! [A_14: arrow_1092341143e_indi > $o,B_5: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ A_14 @ B_5 )
% 0.19/0.48 => ~ ( ord_le316791758indi_o @ B_5 @ A_14 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_71_order__less__asym_H,axiom,
% 0.19/0.48 ! [A_14: nat,B_5: nat] :
% 0.19/0.48 ( ( ord_less_nat @ A_14 @ B_5 )
% 0.19/0.48 => ~ ( ord_less_nat @ B_5 @ A_14 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_72_order__less__imp__triv,axiom,
% 0.19/0.48 ! [P_3: $o,X_26: arrow_1092341143e_indi > $o,Y_19: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_26 @ Y_19 )
% 0.19/0.48 => ( ( ord_le316791758indi_o @ Y_19 @ X_26 )
% 0.19/0.48 => P_3 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_73_order__less__imp__triv,axiom,
% 0.19/0.48 ! [P_3: $o,X_26: nat,Y_19: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_26 @ Y_19 )
% 0.19/0.48 => ( ( ord_less_nat @ Y_19 @ X_26 )
% 0.19/0.48 => P_3 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_74_order__less__imp__not__eq2,axiom,
% 0.19/0.48 ! [X_25: arrow_1092341143e_indi > $o,Y_18: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_25 @ Y_18 )
% 0.19/0.48 => ( Y_18 != X_25 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_75_order__less__imp__not__eq2,axiom,
% 0.19/0.48 ! [X_25: nat,Y_18: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_25 @ Y_18 )
% 0.19/0.48 => ( Y_18 != X_25 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_76_order__less__imp__not__eq,axiom,
% 0.19/0.48 ! [X_24: arrow_1092341143e_indi > $o,Y_17: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_24 @ Y_17 )
% 0.19/0.48 => ( X_24 != Y_17 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_77_order__less__imp__not__eq,axiom,
% 0.19/0.48 ! [X_24: nat,Y_17: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_24 @ Y_17 )
% 0.19/0.48 => ( X_24 != Y_17 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_78_order__less__imp__not__less,axiom,
% 0.19/0.48 ! [X_23: arrow_1092341143e_indi > $o,Y_16: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_23 @ Y_16 )
% 0.19/0.48 => ~ ( ord_le316791758indi_o @ Y_16 @ X_23 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_79_order__less__imp__not__less,axiom,
% 0.19/0.48 ! [X_23: nat,Y_16: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_23 @ Y_16 )
% 0.19/0.48 => ~ ( ord_less_nat @ Y_16 @ X_23 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_80_order__less__not__sym,axiom,
% 0.19/0.48 ! [X_22: arrow_1092341143e_indi > $o,Y_15: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_22 @ Y_15 )
% 0.19/0.48 => ~ ( ord_le316791758indi_o @ Y_15 @ X_22 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_81_order__less__not__sym,axiom,
% 0.19/0.48 ! [X_22: nat,Y_15: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_22 @ Y_15 )
% 0.19/0.48 => ~ ( ord_less_nat @ Y_15 @ X_22 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_82_less__imp__neq,axiom,
% 0.19/0.48 ! [X_21: arrow_1092341143e_indi > $o,Y_14: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( ord_le316791758indi_o @ X_21 @ Y_14 )
% 0.19/0.48 => ( X_21 != Y_14 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_83_less__imp__neq,axiom,
% 0.19/0.48 ! [X_21: nat,Y_14: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_21 @ Y_14 )
% 0.19/0.48 => ( X_21 != Y_14 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_84_linorder__neqE,axiom,
% 0.19/0.48 ! [X_20: nat,Y_13: nat] :
% 0.19/0.48 ( ( X_20 != Y_13 )
% 0.19/0.48 => ( ~ ( ord_less_nat @ X_20 @ Y_13 )
% 0.19/0.48 => ( ord_less_nat @ Y_13 @ X_20 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_85_linorder__antisym__conv3,axiom,
% 0.19/0.48 ! [Y_12: nat,X_19: nat] :
% 0.19/0.48 ( ~ ( ord_less_nat @ Y_12 @ X_19 )
% 0.19/0.48 => ( ~ ( ord_less_nat @ X_19 @ Y_12 )
% 0.19/0.48 <=> ( X_19 = Y_12 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_86_linorder__less__linear,axiom,
% 0.19/0.48 ! [X_18: nat,Y_11: nat] :
% 0.19/0.48 ( ( ord_less_nat @ X_18 @ Y_11 )
% 0.19/0.48 | ( X_18 = Y_11 )
% 0.19/0.48 | ( ord_less_nat @ Y_11 @ X_18 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_87_not__less__iff__gr__or__eq,axiom,
% 0.19/0.48 ! [X_17: nat,Y_10: nat] :
% 0.19/0.48 ( ~ ( ord_less_nat @ X_17 @ Y_10 )
% 0.19/0.48 <=> ( ( ord_less_nat @ Y_10 @ X_17 )
% 0.19/0.48 | ( X_17 = Y_10 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_88_linorder__neq__iff,axiom,
% 0.19/0.48 ! [X_16: nat,Y_9: nat] :
% 0.19/0.48 ( ( X_16 != Y_9 )
% 0.19/0.48 <=> ( ( ord_less_nat @ X_16 @ Y_9 )
% 0.19/0.48 | ( ord_less_nat @ Y_9 @ X_16 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_89_order__less__irrefl,axiom,
% 0.19/0.48 ! [X_15: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ~ ( ord_le316791758indi_o @ X_15 @ X_15 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_90_order__less__irrefl,axiom,
% 0.19/0.48 ! [X_15: nat] :
% 0.19/0.48 ~ ( ord_less_nat @ X_15 @ X_15 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_91_UNIV__def,axiom,
% 0.19/0.48 ( top_to1830848411lt_o_o
% 0.19/0.48 = ( collec1079683069_alt_o
% 0.19/0.48 @ ^ [X_1: produc1832616231le_alt > $o] : $true ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_92_UNIV__def,axiom,
% 0.19/0.48 ( top_to790289938lt_o_o
% 0.19/0.48 = ( collec1718651462_alt_o
% 0.19/0.48 @ ^ [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] : $true ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_93_UNIV__def,axiom,
% 0.19/0.48 ( top_to1049332548lt_o_o
% 0.19/0.48 = ( collec2125720304_alt_o
% 0.19/0.48 @ ^ [X_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : $true ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_94_UNIV__def,axiom,
% 0.19/0.48 ( top_to679332578_alt_o
% 0.19/0.48 = ( collec1201320914le_alt
% 0.19/0.48 @ ^ [X_1: produc1832616231le_alt] : $true ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_95_UNIV__def,axiom,
% 0.19/0.48 ( top_to527331954indi_o
% 0.19/0.48 = ( collec1832628290e_indi
% 0.19/0.48 @ ^ [X_1: arrow_1092341143e_indi] : $true ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_96_pred__equals__eq2,axiom,
% 0.19/0.48 ! [S: produc1832616231le_alt > $o,R: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ! [X_1: arrow_1346734812le_alt,Xa: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ X_1 @ Xa ) @ R )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ X_1 @ Xa ) @ S ) )
% 0.19/0.48 <=> ( R = S ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_97_less__top,axiom,
% 0.19/0.48 ! [A_13: ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( A_13 != top_to1830848411lt_o_o )
% 0.19/0.48 <=> ( ord_le898419007lt_o_o @ A_13 @ top_to1830848411lt_o_o ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_98_less__top,axiom,
% 0.19/0.48 ! [A_13: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( A_13 != top_to790289938lt_o_o )
% 0.19/0.48 <=> ( ord_le972845494lt_o_o @ A_13 @ top_to790289938lt_o_o ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_99_less__top,axiom,
% 0.19/0.48 ! [A_13: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( A_13 != top_to1049332548lt_o_o )
% 0.19/0.48 <=> ( ord_le939309728lt_o_o @ A_13 @ top_to1049332548lt_o_o ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_100_less__top,axiom,
% 0.19/0.48 ! [A_13: $o] :
% 0.19/0.48 ( ~ ( A_13
% 0.19/0.48 <=> top_top_o )
% 0.19/0.48 <=> ( ord_less_o @ A_13 @ top_top_o ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_101_less__top,axiom,
% 0.19/0.48 ! [A_13: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( A_13 != top_to679332578_alt_o )
% 0.19/0.48 <=> ( ord_le1973646398_alt_o @ A_13 @ top_to679332578_alt_o ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_102_less__top,axiom,
% 0.19/0.48 ! [A_13: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( A_13 != top_to527331954indi_o )
% 0.19/0.48 <=> ( ord_le316791758indi_o @ A_13 @ top_to527331954indi_o ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_103_inv__f__eq,axiom,
% 0.19/0.48 ! [X_14: arrow_1092341143e_indi,Y_8: nat,F_15: arrow_1092341143e_indi > nat] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_15 @ top_to527331954indi_o )
% 0.19/0.48 => ( ( ( F_15 @ X_14 )
% 0.19/0.48 = Y_8 )
% 0.19/0.48 => ( ( hilber564731065di_nat @ top_to527331954indi_o @ F_15 @ Y_8 )
% 0.19/0.48 = X_14 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_104_inv__f__f,axiom,
% 0.19/0.48 ! [X_13: arrow_1092341143e_indi,F_14: arrow_1092341143e_indi > nat] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_14 @ top_to527331954indi_o )
% 0.19/0.48 => ( ( hilber564731065di_nat @ top_to527331954indi_o @ F_14 @ ( F_14 @ X_13 ) )
% 0.19/0.48 = X_13 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_105_inv__into__f__f,axiom,
% 0.19/0.48 ! [X_12: arrow_1092341143e_indi,F_13: arrow_1092341143e_indi > nat,A_12: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_13 @ A_12 )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_12 @ A_12 )
% 0.19/0.48 => ( ( hilber564731065di_nat @ A_12 @ F_13 @ ( F_13 @ X_12 ) )
% 0.19/0.48 = X_12 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_106_inv__into__f__eq,axiom,
% 0.19/0.48 ! [Y_7: nat,X_11: arrow_1092341143e_indi,F_12: arrow_1092341143e_indi > nat,A_11: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_12 @ A_11 )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_11 @ A_11 )
% 0.19/0.48 => ( ( ( F_12 @ X_11 )
% 0.19/0.48 = Y_7 )
% 0.19/0.48 => ( ( hilber564731065di_nat @ A_11 @ F_12 @ Y_7 )
% 0.19/0.48 = X_11 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_107_inj__eq,axiom,
% 0.19/0.48 ! [X_10: arrow_1092341143e_indi,Y_6: arrow_1092341143e_indi,F_11: arrow_1092341143e_indi > nat] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_11 @ top_to527331954indi_o )
% 0.19/0.48 => ( ( ( F_11 @ X_10 )
% 0.19/0.48 = ( F_11 @ Y_6 ) )
% 0.19/0.48 <=> ( X_10 = Y_6 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_108_inj__on__def,axiom,
% 0.19/0.48 ! [F_10: arrow_1092341143e_indi > nat,A_10: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_10 @ A_10 )
% 0.19/0.48 <=> ! [X_1: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member1714766084e_indi @ X_1 @ A_10 )
% 0.19/0.48 => ! [Xa: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( member1714766084e_indi @ Xa @ A_10 )
% 0.19/0.48 => ( ( ( F_10 @ X_1 )
% 0.19/0.48 = ( F_10 @ Xa ) )
% 0.19/0.48 => ( X_1 = Xa ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_109_inj__on__contraD,axiom,
% 0.19/0.48 ! [X_9: arrow_1092341143e_indi,Y_5: arrow_1092341143e_indi,F_9: arrow_1092341143e_indi > nat,A_9: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_9 @ A_9 )
% 0.19/0.48 => ( ( X_9 != Y_5 )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_9 @ A_9 )
% 0.19/0.48 => ( ( member1714766084e_indi @ Y_5 @ A_9 )
% 0.19/0.48 => ( ( F_9 @ X_9 )
% 0.19/0.48 != ( F_9 @ Y_5 ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_110_inj__on__iff,axiom,
% 0.19/0.48 ! [Y_4: arrow_1092341143e_indi,X_8: arrow_1092341143e_indi,F_8: arrow_1092341143e_indi > nat,A_8: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_8 @ A_8 )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_8 @ A_8 )
% 0.19/0.48 => ( ( member1714766084e_indi @ Y_4 @ A_8 )
% 0.19/0.48 => ( ( ( F_8 @ X_8 )
% 0.19/0.48 = ( F_8 @ Y_4 ) )
% 0.19/0.48 <=> ( X_8 = Y_4 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_111_inj__onD,axiom,
% 0.19/0.48 ! [X_7: arrow_1092341143e_indi,Y_3: arrow_1092341143e_indi,F_7: arrow_1092341143e_indi > nat,A_7: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_7 @ A_7 )
% 0.19/0.48 => ( ( ( F_7 @ X_7 )
% 0.19/0.48 = ( F_7 @ Y_3 ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_7 @ A_7 )
% 0.19/0.48 => ( ( member1714766084e_indi @ Y_3 @ A_7 )
% 0.19/0.48 => ( X_7 = Y_3 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_112_injD,axiom,
% 0.19/0.48 ! [X_6: arrow_1092341143e_indi,Y_2: arrow_1092341143e_indi,F_6: arrow_1092341143e_indi > nat] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_6 @ top_to527331954indi_o )
% 0.19/0.48 => ( ( ( F_6 @ X_6 )
% 0.19/0.48 = ( F_6 @ Y_2 ) )
% 0.19/0.48 => ( X_6 = Y_2 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_113_inj__imp__inv__eq,axiom,
% 0.19/0.48 ! [G: nat > arrow_1092341143e_indi,F_5: arrow_1092341143e_indi > nat] :
% 0.19/0.48 ( ( inj_on945046484di_nat @ F_5 @ top_to527331954indi_o )
% 0.19/0.48 => ( ! [X_1: nat] :
% 0.19/0.48 ( ( F_5 @ ( G @ X_1 ) )
% 0.19/0.48 = X_1 )
% 0.19/0.48 => ( ( hilber564731065di_nat @ top_to527331954indi_o @ F_5 )
% 0.19/0.48 = G ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_114_injI,axiom,
% 0.19/0.48 ! [F_4: arrow_1092341143e_indi > nat] :
% 0.19/0.48 ( ! [X_1: arrow_1092341143e_indi,Y_1: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( ( F_4 @ X_1 )
% 0.19/0.48 = ( F_4 @ Y_1 ) )
% 0.19/0.48 => ( X_1 = Y_1 ) )
% 0.19/0.48 => ( inj_on945046484di_nat @ F_4 @ top_to527331954indi_o ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_115_assms_I1_J,axiom,
% 0.19/0.48 ( member733327538_alt_o @ f
% 0.19/0.48 @ ( pi_Arr1021537730_alt_o @ arrow_1605628760e_Prof
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : arrow_1751445586le_Lin ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_116__096Lba_A_058_ALin_096,axiom,
% 0.19/0.48 member1362619835_alt_o @ lba @ arrow_1751445586le_Lin ).
% 0.19/0.48
% 0.19/0.48 thf(fact_117__096Lab_A_058_ALin_096,axiom,
% 0.19/0.48 member1362619835_alt_o @ lab @ arrow_1751445586le_Lin ).
% 0.19/0.48
% 0.19/0.48 thf(fact_118_Lin__irrefl,axiom,
% 0.19/0.48 ! [A_3: arrow_1346734812le_alt,B_2: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_3 @ B_2 ) @ L )
% 0.19/0.48 => ~ ( member545531028le_alt @ ( produc990411159le_alt @ B_2 @ A_3 ) @ L ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_119_notin__Lin__iff,axiom,
% 0.19/0.48 ! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
% 0.19/0.48 => ( ( X != Y )
% 0.19/0.48 => ( ~ ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ Y @ X ) @ L ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_120_mem__def,axiom,
% 0.19/0.48 ! [X_5: arrow_1092341143e_indi,A_6: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1714766084e_indi @ X_5 @ A_6 )
% 0.19/0.48 <=> ( A_6 @ X_5 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_121_mem__def,axiom,
% 0.19/0.48 ! [X_5: $o,A_6: $o > $o] :
% 0.19/0.48 ( ( member_o @ X_5 @ A_6 )
% 0.19/0.48 <=> ( A_6 @ X_5 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_122_mem__def,axiom,
% 0.19/0.48 ! [X_5: produc1832616231le_alt,A_6: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member545531028le_alt @ X_5 @ A_6 )
% 0.19/0.48 <=> ( A_6 @ X_5 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_123_mem__def,axiom,
% 0.19/0.48 ! [X_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ X_5 @ A_6 )
% 0.19/0.48 <=> ( A_6 @ X_5 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_124_mem__def,axiom,
% 0.19/0.48 ! [X_5: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_6: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member733327538_alt_o @ X_5 @ A_6 )
% 0.19/0.48 <=> ( A_6 @ X_5 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_125_mem__def,axiom,
% 0.19/0.48 ! [X_5: produc1832616231le_alt > $o,A_6: ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ X_5 @ A_6 )
% 0.19/0.48 <=> ( A_6 @ X_5 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_126_Collect__def,axiom,
% 0.19/0.48 ! [P_2: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( collec1832628290e_indi @ P_2 )
% 0.19/0.48 = P_2 ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_127_mktop__Lin,axiom,
% 0.19/0.48 ! [X: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
% 0.19/0.48 => ( member1362619835_alt_o @ ( arrow_1865892024_mktop @ L @ X ) @ arrow_1751445586le_Lin ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_128_mkbot__Lin,axiom,
% 0.19/0.48 ! [X: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
% 0.19/0.48 => ( member1362619835_alt_o @ ( arrow_1717184938_mkbot @ L @ X ) @ arrow_1751445586le_Lin ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_129_above__Lin,axiom,
% 0.19/0.48 ! [L: produc1832616231le_alt > $o,X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( X != Y )
% 0.19/0.48 => ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
% 0.19/0.48 => ( member1362619835_alt_o @ ( arrow_452340254_above @ L @ X @ Y ) @ arrow_1751445586le_Lin ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_130_const__Lin__Prof,axiom,
% 0.19/0.48 ! [L: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
% 0.19/0.48 => ( member1561882372_alt_o
% 0.19/0.48 @ ^ [P_1: arrow_1092341143e_indi] : L
% 0.19/0.48 @ arrow_1605628760e_Prof ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_131_in__above,axiom,
% 0.19/0.48 ! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o,A_3: arrow_1346734812le_alt,B_2: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_3 != B_2 )
% 0.19/0.48 => ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ ( arrow_452340254_above @ L @ A_3 @ B_2 ) )
% 0.19/0.48 <=> ( ( X != Y )
% 0.19/0.48 & ( ( X = B_2 )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ A_3 @ Y ) @ L ) )
% 0.19/0.48 & ( ( X != B_2 )
% 0.19/0.48 => ( ( ( Y = B_2 )
% 0.19/0.48 => ( ( X = A_3 )
% 0.19/0.48 | ( member545531028le_alt @ ( produc990411159le_alt @ X @ A_3 ) @ L ) ) )
% 0.19/0.48 & ( ( Y != B_2 )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_132_dictatorI,axiom,
% 0.19/0.48 ! [I_1: arrow_1092341143e_indi,F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member733327538_alt_o @ F
% 0.19/0.48 @ ( pi_Arr1021537730_alt_o @ arrow_1605628760e_Prof
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : arrow_1751445586le_Lin ) )
% 0.19/0.48 => ( ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_5 != B_4 )
% 0.19/0.48 => ( ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( X_1 @ I_1 ) )
% 0.19/0.48 => ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ X_1 ) ) ) ) )
% 0.19/0.48 => ( arrow_1098709355ctator @ F @ I_1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_133_PiE,axiom,
% 0.19/0.48 ! [X_4: produc1832616231le_alt,F_3: produc1832616231le_alt > $o,A_4: produc1832616231le_alt > $o,B_3: produc1832616231le_alt > $o > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ F_3 @ ( pi_Pro539263375_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member545531028le_alt @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_134_PiE,axiom,
% 0.19/0.48 ! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > produc1832616231le_alt,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1621875105le_alt @ F_3 @ ( pi_Arr1055270199le_alt @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member545531028le_alt @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_135_PiE,axiom,
% 0.19/0.48 ! [X_4: $o,F_3: $o > produc1832616231le_alt,A_4: $o > $o,B_3: $o > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1368218865le_alt @ F_3 @ ( pi_o_P988780107le_alt @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member545531028le_alt @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_136_PiE,axiom,
% 0.19/0.48 ! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1079651021_alt_o @ F_3 @ ( pi_Arr651234977_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1561882372_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_137_PiE,axiom,
% 0.19/0.48 ! [X_4: $o,F_3: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_4: $o > $o,B_3: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member537117565_alt_o @ F_3 @ ( pi_o_A71242893_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1561882372_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_138_PiE,axiom,
% 0.19/0.48 ! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member24189887_alt_o @ F_3 @ ( pi_Arr1140519125_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member733327538_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_139_PiE,axiom,
% 0.19/0.48 ! [X_4: $o,F_3: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_4: $o > $o,B_3: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1710515983_alt_o @ F_3 @ ( pi_o_A1302557673_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member733327538_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_140_PiE,axiom,
% 0.19/0.48 ! [X_4: $o,F_3: $o > produc1832616231le_alt > $o,A_4: $o > $o,B_3: $o > ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1099673524_alt_o @ F_3 @ ( pi_o_P1538584260_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1362619835_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_141_PiE,axiom,
% 0.19/0.48 ! [X_4: produc1832616231le_alt,F_3: produc1832616231le_alt > arrow_1092341143e_indi,A_4: produc1832616231le_alt > $o,B_3: produc1832616231le_alt > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1486844321e_indi @ F_3 @ ( pi_Pro1535452471e_indi @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member545531028le_alt @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_142_PiE,axiom,
% 0.19/0.48 ! [X_4: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1208133347e_indi @ F_3 @ ( pi_Arr170420797e_indi @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1561882372_alt_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_143_PiE,axiom,
% 0.19/0.48 ! [X_4: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o] :
% 0.19/0.48 ( ( member1754345465lt_o_o @ F_3 @ ( pi_Arr1767527177lt_o_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1561882372_alt_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_144_PiE,axiom,
% 0.19/0.48 ! [X_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_4: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member986213183e_indi @ F_3 @ ( pi_Arr1941314005e_indi @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member733327538_alt_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_145_PiE,axiom,
% 0.19/0.48 ! [X_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_4: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o] :
% 0.19/0.48 ( ( member903234717lt_o_o @ F_3 @ ( pi_Arr1422400881lt_o_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member733327538_alt_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_146_PiE,axiom,
% 0.19/0.48 ! [X_4: produc1832616231le_alt > $o,F_3: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_4: ( produc1832616231le_alt > $o ) > $o,B_3: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1255309082e_indi @ F_3 @ ( pi_Pro1340600692e_indi @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1362619835_alt_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_147_PiE,axiom,
% 0.19/0.48 ! [X_4: produc1832616231le_alt > $o,F_3: ( produc1832616231le_alt > $o ) > $o,A_4: ( produc1832616231le_alt > $o ) > $o,B_3: ( produc1832616231le_alt > $o ) > $o > $o] :
% 0.19/0.48 ( ( member1949484546lt_o_o @ F_3 @ ( pi_Pro410810898lt_o_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1362619835_alt_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_148_PiE,axiom,
% 0.19/0.48 ! [X_4: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member733327538_alt_o @ F_3 @ ( pi_Arr1021537730_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1362619835_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1561882372_alt_o @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_149_PiE,axiom,
% 0.19/0.48 ! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ F_3 @ ( pi_Arr418143960_alt_o @ A_4 @ B_3 ) )
% 0.19/0.48 => ( ~ ( member1362619835_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
% 0.19/0.48 => ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_150_complete__Lin,axiom,
% 0.19/0.48 ! [A_3: arrow_1346734812le_alt,B_2: arrow_1346734812le_alt] :
% 0.19/0.48 ( ( A_3 != B_2 )
% 0.19/0.48 => ? [X_1: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ X_1 @ arrow_1751445586le_Lin )
% 0.19/0.48 & ( member545531028le_alt @ ( produc990411159le_alt @ A_3 @ B_2 ) @ X_1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_151_PiProf,axiom,
% 0.19/0.48 ! [N: nat] :
% 0.19/0.48 ( member1561882372_alt_o
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] : ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ N ) @ lab @ lba )
% 0.19/0.48 @ arrow_1605628760e_Prof ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_152_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: produc1832616231le_alt,F_2: produc1832616231le_alt > $o,A_2: produc1832616231le_alt > $o,B_1: produc1832616231le_alt > $o > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ F_2 @ ( pi_Pro539263375_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member545531028le_alt @ X_3 @ A_2 )
% 0.19/0.48 => ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_153_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: produc1832616231le_alt,F_2: produc1832616231le_alt > arrow_1092341143e_indi,A_2: produc1832616231le_alt > $o,B_1: produc1832616231le_alt > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1486844321e_indi @ F_2 @ ( pi_Pro1535452471e_indi @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member545531028le_alt @ X_3 @ A_2 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_154_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1208133347e_indi @ F_2 @ ( pi_Arr170420797e_indi @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1561882372_alt_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_155_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o] :
% 0.19/0.48 ( ( member1754345465lt_o_o @ F_2 @ ( pi_Arr1767527177lt_o_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1561882372_alt_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_156_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member986213183e_indi @ F_2 @ ( pi_Arr1941314005e_indi @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member733327538_alt_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_157_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o] :
% 0.19/0.48 ( ( member903234717lt_o_o @ F_2 @ ( pi_Arr1422400881lt_o_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member733327538_alt_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_158_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: produc1832616231le_alt > $o,F_2: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_2: ( produc1832616231le_alt > $o ) > $o,B_1: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1255309082e_indi @ F_2 @ ( pi_Pro1340600692e_indi @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1362619835_alt_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_159_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: produc1832616231le_alt > $o,F_2: ( produc1832616231le_alt > $o ) > $o,A_2: ( produc1832616231le_alt > $o ) > $o,B_1: ( produc1832616231le_alt > $o ) > $o > $o] :
% 0.19/0.48 ( ( member1949484546lt_o_o @ F_2 @ ( pi_Pro410810898lt_o_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1362619835_alt_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_160_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > produc1832616231le_alt,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1621875105le_alt @ F_2 @ ( pi_Arr1055270199le_alt @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_3 @ A_2 )
% 0.19/0.48 => ( member545531028le_alt @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_161_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: $o,F_2: $o > produc1832616231le_alt,A_2: $o > $o,B_1: $o > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1368218865le_alt @ F_2 @ ( pi_o_P988780107le_alt @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member545531028le_alt @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_162_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1079651021_alt_o @ F_2 @ ( pi_Arr651234977_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_3 @ A_2 )
% 0.19/0.48 => ( member1561882372_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_163_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: $o,F_2: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_2: $o > $o,B_1: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member537117565_alt_o @ F_2 @ ( pi_o_A71242893_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member1561882372_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_164_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member24189887_alt_o @ F_2 @ ( pi_Arr1140519125_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_3 @ A_2 )
% 0.19/0.48 => ( member733327538_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_165_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: $o,F_2: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_2: $o > $o,B_1: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1710515983_alt_o @ F_2 @ ( pi_o_A1302557673_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member733327538_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_166_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: $o,F_2: $o > produc1832616231le_alt > $o,A_2: $o > $o,B_1: $o > ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1099673524_alt_o @ F_2 @ ( pi_o_P1538584260_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member1362619835_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_167_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member733327538_alt_o @ F_2 @ ( pi_Arr1021537730_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1561882372_alt_o @ X_3 @ A_2 )
% 0.19/0.48 => ( member1362619835_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_168_Pi__mem,axiom,
% 0.19/0.48 ! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ F_2 @ ( pi_Arr418143960_alt_o @ A_2 @ B_1 ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_3 @ A_2 )
% 0.19/0.48 => ( member1362619835_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_169_Prof__def,axiom,
% 0.19/0.48 ( arrow_1605628760e_Prof
% 0.19/0.48 = ( pi_Arr418143960_alt_o @ top_to527331954indi_o
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi] : arrow_1751445586le_Lin ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_170_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: produc1832616231le_alt,F_1: produc1832616231le_alt > $o,A_1: produc1832616231le_alt > $o,B: $o > $o] :
% 0.19/0.48 ( ( member1362619835_alt_o @ F_1
% 0.19/0.48 @ ( pi_Pro539263375_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: produc1832616231le_alt] : B ) )
% 0.19/0.48 => ( ( member545531028le_alt @ X_2 @ A_1 )
% 0.19/0.48 => ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_171_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: produc1832616231le_alt,F_1: produc1832616231le_alt > arrow_1092341143e_indi,A_1: produc1832616231le_alt > $o,B: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1486844321e_indi @ F_1
% 0.19/0.48 @ ( pi_Pro1535452471e_indi @ A_1
% 0.19/0.48 @ ^ [Uu: produc1832616231le_alt] : B ) )
% 0.19/0.48 => ( ( member545531028le_alt @ X_2 @ A_1 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_172_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1208133347e_indi @ F_1
% 0.19/0.48 @ ( pi_Arr170420797e_indi @ A_1
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B ) )
% 0.19/0.48 => ( ( member1561882372_alt_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_173_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B: $o > $o] :
% 0.19/0.48 ( ( member1754345465lt_o_o @ F_1
% 0.19/0.48 @ ( pi_Arr1767527177lt_o_o @ A_1
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B ) )
% 0.19/0.48 => ( ( member1561882372_alt_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_174_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member986213183e_indi @ F_1
% 0.19/0.48 @ ( pi_Arr1941314005e_indi @ A_1
% 0.19/0.48 @ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B ) )
% 0.19/0.48 => ( ( member733327538_alt_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_175_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B: $o > $o] :
% 0.19/0.48 ( ( member903234717lt_o_o @ F_1
% 0.19/0.48 @ ( pi_Arr1422400881lt_o_o @ A_1
% 0.19/0.48 @ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B ) )
% 0.19/0.48 => ( ( member733327538_alt_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_176_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: produc1832616231le_alt > $o,F_1: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_1: ( produc1832616231le_alt > $o ) > $o,B: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( member1255309082e_indi @ F_1
% 0.19/0.48 @ ( pi_Pro1340600692e_indi @ A_1
% 0.19/0.48 @ ^ [Uu: produc1832616231le_alt > $o] : B ) )
% 0.19/0.48 => ( ( member1362619835_alt_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_177_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: produc1832616231le_alt > $o,F_1: ( produc1832616231le_alt > $o ) > $o,A_1: ( produc1832616231le_alt > $o ) > $o,B: $o > $o] :
% 0.19/0.48 ( ( member1949484546lt_o_o @ F_1
% 0.19/0.48 @ ( pi_Pro410810898lt_o_o @ A_1
% 0.19/0.48 @ ^ [Uu: produc1832616231le_alt > $o] : B ) )
% 0.19/0.48 => ( ( member1362619835_alt_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_178_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > produc1832616231le_alt,A_1: arrow_1092341143e_indi > $o,B: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1621875105le_alt @ F_1
% 0.19/0.48 @ ( pi_Arr1055270199le_alt @ A_1
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi] : B ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_2 @ A_1 )
% 0.19/0.48 => ( member545531028le_alt @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_179_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: $o,F_1: $o > produc1832616231le_alt,A_1: $o > $o,B: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1368218865le_alt @ F_1
% 0.19/0.48 @ ( pi_o_P988780107le_alt @ A_1
% 0.19/0.48 @ ^ [Uu: $o] : B ) )
% 0.19/0.48 => ( ( member_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member545531028le_alt @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_180_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_1: arrow_1092341143e_indi > $o,B: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1079651021_alt_o @ F_1
% 0.19/0.48 @ ( pi_Arr651234977_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi] : B ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_2 @ A_1 )
% 0.19/0.48 => ( member1561882372_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_181_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: $o,F_1: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_1: $o > $o,B: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member537117565_alt_o @ F_1
% 0.19/0.48 @ ( pi_o_A71242893_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: $o] : B ) )
% 0.19/0.48 => ( ( member_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member1561882372_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_182_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_1: arrow_1092341143e_indi > $o,B: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member24189887_alt_o @ F_1
% 0.19/0.48 @ ( pi_Arr1140519125_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi] : B ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_2 @ A_1 )
% 0.19/0.48 => ( member733327538_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_183_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: $o,F_1: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_1: $o > $o,B: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1710515983_alt_o @ F_1
% 0.19/0.48 @ ( pi_o_A1302557673_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: $o] : B ) )
% 0.19/0.48 => ( ( member_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member733327538_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_184_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: $o,F_1: $o > produc1832616231le_alt > $o,A_1: $o > $o,B: ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1099673524_alt_o @ F_1
% 0.19/0.48 @ ( pi_o_P1538584260_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: $o] : B ) )
% 0.19/0.48 => ( ( member_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member1362619835_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_185_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B: ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member733327538_alt_o @ F_1
% 0.19/0.48 @ ( pi_Arr1021537730_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B ) )
% 0.19/0.48 => ( ( member1561882372_alt_o @ X_2 @ A_1 )
% 0.19/0.48 => ( member1362619835_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_186_funcset__mem,axiom,
% 0.19/0.48 ! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_1: arrow_1092341143e_indi > $o,B: ( produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ F_1
% 0.19/0.48 @ ( pi_Arr418143960_alt_o @ A_1
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi] : B ) )
% 0.19/0.48 => ( ( member1714766084e_indi @ X_2 @ A_1 )
% 0.19/0.48 => ( member1362619835_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_187_dictator__def,axiom,
% 0.19/0.48 ! [F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,I_1: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( arrow_1098709355ctator @ F @ I_1 )
% 0.19/0.48 <=> ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
% 0.19/0.48 => ( ( F @ X_1 )
% 0.19/0.48 = ( X_1 @ I_1 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_188_Pi__UNIV,axiom,
% 0.19/0.48 ! [A: produc1832616231le_alt > $o] :
% 0.19/0.48 ( ( pi_Pro539263375_alt_o @ A
% 0.19/0.48 @ ^ [Uu: produc1832616231le_alt] : top_top_o_o )
% 0.19/0.48 = top_to1830848411lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_189_Pi__UNIV,axiom,
% 0.19/0.48 ! [A: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
% 0.19/0.48 ( ( pi_Arr1021537730_alt_o @ A
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : top_to1830848411lt_o_o )
% 0.19/0.48 = top_to1049332548lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_190_Pi__UNIV,axiom,
% 0.19/0.48 ! [A: arrow_1092341143e_indi > $o] :
% 0.19/0.48 ( ( pi_Arr418143960_alt_o @ A
% 0.19/0.48 @ ^ [Uu: arrow_1092341143e_indi] : top_to1830848411lt_o_o )
% 0.19/0.48 = top_to790289938lt_o_o ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
% 0.19/0.48 ( ( member545531028le_alt @ ( produc990411159le_alt @ e @ d )
% 0.19/0.48 @ ( f
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
% 0.19/0.48 @ ( if_Pro399136856_alt_o
% 0.19/0.48 @ ( ( h @ I )
% 0.19/0.48 = n )
% 0.19/0.48 @ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
% 0.19/0.48 @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) )
% 0.19/0.48 <=> ( member545531028le_alt @ ( produc990411159le_alt @ b @ a )
% 0.19/0.48 @ ( f
% 0.19/0.48 @ ^ [I: arrow_1092341143e_indi] : ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ lab @ lba ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
% 0.19/0.48 ! [I: arrow_1092341143e_indi] :
% 0.19/0.48 ( ( ( ( ord_less_nat @ ( h @ I ) @ n )
% 0.19/0.52 => ( member545531028le_alt @ ( produc990411159le_alt @ e @ d ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e ) ) )
% 0.19/0.52 & ( ~ ( ord_less_nat @ ( h @ I ) @ n )
% 0.19/0.52 => ( ( ( ( h @ I )
% 0.19/0.52 = n )
% 0.19/0.52 => ( member545531028le_alt @ ( produc990411159le_alt @ e @ d ) @ ( arrow_452340254_above @ ( p @ I ) @ c @ e ) ) )
% 0.19/0.52 & ( ( ( h @ I )
% 0.19/0.52 != n )
% 0.19/0.52 => ( member545531028le_alt @ ( produc990411159le_alt @ e @ d ) @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) )
% 0.19/0.52 <=> ( ( ( ord_less_nat @ ( h @ I ) @ n )
% 0.19/0.52 => ( member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lab ) )
% 0.19/0.52 & ( ~ ( ord_less_nat @ ( h @ I ) @ n )
% 0.19/0.52 => ( member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lba ) ) ) ) ).
% 0.19/0.52
% 0.19/0.52 thf(fact_193__096a_A_126_061_Ab_096,axiom,
% 0.19/0.52 a != b ).
% 0.19/0.52
% 0.19/0.52 thf(fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
% 0.19/0.52 member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lba ).
% 0.19/0.52
% 0.19/0.52 thf(fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
% 0.19/0.52 member545531028le_alt @ ( produc990411159le_alt @ a @ b ) @ lab ).
% 0.19/0.52
% 0.19/0.52 thf(fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
% 0.19/0.52 ~ ( member545531028le_alt @ ( produc990411159le_alt @ a @ b ) @ lba ) ).
% 0.19/0.52
% 0.19/0.52 thf(fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
% 0.19/0.52 ~ ( member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lab ) ).
% 0.19/0.52
% 0.19/0.52 %----Helper facts (3)
% 0.19/0.52 thf(help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_,axiom,
% 0.19/0.52 ! [X: produc1832616231le_alt > $o,Y: produc1832616231le_alt > $o] :
% 0.19/0.52 ( ( if_Pro399136856_alt_o @ $true @ X @ Y )
% 0.19/0.52 = X ) ).
% 0.19/0.52
% 0.19/0.52 thf(help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_,axiom,
% 0.19/0.52 ! [X: produc1832616231le_alt > $o,Y: produc1832616231le_alt > $o] :
% 0.19/0.52 ( ( if_Pro399136856_alt_o @ $false @ X @ Y )
% 0.19/0.52 = Y ) ).
% 0.19/0.52
% 0.19/0.52 thf(help_If_3_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_,axiom,
% 0.19/0.52 ! [P: $o] :
% 0.19/0.52 ( ( P = $true )
% 0.19/0.52 | ( P = $false ) ) ).
% 0.19/0.52
% 0.19/0.52 %----Conjectures (1)
% 0.19/0.52 thf(conj_0,conjecture,
% 0.19/0.52 member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) ).
% 0.19/0.52
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.IGafM7YWcc/cvc5---1.0.5_16766.p...
% 0.19/0.52 (declare-sort $$unsorted 0)
% 0.19/0.52 (declare-sort tptp.arrow_1346734812le_alt 0)
% 0.19/0.52 (declare-sort tptp.arrow_1092341143e_indi 0)
% 0.19/0.52 (declare-sort tptp.nat 0)
% 0.19/0.52 (declare-sort tptp.produc1832616231le_alt 0)
% 0.19/0.52 (declare-fun tptp.all ((-> tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_1724561858le_IIA ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_1751445586le_Lin ((-> tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_1605628760e_Prof ((-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_452340254_above ((-> tptp.produc1832616231le_alt Bool) tptp.arrow_1346734812le_alt tptp.arrow_1346734812le_alt tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_1098709355ctator ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_1717184938_mkbot ((-> tptp.produc1832616231le_alt Bool) tptp.arrow_1346734812le_alt tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_1865892024_mktop ((-> tptp.produc1832616231le_alt Bool) tptp.arrow_1346734812le_alt tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.arrow_1889221221nimity ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.finite1907699781e_indi ((-> tptp.arrow_1092341143e_indi Bool)) tptp.nat)
% 0.19/0.52 (declare-fun tptp.inj_on945046484di_nat ((-> tptp.arrow_1092341143e_indi tptp.nat) (-> tptp.arrow_1092341143e_indi Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr1422400881lt_o_o ((-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool Bool) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr1941314005e_indi ((-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr1021537730_alt_o ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) (-> tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr1767527177lt_o_o ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr170420797e_indi ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Pro410810898lt_o_o ((-> (-> tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.produc1832616231le_alt Bool) Bool Bool) (-> (-> tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Pro1340600692e_indi ((-> (-> tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool) (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_o_A1302557673_alt_o ((-> Bool Bool) (-> Bool (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_o_A71242893_alt_o ((-> Bool Bool) (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> Bool tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_o_P1538584260_alt_o ((-> Bool Bool) (-> Bool (-> tptp.produc1832616231le_alt Bool) Bool) (-> Bool tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_o_P988780107le_alt ((-> Bool Bool) (-> Bool tptp.produc1832616231le_alt Bool) (-> Bool tptp.produc1832616231le_alt)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr1140519125_alt_o ((-> tptp.arrow_1092341143e_indi Bool) (-> tptp.arrow_1092341143e_indi (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr651234977_alt_o ((-> tptp.arrow_1092341143e_indi Bool) (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> tptp.arrow_1092341143e_indi tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr418143960_alt_o ((-> tptp.arrow_1092341143e_indi Bool) (-> tptp.arrow_1092341143e_indi (-> tptp.produc1832616231le_alt Bool) Bool) (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Arr1055270199le_alt ((-> tptp.arrow_1092341143e_indi Bool) (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Pro539263375_alt_o ((-> tptp.produc1832616231le_alt Bool) (-> tptp.produc1832616231le_alt Bool Bool) (-> tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.pi_Pro1535452471e_indi ((-> tptp.produc1832616231le_alt Bool) (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi Bool) (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi)) Bool)
% 0.19/0.52 (declare-fun tptp.hilber564731065di_nat ((-> tptp.arrow_1092341143e_indi Bool) (-> tptp.arrow_1092341143e_indi tptp.nat) tptp.nat) tptp.arrow_1092341143e_indi)
% 0.19/0.52 (declare-fun tptp.if_Pro399136856_alt_o (Bool (-> tptp.produc1832616231le_alt Bool) (-> tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.ord_le939309728lt_o_o ((-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.ord_le972845494lt_o_o ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.ord_le898419007lt_o_o ((-> (-> tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.ord_le316791758indi_o ((-> tptp.arrow_1092341143e_indi Bool) (-> tptp.arrow_1092341143e_indi Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.ord_le1973646398_alt_o ((-> tptp.produc1832616231le_alt Bool) (-> tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 0.19/0.52 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.19/0.52 (declare-fun tptp.top_to1049332548lt_o_o ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.top_to790289938lt_o_o ((-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.top_to1830848411lt_o_o ((-> tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.top_top_o_o (Bool) Bool)
% 0.19/0.52 (declare-fun tptp.top_to527331954indi_o (tptp.arrow_1092341143e_indi) Bool)
% 0.19/0.52 (declare-fun tptp.top_to679332578_alt_o (tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.top_top_o () Bool)
% 0.19/0.52 (declare-fun tptp.produc990411159le_alt (tptp.arrow_1346734812le_alt tptp.arrow_1346734812le_alt) tptp.produc1832616231le_alt)
% 0.19/0.52 (declare-fun tptp.collec2125720304_alt_o ((-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.collec1718651462_alt_o ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.collec1079683069_alt_o ((-> (-> tptp.produc1832616231le_alt Bool) Bool) (-> tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.collec1832628290e_indi ((-> tptp.arrow_1092341143e_indi Bool) tptp.arrow_1092341143e_indi) Bool)
% 0.19/0.52 (declare-fun tptp.collec1201320914le_alt ((-> tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.member903234717lt_o_o ((-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) (-> (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member986213183e_indi ((-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi) (-> (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member733327538_alt_o ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1754345465lt_o_o ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1208133347e_indi ((-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi) (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1949484546lt_o_o ((-> (-> tptp.produc1832616231le_alt Bool) Bool) (-> (-> (-> tptp.produc1832616231le_alt Bool) Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1255309082e_indi ((-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi) (-> (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1710515983_alt_o ((-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) (-> (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member537117565_alt_o ((-> Bool tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) (-> (-> Bool tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1099673524_alt_o ((-> Bool tptp.produc1832616231le_alt Bool) (-> (-> Bool tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1368218865le_alt ((-> Bool tptp.produc1832616231le_alt) (-> (-> Bool tptp.produc1832616231le_alt) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member24189887_alt_o ((-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) (-> (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1079651021_alt_o ((-> tptp.arrow_1092341143e_indi tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1561882372_alt_o ((-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1621875105le_alt ((-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt) (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1362619835_alt_o ((-> tptp.produc1832616231le_alt Bool) (-> (-> tptp.produc1832616231le_alt Bool) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1486844321e_indi ((-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi) (-> (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi) Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member_o (Bool (-> Bool Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member1714766084e_indi (tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.member545531028le_alt (tptp.produc1832616231le_alt (-> tptp.produc1832616231le_alt Bool)) Bool)
% 0.19/0.52 (declare-fun tptp.f ((-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.lab (tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.lba (tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.p (tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt) Bool)
% 0.19/0.52 (declare-fun tptp.a () tptp.arrow_1346734812le_alt)
% 0.19/0.52 (declare-fun tptp.b () tptp.arrow_1346734812le_alt)
% 0.19/0.52 (declare-fun tptp.c () tptp.arrow_1346734812le_alt)
% 0.19/0.52 (declare-fun tptp.d () tptp.arrow_1346734812le_alt)
% 0.19/0.52 (declare-fun tptp.e () tptp.arrow_1346734812le_alt)
% 0.19/0.52 (declare-fun tptp.h (tptp.arrow_1092341143e_indi) tptp.nat)
% 0.19/0.52 (declare-fun tptp.n () tptp.nat)
% 0.19/0.52 (assert (@ tptp.arrow_1724561858le_IIA tptp.f))
% 0.19/0.52 (assert (@ tptp.arrow_1889221221nimity tptp.f))
% 0.19/0.52 (assert (not (= tptp.c tptp.d)))
% 0.19/0.52 (assert (@ (@ tptp.member1561882372_alt_o tptp.p) tptp.arrow_1605628760e_Prof))
% 0.19/0.52 (assert (forall ((X tptp.arrow_1346734812le_alt) (Y tptp.arrow_1346734812le_alt) (L (-> tptp.produc1832616231le_alt Bool)) (Z_2 tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt X) Y)))) (let ((_let_2 (= X Z_2))) (= (@ _let_1 (@ (@ tptp.arrow_1717184938_mkbot L) Z_2)) (and (not (= Y Z_2)) (=> _let_2 (not (= X Y))) (=> (not _let_2) (@ _let_1 L))))))))
% 0.19/0.52 (assert (forall ((X tptp.arrow_1346734812le_alt) (Y tptp.arrow_1346734812le_alt) (L (-> tptp.produc1832616231le_alt Bool)) (Z_2 tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt X) Y)))) (let ((_let_2 (= Y Z_2))) (= (@ _let_1 (@ (@ tptp.arrow_1865892024_mktop L) Z_2)) (and (not (= X Z_2)) (=> _let_2 (not (= X Y))) (=> (not _let_2) (@ _let_1 L))))))))
% 0.19/0.52 (assert (forall ((P_6 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (P_5 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_26 tptp.arrow_1346734812le_alt) (B_16 tptp.arrow_1346734812le_alt) (A_25 tptp.arrow_1346734812le_alt) (B_15 tptp.arrow_1346734812le_alt)) (=> (not (= A_25 B_15)) (=> (not (= A_26 B_16)) (=> (not (= A_25 B_16)) (=> (not (= B_15 A_26)) (=> (@ (@ tptp.member1561882372_alt_o P_5) tptp.arrow_1605628760e_Prof) (=> (@ (@ tptp.member1561882372_alt_o P_6) tptp.arrow_1605628760e_Prof) (=> (forall ((I tptp.arrow_1092341143e_indi)) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ P_5 I)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_26) B_16)) (@ P_6 I)))) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ tptp.f P_5)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_26) B_16)) (@ tptp.f P_6))))))))))))
% 0.19/0.52 (assert (forall ((P_6 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (P_5 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_26 tptp.arrow_1346734812le_alt) (B_16 tptp.arrow_1346734812le_alt) (A_25 tptp.arrow_1346734812le_alt) (B_15 tptp.arrow_1346734812le_alt)) (=> (not (= A_25 B_15)) (=> (not (= A_26 B_16)) (=> (not (= A_25 B_16)) (=> (not (= B_15 A_26)) (=> (@ (@ tptp.member1561882372_alt_o P_5) tptp.arrow_1605628760e_Prof) (=> (@ (@ tptp.member1561882372_alt_o P_6) tptp.arrow_1605628760e_Prof) (=> (forall ((I tptp.arrow_1092341143e_indi)) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ P_5 I)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_26) B_16)) (@ P_6 I)))) (=> (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ tptp.f P_5)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_26) B_16)) (@ tptp.f P_6))))))))))))
% 0.19/0.52 (assert (forall ((P_6 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (P_5 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (C_4 tptp.arrow_1346734812le_alt) (A_25 tptp.arrow_1346734812le_alt) (B_15 tptp.arrow_1346734812le_alt)) (=> (not (= A_25 B_15)) (=> (not (= B_15 C_4)) (=> (not (= A_25 C_4)) (=> (@ (@ tptp.member1561882372_alt_o P_5) tptp.arrow_1605628760e_Prof) (=> (@ (@ tptp.member1561882372_alt_o P_6) tptp.arrow_1605628760e_Prof) (=> (forall ((I tptp.arrow_1092341143e_indi)) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ P_5 I)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt B_15) C_4)) (@ P_6 I)))) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ tptp.f P_5)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt B_15) C_4)) (@ tptp.f P_6)))))))))))
% 0.19/0.52 (assert (forall ((P_6 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (P_5 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_26 tptp.arrow_1346734812le_alt) (B_16 tptp.arrow_1346734812le_alt) (A_25 tptp.arrow_1346734812le_alt) (B_15 tptp.arrow_1346734812le_alt)) (=> (not (= A_25 B_15)) (=> (not (= A_26 B_16)) (=> (@ (@ tptp.member1561882372_alt_o P_5) tptp.arrow_1605628760e_Prof) (=> (@ (@ tptp.member1561882372_alt_o P_6) tptp.arrow_1605628760e_Prof) (=> (forall ((I tptp.arrow_1092341143e_indi)) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ P_5 I)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_26) B_16)) (@ P_6 I)))) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ tptp.f P_5)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_26) B_16)) (@ tptp.f P_6))))))))))
% 0.19/0.52 (assert (forall ((P_6 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (P_5 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_25 tptp.arrow_1346734812le_alt) (B_15 tptp.arrow_1346734812le_alt)) (=> (not (= A_25 B_15)) (=> (@ (@ tptp.member1561882372_alt_o P_5) tptp.arrow_1605628760e_Prof) (=> (@ (@ tptp.member1561882372_alt_o P_6) tptp.arrow_1605628760e_Prof) (=> (forall ((I tptp.arrow_1092341143e_indi)) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ P_5 I)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt B_15) A_25)) (@ P_6 I)))) (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_25) B_15)) (@ tptp.f P_5)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt B_15) A_25)) (@ tptp.f P_6)))))))))
% 0.19/0.52 (assert (forall ((I tptp.arrow_1092341143e_indi)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.c) tptp.d)))) (let ((_let_3 (@ tptp.h I))) (let ((_let_4 (= _let_3 tptp.n))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_3) tptp.n))) (= (@ _let_2 _let_1) (and (=> _let_5 (@ _let_2 (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e))) (=> (not _let_5) (and (=> _let_4 (@ _let_2 (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e))) (=> (not _let_4) (@ _let_2 (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))))))))))))))
% 0.19/0.52 (assert (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.c) tptp.d)) (@ tptp.p (@ (@ (@ tptp.hilber564731065di_nat tptp.top_to527331954indi_o) tptp.h) tptp.n))))
% 0.19/0.52 (assert (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.c) tptp.d)) (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))))))
% 0.19/0.52 (assert (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.c) tptp.d)))) (= (@ _let_1 (@ tptp.f tptp.p)) (@ _let_1 (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))))))))
% 0.19/0.52 (assert (forall ((P_4 (-> tptp.produc1832616231le_alt Bool))) (= (@ tptp.all P_4) (forall ((A_5 tptp.arrow_1346734812le_alt) (B_4 tptp.arrow_1346734812le_alt)) (@ P_4 (@ (@ tptp.produc990411159le_alt A_5) B_4))))))
% 0.19/0.52 (assert (@ (@ tptp.member1561882372_alt_o (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0))))) tptp.arrow_1605628760e_Prof))
% 0.19/0.52 (assert (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.c) tptp.e)) (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))))))
% 0.19/0.52 (assert (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.e) tptp.d)) (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))))))
% 0.19/0.52 (assert (@ (@ tptp.ord_less_nat tptp.n) (@ tptp.finite1907699781e_indi tptp.top_to527331954indi_o)))
% 0.19/0.52 (assert (@ (@ tptp.inj_on945046484di_nat tptp.h) tptp.top_to527331954indi_o))
% 0.19/0.52 (assert (forall ((A_24 tptp.arrow_1346734812le_alt) (B_14 tptp.arrow_1346734812le_alt) (A_23 tptp.arrow_1346734812le_alt) (B_13 tptp.arrow_1346734812le_alt)) (=> (= (@ (@ tptp.produc990411159le_alt A_24) B_14) (@ (@ tptp.produc990411159le_alt A_23) B_13)) (not (=> (= A_24 A_23) (not (= B_14 B_13)))))))
% 0.19/0.52 (assert (forall ((A_22 tptp.arrow_1346734812le_alt) (B_12 tptp.arrow_1346734812le_alt) (A_21 tptp.arrow_1346734812le_alt) (B_11 tptp.arrow_1346734812le_alt)) (= (= (@ (@ tptp.produc990411159le_alt A_22) B_12) (@ (@ tptp.produc990411159le_alt A_21) B_11)) (and (= A_22 A_21) (= B_12 B_11)))))
% 0.19/0.52 (assert (forall ((F (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (= (@ tptp.arrow_1724561858le_IIA F) (forall ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o X_1) tptp.arrow_1605628760e_Prof) (forall ((Xa (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o Xa) tptp.arrow_1605628760e_Prof) (forall ((A_5 tptp.arrow_1346734812le_alt) (B_4 tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)))) (=> (forall ((I tptp.arrow_1092341143e_indi)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)))) (= (@ _let_1 (@ X_1 I)) (@ _let_1 (@ Xa I))))) (= (@ _let_1 (@ F X_1)) (@ _let_1 (@ F Xa)))))))))))))
% 0.19/0.52 (assert (forall ((F (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (= (@ tptp.arrow_1889221221nimity F) (forall ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o X_1) tptp.arrow_1605628760e_Prof) (forall ((A_5 tptp.arrow_1346734812le_alt) (B_4 tptp.arrow_1346734812le_alt)) (=> (forall ((I tptp.arrow_1092341143e_indi)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)) (@ X_1 I))) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)) (@ F X_1)))))))))
% 0.19/0.52 (assert (forall ((X_34 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1830848411lt_o_o X_34)))
% 0.19/0.52 (assert (forall ((X_34 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ tptp.top_to790289938lt_o_o X_34)))
% 0.19/0.52 (assert (forall ((X_34 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1049332548lt_o_o X_34)))
% 0.19/0.52 (assert (forall ((X_34 tptp.produc1832616231le_alt)) (@ tptp.top_to679332578_alt_o X_34)))
% 0.19/0.52 (assert (forall ((X_34 tptp.arrow_1092341143e_indi)) (@ tptp.top_to527331954indi_o X_34)))
% 0.19/0.52 (assert (forall ((X_33 Bool)) (@ (@ tptp.member_o X_33) tptp.top_top_o_o)))
% 0.19/0.52 (assert (forall ((X_33 tptp.arrow_1092341143e_indi)) (@ (@ tptp.member1714766084e_indi X_33) tptp.top_to527331954indi_o)))
% 0.19/0.52 (assert (forall ((X_33 tptp.produc1832616231le_alt)) (@ (@ tptp.member545531028le_alt X_33) tptp.top_to679332578_alt_o)))
% 0.19/0.52 (assert (forall ((X_33 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1561882372_alt_o X_33) tptp.top_to790289938lt_o_o)))
% 0.19/0.52 (assert (forall ((X_33 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member733327538_alt_o X_33) tptp.top_to1049332548lt_o_o)))
% 0.19/0.52 (assert (forall ((X_33 (-> tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1362619835_alt_o X_33) tptp.top_to1830848411lt_o_o)))
% 0.19/0.52 (assert (forall ((X_32 Bool)) (@ (@ tptp.member_o X_32) tptp.top_top_o_o)))
% 0.19/0.52 (assert (forall ((X_32 tptp.arrow_1092341143e_indi)) (@ (@ tptp.member1714766084e_indi X_32) tptp.top_to527331954indi_o)))
% 0.19/0.52 (assert (forall ((X_32 tptp.produc1832616231le_alt)) (@ (@ tptp.member545531028le_alt X_32) tptp.top_to679332578_alt_o)))
% 0.19/0.52 (assert (forall ((X_32 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1561882372_alt_o X_32) tptp.top_to790289938lt_o_o)))
% 0.19/0.52 (assert (forall ((X_32 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member733327538_alt_o X_32) tptp.top_to1049332548lt_o_o)))
% 0.19/0.52 (assert (forall ((X_32 (-> tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1362619835_alt_o X_32) tptp.top_to1830848411lt_o_o)))
% 0.19/0.52 (assert (forall ((X_31 (-> tptp.produc1832616231le_alt Bool))) (= (@ tptp.top_to1830848411lt_o_o X_31) tptp.top_top_o)))
% 0.19/0.52 (assert (forall ((X_31 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (= (@ tptp.top_to790289938lt_o_o X_31) tptp.top_top_o)))
% 0.19/0.52 (assert (forall ((X_31 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (= (@ tptp.top_to1049332548lt_o_o X_31) tptp.top_top_o)))
% 0.19/0.52 (assert (forall ((X_31 tptp.produc1832616231le_alt)) (= (@ tptp.top_to679332578_alt_o X_31) tptp.top_top_o)))
% 0.19/0.52 (assert (forall ((X_31 tptp.arrow_1092341143e_indi)) (= (@ tptp.top_to527331954indi_o X_31) tptp.top_top_o)))
% 0.19/0.52 (assert (forall ((A_20 (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (not (@ (@ tptp.ord_le898419007lt_o_o tptp.top_to1830848411lt_o_o) A_20))))
% 0.19/0.52 (assert (forall ((A_20 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (not (@ (@ tptp.ord_le972845494lt_o_o tptp.top_to790289938lt_o_o) A_20))))
% 0.19/0.52 (assert (forall ((A_20 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (not (@ (@ tptp.ord_le939309728lt_o_o tptp.top_to1049332548lt_o_o) A_20))))
% 0.19/0.52 (assert (forall ((A_20 Bool)) (not (@ (@ tptp.ord_less_o tptp.top_top_o) A_20))))
% 0.19/0.52 (assert (forall ((A_20 (-> tptp.produc1832616231le_alt Bool))) (not (@ (@ tptp.ord_le1973646398_alt_o tptp.top_to679332578_alt_o) A_20))))
% 0.19/0.52 (assert (forall ((A_20 (-> tptp.arrow_1092341143e_indi Bool))) (not (@ (@ tptp.ord_le316791758indi_o tptp.top_to527331954indi_o) A_20))))
% 0.19/0.52 (assert (forall ((X_30 tptp.nat) (Y_23 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X_30) Y_23)) (=> (not (= X_30 Y_23)) (@ (@ tptp.ord_less_nat Y_23) X_30)))))
% 0.19/0.52 (assert (forall ((X_29 (-> tptp.arrow_1092341143e_indi Bool)) (Y_22 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_29) Y_22) (not (@ (@ tptp.ord_le316791758indi_o Y_22) X_29)))))
% 0.19/0.52 (assert (forall ((X_29 tptp.nat) (Y_22 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_29) Y_22) (not (@ (@ tptp.ord_less_nat Y_22) X_29)))))
% 0.19/0.52 (assert (forall ((Z_1 (-> tptp.arrow_1092341143e_indi Bool)) (Y_21 (-> tptp.arrow_1092341143e_indi Bool)) (X_28 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o Z_1))) (=> (@ (@ tptp.ord_le316791758indi_o Y_21) X_28) (=> (@ _let_1 Y_21) (@ _let_1 X_28))))))
% 0.19/0.52 (assert (forall ((Z_1 tptp.nat) (Y_21 tptp.nat) (X_28 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z_1))) (=> (@ (@ tptp.ord_less_nat Y_21) X_28) (=> (@ _let_1 Y_21) (@ _let_1 X_28))))))
% 0.19/0.52 (assert (forall ((Z (-> tptp.arrow_1092341143e_indi Bool)) (X_27 (-> tptp.arrow_1092341143e_indi Bool)) (Y_20 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o X_27))) (=> (@ _let_1 Y_20) (=> (@ (@ tptp.ord_le316791758indi_o Y_20) Z) (@ _let_1 Z))))))
% 0.19/0.52 (assert (forall ((Z tptp.nat) (X_27 tptp.nat) (Y_20 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_27))) (=> (@ _let_1 Y_20) (=> (@ (@ tptp.ord_less_nat Y_20) Z) (@ _let_1 Z))))))
% 0.19/0.52 (assert (forall ((C_3 (-> tptp.arrow_1092341143e_indi Bool)) (B_10 (-> tptp.arrow_1092341143e_indi Bool)) (A_19 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o B_10) A_19) (=> (= B_10 C_3) (@ (@ tptp.ord_le316791758indi_o C_3) A_19)))))
% 0.19/0.52 (assert (forall ((C_3 tptp.nat) (B_10 tptp.nat) (A_19 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B_10) A_19) (=> (= B_10 C_3) (@ (@ tptp.ord_less_nat C_3) A_19)))))
% 0.19/0.52 (assert (forall ((C_2 (-> tptp.arrow_1092341143e_indi Bool)) (A_18 (-> tptp.arrow_1092341143e_indi Bool)) (B_9 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o A_18))) (=> (@ _let_1 B_9) (=> (= B_9 C_2) (@ _let_1 C_2))))))
% 0.19/0.52 (assert (forall ((C_2 tptp.nat) (A_18 tptp.nat) (B_9 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A_18))) (=> (@ _let_1 B_9) (=> (= B_9 C_2) (@ _let_1 C_2))))))
% 0.19/0.52 (assert (forall ((C_1 (-> tptp.arrow_1092341143e_indi Bool)) (A_17 (-> tptp.arrow_1092341143e_indi Bool)) (B_8 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o C_1))) (=> (= A_17 B_8) (=> (@ _let_1 B_8) (@ _let_1 A_17))))))
% 0.19/0.52 (assert (forall ((C_1 tptp.nat) (A_17 tptp.nat) (B_8 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C_1))) (=> (= A_17 B_8) (=> (@ _let_1 B_8) (@ _let_1 A_17))))))
% 0.19/0.52 (assert (forall ((C (-> tptp.arrow_1092341143e_indi Bool)) (A_16 (-> tptp.arrow_1092341143e_indi Bool)) (B_7 (-> tptp.arrow_1092341143e_indi Bool))) (=> (= A_16 B_7) (=> (@ (@ tptp.ord_le316791758indi_o B_7) C) (@ (@ tptp.ord_le316791758indi_o A_16) C)))))
% 0.19/0.52 (assert (forall ((C tptp.nat) (A_16 tptp.nat) (B_7 tptp.nat)) (=> (= A_16 B_7) (=> (@ (@ tptp.ord_less_nat B_7) C) (@ (@ tptp.ord_less_nat A_16) C)))))
% 0.19/0.52 (assert (forall ((B_6 (-> tptp.arrow_1092341143e_indi Bool)) (A_15 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o B_6) A_15) (not (@ (@ tptp.ord_le316791758indi_o A_15) B_6)))))
% 0.19/0.52 (assert (forall ((B_6 tptp.nat) (A_15 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B_6) A_15) (not (@ (@ tptp.ord_less_nat A_15) B_6)))))
% 0.19/0.52 (assert (forall ((A_14 (-> tptp.arrow_1092341143e_indi Bool)) (B_5 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o A_14) B_5) (not (@ (@ tptp.ord_le316791758indi_o B_5) A_14)))))
% 0.19/0.52 (assert (forall ((A_14 tptp.nat) (B_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_14) B_5) (not (@ (@ tptp.ord_less_nat B_5) A_14)))))
% 0.19/0.52 (assert (forall ((P_3 Bool) (X_26 (-> tptp.arrow_1092341143e_indi Bool)) (Y_19 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_26) Y_19) (=> (@ (@ tptp.ord_le316791758indi_o Y_19) X_26) P_3))))
% 0.19/0.52 (assert (forall ((P_3 Bool) (X_26 tptp.nat) (Y_19 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_26) Y_19) (=> (@ (@ tptp.ord_less_nat Y_19) X_26) P_3))))
% 0.19/0.52 (assert (forall ((X_25 (-> tptp.arrow_1092341143e_indi Bool)) (Y_18 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_25) Y_18) (not (= Y_18 X_25)))))
% 0.19/0.52 (assert (forall ((X_25 tptp.nat) (Y_18 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_25) Y_18) (not (= Y_18 X_25)))))
% 0.19/0.52 (assert (forall ((X_24 (-> tptp.arrow_1092341143e_indi Bool)) (Y_17 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_24) Y_17) (not (= X_24 Y_17)))))
% 0.19/0.52 (assert (forall ((X_24 tptp.nat) (Y_17 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_24) Y_17) (not (= X_24 Y_17)))))
% 0.19/0.52 (assert (forall ((X_23 (-> tptp.arrow_1092341143e_indi Bool)) (Y_16 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_23) Y_16) (not (@ (@ tptp.ord_le316791758indi_o Y_16) X_23)))))
% 0.19/0.52 (assert (forall ((X_23 tptp.nat) (Y_16 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_23) Y_16) (not (@ (@ tptp.ord_less_nat Y_16) X_23)))))
% 0.19/0.52 (assert (forall ((X_22 (-> tptp.arrow_1092341143e_indi Bool)) (Y_15 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_22) Y_15) (not (@ (@ tptp.ord_le316791758indi_o Y_15) X_22)))))
% 0.19/0.52 (assert (forall ((X_22 tptp.nat) (Y_15 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_22) Y_15) (not (@ (@ tptp.ord_less_nat Y_15) X_22)))))
% 0.19/0.52 (assert (forall ((X_21 (-> tptp.arrow_1092341143e_indi Bool)) (Y_14 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_21) Y_14) (not (= X_21 Y_14)))))
% 0.19/0.52 (assert (forall ((X_21 tptp.nat) (Y_14 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_21) Y_14) (not (= X_21 Y_14)))))
% 0.19/0.52 (assert (forall ((X_20 tptp.nat) (Y_13 tptp.nat)) (=> (not (= X_20 Y_13)) (=> (not (@ (@ tptp.ord_less_nat X_20) Y_13)) (@ (@ tptp.ord_less_nat Y_13) X_20)))))
% 0.19/0.52 (assert (forall ((Y_12 tptp.nat) (X_19 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y_12) X_19)) (= (not (@ (@ tptp.ord_less_nat X_19) Y_12)) (= X_19 Y_12)))))
% 0.19/0.52 (assert (forall ((X_18 tptp.nat) (Y_11 tptp.nat)) (or (@ (@ tptp.ord_less_nat X_18) Y_11) (= X_18 Y_11) (@ (@ tptp.ord_less_nat Y_11) X_18))))
% 0.19/0.52 (assert (forall ((X_17 tptp.nat) (Y_10 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X_17) Y_10)) (or (@ (@ tptp.ord_less_nat Y_10) X_17) (= X_17 Y_10)))))
% 0.19/0.52 (assert (forall ((X_16 tptp.nat) (Y_9 tptp.nat)) (= (not (= X_16 Y_9)) (or (@ (@ tptp.ord_less_nat X_16) Y_9) (@ (@ tptp.ord_less_nat Y_9) X_16)))))
% 0.19/0.52 (assert (forall ((X_15 (-> tptp.arrow_1092341143e_indi Bool))) (not (@ (@ tptp.ord_le316791758indi_o X_15) X_15))))
% 0.19/0.52 (assert (forall ((X_15 tptp.nat)) (not (@ (@ tptp.ord_less_nat X_15) X_15))))
% 0.19/0.52 (assert (= tptp.top_to1830848411lt_o_o (@ tptp.collec1079683069_alt_o (lambda ((X_1 (-> tptp.produc1832616231le_alt Bool))) true))))
% 0.19/0.52 (assert (= tptp.top_to790289938lt_o_o (@ tptp.collec1718651462_alt_o (lambda ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) true))))
% 0.19/0.52 (assert (= tptp.top_to1049332548lt_o_o (@ tptp.collec2125720304_alt_o (lambda ((X_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) true))))
% 0.19/0.52 (assert (= tptp.top_to679332578_alt_o (@ tptp.collec1201320914le_alt (lambda ((X_1 tptp.produc1832616231le_alt)) true))))
% 0.19/0.52 (assert (= tptp.top_to527331954indi_o (@ tptp.collec1832628290e_indi (lambda ((X_1 tptp.arrow_1092341143e_indi)) true))))
% 0.19/0.52 (assert (forall ((S (-> tptp.produc1832616231le_alt Bool)) (R (-> tptp.produc1832616231le_alt Bool))) (= (forall ((X_1 tptp.arrow_1346734812le_alt) (Xa tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt X_1) Xa)))) (= (@ _let_1 R) (@ _let_1 S)))) (= R S))))
% 0.19/0.52 (assert (forall ((A_13 (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (= (not (= A_13 tptp.top_to1830848411lt_o_o)) (@ (@ tptp.ord_le898419007lt_o_o A_13) tptp.top_to1830848411lt_o_o))))
% 0.19/0.52 (assert (forall ((A_13 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (= (not (= A_13 tptp.top_to790289938lt_o_o)) (@ (@ tptp.ord_le972845494lt_o_o A_13) tptp.top_to790289938lt_o_o))))
% 0.19/0.52 (assert (forall ((A_13 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (= (not (= A_13 tptp.top_to1049332548lt_o_o)) (@ (@ tptp.ord_le939309728lt_o_o A_13) tptp.top_to1049332548lt_o_o))))
% 0.19/0.52 (assert (forall ((A_13 Bool)) (= (not (= A_13 tptp.top_top_o)) (@ (@ tptp.ord_less_o A_13) tptp.top_top_o))))
% 0.19/0.52 (assert (forall ((A_13 (-> tptp.produc1832616231le_alt Bool))) (= (not (= A_13 tptp.top_to679332578_alt_o)) (@ (@ tptp.ord_le1973646398_alt_o A_13) tptp.top_to679332578_alt_o))))
% 0.19/0.52 (assert (forall ((A_13 (-> tptp.arrow_1092341143e_indi Bool))) (= (not (= A_13 tptp.top_to527331954indi_o)) (@ (@ tptp.ord_le316791758indi_o A_13) tptp.top_to527331954indi_o))))
% 0.19/0.52 (assert (forall ((X_14 tptp.arrow_1092341143e_indi) (Y_8 tptp.nat) (F_15 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_15) tptp.top_to527331954indi_o) (=> (= (@ F_15 X_14) Y_8) (= (@ (@ (@ tptp.hilber564731065di_nat tptp.top_to527331954indi_o) F_15) Y_8) X_14)))))
% 0.19/0.52 (assert (forall ((X_13 tptp.arrow_1092341143e_indi) (F_14 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_14) tptp.top_to527331954indi_o) (= (@ (@ (@ tptp.hilber564731065di_nat tptp.top_to527331954indi_o) F_14) (@ F_14 X_13)) X_13))))
% 0.19/0.52 (assert (forall ((X_12 tptp.arrow_1092341143e_indi) (F_13 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_12 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_13) A_12) (=> (@ (@ tptp.member1714766084e_indi X_12) A_12) (= (@ (@ (@ tptp.hilber564731065di_nat A_12) F_13) (@ F_13 X_12)) X_12)))))
% 0.19/0.52 (assert (forall ((Y_7 tptp.nat) (X_11 tptp.arrow_1092341143e_indi) (F_12 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_11 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_12) A_11) (=> (@ (@ tptp.member1714766084e_indi X_11) A_11) (=> (= (@ F_12 X_11) Y_7) (= (@ (@ (@ tptp.hilber564731065di_nat A_11) F_12) Y_7) X_11))))))
% 0.19/0.52 (assert (forall ((X_10 tptp.arrow_1092341143e_indi) (Y_6 tptp.arrow_1092341143e_indi) (F_11 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_11) tptp.top_to527331954indi_o) (= (= (@ F_11 X_10) (@ F_11 Y_6)) (= X_10 Y_6)))))
% 0.19/0.52 (assert (forall ((F_10 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_10 (-> tptp.arrow_1092341143e_indi Bool))) (= (@ (@ tptp.inj_on945046484di_nat F_10) A_10) (forall ((X_1 tptp.arrow_1092341143e_indi)) (=> (@ (@ tptp.member1714766084e_indi X_1) A_10) (forall ((Xa tptp.arrow_1092341143e_indi)) (=> (@ (@ tptp.member1714766084e_indi Xa) A_10) (=> (= (@ F_10 X_1) (@ F_10 Xa)) (= X_1 Xa)))))))))
% 0.19/0.52 (assert (forall ((X_9 tptp.arrow_1092341143e_indi) (Y_5 tptp.arrow_1092341143e_indi) (F_9 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_9 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_9) A_9) (=> (not (= X_9 Y_5)) (=> (@ (@ tptp.member1714766084e_indi X_9) A_9) (=> (@ (@ tptp.member1714766084e_indi Y_5) A_9) (not (= (@ F_9 X_9) (@ F_9 Y_5)))))))))
% 0.19/0.52 (assert (forall ((Y_4 tptp.arrow_1092341143e_indi) (X_8 tptp.arrow_1092341143e_indi) (F_8 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_8 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_8) A_8) (=> (@ (@ tptp.member1714766084e_indi X_8) A_8) (=> (@ (@ tptp.member1714766084e_indi Y_4) A_8) (= (= (@ F_8 X_8) (@ F_8 Y_4)) (= X_8 Y_4)))))))
% 0.19/0.52 (assert (forall ((X_7 tptp.arrow_1092341143e_indi) (Y_3 tptp.arrow_1092341143e_indi) (F_7 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_7 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_7) A_7) (=> (= (@ F_7 X_7) (@ F_7 Y_3)) (=> (@ (@ tptp.member1714766084e_indi X_7) A_7) (=> (@ (@ tptp.member1714766084e_indi Y_3) A_7) (= X_7 Y_3)))))))
% 0.19/0.52 (assert (forall ((X_6 tptp.arrow_1092341143e_indi) (Y_2 tptp.arrow_1092341143e_indi) (F_6 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_6) tptp.top_to527331954indi_o) (=> (= (@ F_6 X_6) (@ F_6 Y_2)) (= X_6 Y_2)))))
% 0.19/0.52 (assert (forall ((G (-> tptp.nat tptp.arrow_1092341143e_indi)) (F_5 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_5) tptp.top_to527331954indi_o) (=> (forall ((X_1 tptp.nat)) (= (@ F_5 (@ G X_1)) X_1)) (= (@ (@ tptp.hilber564731065di_nat tptp.top_to527331954indi_o) F_5) G)))))
% 0.19/0.52 (assert (forall ((F_4 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (forall ((X_1 tptp.arrow_1092341143e_indi) (Y_1 tptp.arrow_1092341143e_indi)) (=> (= (@ F_4 X_1) (@ F_4 Y_1)) (= X_1 Y_1))) (@ (@ tptp.inj_on945046484di_nat F_4) tptp.top_to527331954indi_o))))
% 0.19/0.52 (assert (@ (@ tptp.member733327538_alt_o tptp.f) (@ (@ tptp.pi_Arr1021537730_alt_o tptp.arrow_1605628760e_Prof) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.arrow_1751445586le_Lin __flatten_var_0)))))
% 0.19/0.52 (assert (@ (@ tptp.member1362619835_alt_o tptp.lba) tptp.arrow_1751445586le_Lin))
% 0.19/0.52 (assert (@ (@ tptp.member1362619835_alt_o tptp.lab) tptp.arrow_1751445586le_Lin))
% 0.19/0.52 (assert (forall ((A_3 tptp.arrow_1346734812le_alt) (B_2 tptp.arrow_1346734812le_alt) (L (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1362619835_alt_o L) tptp.arrow_1751445586le_Lin) (=> (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_3) B_2)) L) (not (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt B_2) A_3)) L))))))
% 0.19/0.52 (assert (forall ((X tptp.arrow_1346734812le_alt) (Y tptp.arrow_1346734812le_alt) (L (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1362619835_alt_o L) tptp.arrow_1751445586le_Lin) (=> (not (= X Y)) (= (not (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt X) Y)) L)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt Y) X)) L))))))
% 0.19/0.52 (assert (forall ((X_5 tptp.arrow_1092341143e_indi) (A_6 (-> tptp.arrow_1092341143e_indi Bool))) (= (@ (@ tptp.member1714766084e_indi X_5) A_6) (@ A_6 X_5))))
% 0.19/0.52 (assert (forall ((X_5 Bool) (A_6 (-> Bool Bool))) (= (@ (@ tptp.member_o X_5) A_6) (@ A_6 X_5))))
% 0.19/0.52 (assert (forall ((X_5 tptp.produc1832616231le_alt) (A_6 (-> tptp.produc1832616231le_alt Bool))) (= (@ (@ tptp.member545531028le_alt X_5) A_6) (@ A_6 X_5))))
% 0.19/0.52 (assert (forall ((X_5 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_6 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (= (@ (@ tptp.member1561882372_alt_o X_5) A_6) (@ A_6 X_5))))
% 0.19/0.52 (assert (forall ((X_5 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_6 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (= (@ (@ tptp.member733327538_alt_o X_5) A_6) (@ A_6 X_5))))
% 0.19/0.52 (assert (forall ((X_5 (-> tptp.produc1832616231le_alt Bool)) (A_6 (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (= (@ (@ tptp.member1362619835_alt_o X_5) A_6) (@ A_6 X_5))))
% 0.19/0.52 (assert (forall ((P_2 (-> tptp.arrow_1092341143e_indi Bool))) (= (@ tptp.collec1832628290e_indi P_2) P_2)))
% 0.19/0.52 (assert (forall ((X tptp.arrow_1346734812le_alt) (L (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1362619835_alt_o L) tptp.arrow_1751445586le_Lin) (@ (@ tptp.member1362619835_alt_o (@ (@ tptp.arrow_1865892024_mktop L) X)) tptp.arrow_1751445586le_Lin))))
% 0.19/0.52 (assert (forall ((X tptp.arrow_1346734812le_alt) (L (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1362619835_alt_o L) tptp.arrow_1751445586le_Lin) (@ (@ tptp.member1362619835_alt_o (@ (@ tptp.arrow_1717184938_mkbot L) X)) tptp.arrow_1751445586le_Lin))))
% 0.19/0.52 (assert (forall ((L (-> tptp.produc1832616231le_alt Bool)) (X tptp.arrow_1346734812le_alt) (Y tptp.arrow_1346734812le_alt)) (=> (not (= X Y)) (=> (@ (@ tptp.member1362619835_alt_o L) tptp.arrow_1751445586le_Lin) (@ (@ tptp.member1362619835_alt_o (@ (@ (@ tptp.arrow_452340254_above L) X) Y)) tptp.arrow_1751445586le_Lin)))))
% 0.19/0.52 (assert (forall ((L (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1362619835_alt_o L) tptp.arrow_1751445586le_Lin) (@ (@ tptp.member1561882372_alt_o (lambda ((P_1 tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ L __flatten_var_0))) tptp.arrow_1605628760e_Prof))))
% 0.19/0.52 (assert (forall ((X tptp.arrow_1346734812le_alt) (Y tptp.arrow_1346734812le_alt) (L (-> tptp.produc1832616231le_alt Bool)) (A_3 tptp.arrow_1346734812le_alt) (B_2 tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.produc990411159le_alt X))) (let ((_let_2 (@ tptp.member545531028le_alt (@ _let_1 Y)))) (let ((_let_3 (= Y B_2))) (let ((_let_4 (= X B_2))) (=> (not (= A_3 B_2)) (=> (@ (@ tptp.member1362619835_alt_o L) tptp.arrow_1751445586le_Lin) (= (@ _let_2 (@ (@ (@ tptp.arrow_452340254_above L) A_3) B_2)) (and (not (= X Y)) (=> _let_4 (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_3) Y)) L)) (=> (not _let_4) (and (=> _let_3 (or (= X A_3) (@ (@ tptp.member545531028le_alt (@ _let_1 A_3)) L))) (=> (not _let_3) (@ _let_2 L))))))))))))))
% 0.19/0.52 (assert (forall ((I_1 tptp.arrow_1092341143e_indi) (F (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member733327538_alt_o F) (@ (@ tptp.pi_Arr1021537730_alt_o tptp.arrow_1605628760e_Prof) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.arrow_1751445586le_Lin __flatten_var_0)))) (=> (forall ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o X_1) tptp.arrow_1605628760e_Prof) (forall ((A_5 tptp.arrow_1346734812le_alt) (B_4 tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)))) (=> (not (= A_5 B_4)) (=> (@ _let_1 (@ X_1 I_1)) (@ _let_1 (@ F X_1)))))))) (@ (@ tptp.arrow_1098709355ctator F) I_1)))))
% 0.19/0.52 (assert (forall ((X_4 tptp.produc1832616231le_alt) (F_3 (-> tptp.produc1832616231le_alt Bool)) (A_4 (-> tptp.produc1832616231le_alt Bool)) (B_3 (-> tptp.produc1832616231le_alt Bool Bool))) (=> (@ (@ tptp.member1362619835_alt_o F_3) (@ (@ tptp.pi_Pro539263375_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member545531028le_alt X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 tptp.arrow_1092341143e_indi) (F_3 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt)) (A_4 (-> tptp.arrow_1092341143e_indi Bool)) (B_3 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1621875105le_alt F_3) (@ (@ tptp.pi_Arr1055270199le_alt A_4) B_3)) (=> (not (@ (@ tptp.member545531028le_alt (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1714766084e_indi X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 Bool) (F_3 (-> Bool tptp.produc1832616231le_alt)) (A_4 (-> Bool Bool)) (B_3 (-> Bool tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1368218865le_alt F_3) (@ (@ tptp.pi_o_P988780107le_alt A_4) B_3)) (=> (not (@ (@ tptp.member545531028le_alt (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 tptp.arrow_1092341143e_indi) (F_3 (-> tptp.arrow_1092341143e_indi tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_4 (-> tptp.arrow_1092341143e_indi Bool)) (B_3 (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1079651021_alt_o F_3) (@ (@ tptp.pi_Arr651234977_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member1561882372_alt_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1714766084e_indi X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 Bool) (F_3 (-> Bool tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_4 (-> Bool Bool)) (B_3 (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member537117565_alt_o F_3) (@ (@ tptp.pi_o_A71242893_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member1561882372_alt_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 tptp.arrow_1092341143e_indi) (F_3 (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_4 (-> tptp.arrow_1092341143e_indi Bool)) (B_3 (-> tptp.arrow_1092341143e_indi (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member24189887_alt_o F_3) (@ (@ tptp.pi_Arr1140519125_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member733327538_alt_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1714766084e_indi X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 Bool) (F_3 (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_4 (-> Bool Bool)) (B_3 (-> Bool (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1710515983_alt_o F_3) (@ (@ tptp.pi_o_A1302557673_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member733327538_alt_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 Bool) (F_3 (-> Bool tptp.produc1832616231le_alt Bool)) (A_4 (-> Bool Bool)) (B_3 (-> Bool (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1099673524_alt_o F_3) (@ (@ tptp.pi_o_P1538584260_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member1362619835_alt_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 tptp.produc1832616231le_alt) (F_3 (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi)) (A_4 (-> tptp.produc1832616231le_alt Bool)) (B_3 (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1486844321e_indi F_3) (@ (@ tptp.pi_Pro1535452471e_indi A_4) B_3)) (=> (not (@ (@ tptp.member1714766084e_indi (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member545531028le_alt X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_4 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1208133347e_indi F_3) (@ (@ tptp.pi_Arr170420797e_indi A_4) B_3)) (=> (not (@ (@ tptp.member1714766084e_indi (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1561882372_alt_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (A_4 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool Bool))) (=> (@ (@ tptp.member1754345465lt_o_o F_3) (@ (@ tptp.pi_Arr1767527177lt_o_o A_4) B_3)) (=> (not (@ (@ tptp.member_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1561882372_alt_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (F_3 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_4 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (B_3 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member986213183e_indi F_3) (@ (@ tptp.pi_Arr1941314005e_indi A_4) B_3)) (=> (not (@ (@ tptp.member1714766084e_indi (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member733327538_alt_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (F_3 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (A_4 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (B_3 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool Bool))) (=> (@ (@ tptp.member903234717lt_o_o F_3) (@ (@ tptp.pi_Arr1422400881lt_o_o A_4) B_3)) (=> (not (@ (@ tptp.member_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member733327538_alt_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 (-> tptp.produc1832616231le_alt Bool)) (F_3 (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_4 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B_3 (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1255309082e_indi F_3) (@ (@ tptp.pi_Pro1340600692e_indi A_4) B_3)) (=> (not (@ (@ tptp.member1714766084e_indi (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1362619835_alt_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 (-> tptp.produc1832616231le_alt Bool)) (F_3 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (A_4 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B_3 (-> (-> tptp.produc1832616231le_alt Bool) Bool Bool))) (=> (@ (@ tptp.member1949484546lt_o_o F_3) (@ (@ tptp.pi_Pro410810898lt_o_o A_4) B_3)) (=> (not (@ (@ tptp.member_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1362619835_alt_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_4 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member733327538_alt_o F_3) (@ (@ tptp.pi_Arr1021537730_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member1362619835_alt_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1561882372_alt_o X_4) A_4))))))
% 0.19/0.52 (assert (forall ((X_4 tptp.arrow_1092341143e_indi) (F_3 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_4 (-> tptp.arrow_1092341143e_indi Bool)) (B_3 (-> tptp.arrow_1092341143e_indi (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1561882372_alt_o F_3) (@ (@ tptp.pi_Arr418143960_alt_o A_4) B_3)) (=> (not (@ (@ tptp.member1362619835_alt_o (@ F_3 X_4)) (@ B_3 X_4))) (not (@ (@ tptp.member1714766084e_indi X_4) A_4))))))
% 0.19/0.52 (assert (forall ((A_3 tptp.arrow_1346734812le_alt) (B_2 tptp.arrow_1346734812le_alt)) (=> (not (= A_3 B_2)) (exists ((X_1 (-> tptp.produc1832616231le_alt Bool))) (and (@ (@ tptp.member1362619835_alt_o X_1) tptp.arrow_1751445586le_Lin) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_3) B_2)) X_1))))))
% 0.19/0.52 (assert (forall ((N tptp.nat)) (@ (@ tptp.member1561882372_alt_o (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat (@ tptp.h I)) N)) tptp.lab) tptp.lba) __flatten_var_0))) tptp.arrow_1605628760e_Prof)))
% 0.19/0.52 (assert (forall ((X_3 tptp.produc1832616231le_alt) (F_2 (-> tptp.produc1832616231le_alt Bool)) (A_2 (-> tptp.produc1832616231le_alt Bool)) (B_1 (-> tptp.produc1832616231le_alt Bool Bool))) (=> (@ (@ tptp.member1362619835_alt_o F_2) (@ (@ tptp.pi_Pro539263375_alt_o A_2) B_1)) (=> (@ (@ tptp.member545531028le_alt X_3) A_2) (@ (@ tptp.member_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 tptp.produc1832616231le_alt) (F_2 (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi)) (A_2 (-> tptp.produc1832616231le_alt Bool)) (B_1 (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1486844321e_indi F_2) (@ (@ tptp.pi_Pro1535452471e_indi A_2) B_1)) (=> (@ (@ tptp.member545531028le_alt X_3) A_2) (@ (@ tptp.member1714766084e_indi (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1208133347e_indi F_2) (@ (@ tptp.pi_Arr170420797e_indi A_2) B_1)) (=> (@ (@ tptp.member1561882372_alt_o X_3) A_2) (@ (@ tptp.member1714766084e_indi (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (A_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool Bool))) (=> (@ (@ tptp.member1754345465lt_o_o F_2) (@ (@ tptp.pi_Arr1767527177lt_o_o A_2) B_1)) (=> (@ (@ tptp.member1561882372_alt_o X_3) A_2) (@ (@ tptp.member_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (F_2 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_2 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (B_1 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member986213183e_indi F_2) (@ (@ tptp.pi_Arr1941314005e_indi A_2) B_1)) (=> (@ (@ tptp.member733327538_alt_o X_3) A_2) (@ (@ tptp.member1714766084e_indi (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (F_2 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (A_2 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (B_1 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool Bool))) (=> (@ (@ tptp.member903234717lt_o_o F_2) (@ (@ tptp.pi_Arr1422400881lt_o_o A_2) B_1)) (=> (@ (@ tptp.member733327538_alt_o X_3) A_2) (@ (@ tptp.member_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 (-> tptp.produc1832616231le_alt Bool)) (F_2 (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_2 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B_1 (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1255309082e_indi F_2) (@ (@ tptp.pi_Pro1340600692e_indi A_2) B_1)) (=> (@ (@ tptp.member1362619835_alt_o X_3) A_2) (@ (@ tptp.member1714766084e_indi (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 (-> tptp.produc1832616231le_alt Bool)) (F_2 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (A_2 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B_1 (-> (-> tptp.produc1832616231le_alt Bool) Bool Bool))) (=> (@ (@ tptp.member1949484546lt_o_o F_2) (@ (@ tptp.pi_Pro410810898lt_o_o A_2) B_1)) (=> (@ (@ tptp.member1362619835_alt_o X_3) A_2) (@ (@ tptp.member_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 tptp.arrow_1092341143e_indi) (F_2 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt)) (A_2 (-> tptp.arrow_1092341143e_indi Bool)) (B_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1621875105le_alt F_2) (@ (@ tptp.pi_Arr1055270199le_alt A_2) B_1)) (=> (@ (@ tptp.member1714766084e_indi X_3) A_2) (@ (@ tptp.member545531028le_alt (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 Bool) (F_2 (-> Bool tptp.produc1832616231le_alt)) (A_2 (-> Bool Bool)) (B_1 (-> Bool tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1368218865le_alt F_2) (@ (@ tptp.pi_o_P988780107le_alt A_2) B_1)) (=> (@ (@ tptp.member_o X_3) A_2) (@ (@ tptp.member545531028le_alt (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 tptp.arrow_1092341143e_indi) (F_2 (-> tptp.arrow_1092341143e_indi tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_2 (-> tptp.arrow_1092341143e_indi Bool)) (B_1 (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1079651021_alt_o F_2) (@ (@ tptp.pi_Arr651234977_alt_o A_2) B_1)) (=> (@ (@ tptp.member1714766084e_indi X_3) A_2) (@ (@ tptp.member1561882372_alt_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 Bool) (F_2 (-> Bool tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_2 (-> Bool Bool)) (B_1 (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member537117565_alt_o F_2) (@ (@ tptp.pi_o_A71242893_alt_o A_2) B_1)) (=> (@ (@ tptp.member_o X_3) A_2) (@ (@ tptp.member1561882372_alt_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 tptp.arrow_1092341143e_indi) (F_2 (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_2 (-> tptp.arrow_1092341143e_indi Bool)) (B_1 (-> tptp.arrow_1092341143e_indi (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member24189887_alt_o F_2) (@ (@ tptp.pi_Arr1140519125_alt_o A_2) B_1)) (=> (@ (@ tptp.member1714766084e_indi X_3) A_2) (@ (@ tptp.member733327538_alt_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 Bool) (F_2 (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_2 (-> Bool Bool)) (B_1 (-> Bool (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1710515983_alt_o F_2) (@ (@ tptp.pi_o_A1302557673_alt_o A_2) B_1)) (=> (@ (@ tptp.member_o X_3) A_2) (@ (@ tptp.member733327538_alt_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 Bool) (F_2 (-> Bool tptp.produc1832616231le_alt Bool)) (A_2 (-> Bool Bool)) (B_1 (-> Bool (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1099673524_alt_o F_2) (@ (@ tptp.pi_o_P1538584260_alt_o A_2) B_1)) (=> (@ (@ tptp.member_o X_3) A_2) (@ (@ tptp.member1362619835_alt_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member733327538_alt_o F_2) (@ (@ tptp.pi_Arr1021537730_alt_o A_2) B_1)) (=> (@ (@ tptp.member1561882372_alt_o X_3) A_2) (@ (@ tptp.member1362619835_alt_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (forall ((X_3 tptp.arrow_1092341143e_indi) (F_2 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_2 (-> tptp.arrow_1092341143e_indi Bool)) (B_1 (-> tptp.arrow_1092341143e_indi (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1561882372_alt_o F_2) (@ (@ tptp.pi_Arr418143960_alt_o A_2) B_1)) (=> (@ (@ tptp.member1714766084e_indi X_3) A_2) (@ (@ tptp.member1362619835_alt_o (@ F_2 X_3)) (@ B_1 X_3))))))
% 0.19/0.52 (assert (= tptp.arrow_1605628760e_Prof (@ (@ tptp.pi_Arr418143960_alt_o tptp.top_to527331954indi_o) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.arrow_1751445586le_Lin __flatten_var_0)))))
% 0.19/0.52 (assert (forall ((X_2 tptp.produc1832616231le_alt) (F_1 (-> tptp.produc1832616231le_alt Bool)) (A_1 (-> tptp.produc1832616231le_alt Bool)) (B (-> Bool Bool))) (=> (@ (@ tptp.member1362619835_alt_o F_1) (@ (@ tptp.pi_Pro539263375_alt_o A_1) (lambda ((Uu tptp.produc1832616231le_alt) (__flatten_var_0 Bool)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member545531028le_alt X_2) A_1) (@ (@ tptp.member_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 tptp.produc1832616231le_alt) (F_1 (-> tptp.produc1832616231le_alt tptp.arrow_1092341143e_indi)) (A_1 (-> tptp.produc1832616231le_alt Bool)) (B (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1486844321e_indi F_1) (@ (@ tptp.pi_Pro1535452471e_indi A_1) (lambda ((Uu tptp.produc1832616231le_alt) (__flatten_var_0 tptp.arrow_1092341143e_indi)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member545531028le_alt X_2) A_1) (@ (@ tptp.member1714766084e_indi (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1208133347e_indi F_1) (@ (@ tptp.pi_Arr170420797e_indi A_1) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 tptp.arrow_1092341143e_indi)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1561882372_alt_o X_2) A_1) (@ (@ tptp.member1714766084e_indi (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (A_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B (-> Bool Bool))) (=> (@ (@ tptp.member1754345465lt_o_o F_1) (@ (@ tptp.pi_Arr1767527177lt_o_o A_1) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 Bool)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1561882372_alt_o X_2) A_1) (@ (@ tptp.member_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_1 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (B (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member986213183e_indi F_1) (@ (@ tptp.pi_Arr1941314005e_indi A_1) (lambda ((Uu (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (__flatten_var_0 tptp.arrow_1092341143e_indi)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member733327538_alt_o X_2) A_1) (@ (@ tptp.member1714766084e_indi (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (A_1 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (B (-> Bool Bool))) (=> (@ (@ tptp.member903234717lt_o_o F_1) (@ (@ tptp.pi_Arr1422400881lt_o_o A_1) (lambda ((Uu (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (__flatten_var_0 Bool)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member733327538_alt_o X_2) A_1) (@ (@ tptp.member_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 (-> tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_1 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1255309082e_indi F_1) (@ (@ tptp.pi_Pro1340600692e_indi A_1) (lambda ((Uu (-> tptp.produc1832616231le_alt Bool)) (__flatten_var_0 tptp.arrow_1092341143e_indi)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1362619835_alt_o X_2) A_1) (@ (@ tptp.member1714766084e_indi (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 (-> tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (A_1 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B (-> Bool Bool))) (=> (@ (@ tptp.member1949484546lt_o_o F_1) (@ (@ tptp.pi_Pro410810898lt_o_o A_1) (lambda ((Uu (-> tptp.produc1832616231le_alt Bool)) (__flatten_var_0 Bool)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1362619835_alt_o X_2) A_1) (@ (@ tptp.member_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1621875105le_alt F_1) (@ (@ tptp.pi_Arr1055270199le_alt A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member545531028le_alt (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 Bool) (F_1 (-> Bool tptp.produc1832616231le_alt)) (A_1 (-> Bool Bool)) (B (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1368218865le_alt F_1) (@ (@ tptp.pi_o_P988780107le_alt A_1) (lambda ((Uu Bool) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member545531028le_alt (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1079651021_alt_o F_1) (@ (@ tptp.pi_Arr651234977_alt_o A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member1561882372_alt_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 Bool) (F_1 (-> Bool tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_1 (-> Bool Bool)) (B (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member537117565_alt_o F_1) (@ (@ tptp.pi_o_A71242893_alt_o A_1) (lambda ((Uu Bool) (__flatten_var_0 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member1561882372_alt_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member24189887_alt_o F_1) (@ (@ tptp.pi_Arr1140519125_alt_o A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member733327538_alt_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 Bool) (F_1 (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_1 (-> Bool Bool)) (B (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1710515983_alt_o F_1) (@ (@ tptp.pi_o_A1302557673_alt_o A_1) (lambda ((Uu Bool) (__flatten_var_0 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member733327538_alt_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 Bool) (F_1 (-> Bool tptp.produc1832616231le_alt Bool)) (A_1 (-> Bool Bool)) (B (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1099673524_alt_o F_1) (@ (@ tptp.pi_o_P1538584260_alt_o A_1) (lambda ((Uu Bool) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member1362619835_alt_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member733327538_alt_o F_1) (@ (@ tptp.pi_Arr1021537730_alt_o A_1) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1561882372_alt_o X_2) A_1) (@ (@ tptp.member1362619835_alt_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1561882372_alt_o F_1) (@ (@ tptp.pi_Arr418143960_alt_o A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member1362619835_alt_o (@ F_1 X_2)) B)))))
% 0.19/0.52 (assert (forall ((F (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (I_1 tptp.arrow_1092341143e_indi)) (= (@ (@ tptp.arrow_1098709355ctator F) I_1) (forall ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o X_1) tptp.arrow_1605628760e_Prof) (= (@ F X_1) (@ X_1 I_1)))))))
% 0.19/0.52 (assert (forall ((A (-> tptp.produc1832616231le_alt Bool))) (= (@ (@ tptp.pi_Pro539263375_alt_o A) (lambda ((Uu tptp.produc1832616231le_alt) (__flatten_var_0 Bool)) (@ tptp.top_top_o_o __flatten_var_0))) tptp.top_to1830848411lt_o_o)))
% 0.19/0.52 (assert (forall ((A (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (= (@ (@ tptp.pi_Arr1021537730_alt_o A) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1830848411lt_o_o __flatten_var_0))) tptp.top_to1049332548lt_o_o)))
% 40.88/41.43 (assert (forall ((A (-> tptp.arrow_1092341143e_indi Bool))) (= (@ (@ tptp.pi_Arr418143960_alt_o A) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1830848411lt_o_o __flatten_var_0))) tptp.top_to790289938lt_o_o)))
% 40.88/41.43 (assert (= (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.e) tptp.d)) (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))))) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.b) tptp.a)) (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat (@ tptp.h I)) tptp.n)) tptp.lab) tptp.lba) __flatten_var_0))))))
% 40.88/41.43 (assert (forall ((I tptp.arrow_1092341143e_indi)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.b) tptp.a)))) (let ((_let_2 (@ tptp.h I))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) tptp.n))) (let ((_let_4 (not _let_3))) (let ((_let_5 (@ tptp.p I))) (let ((_let_6 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.e) tptp.d)))) (let ((_let_7 (= _let_2 tptp.n))) (= (and (=> _let_3 (@ _let_6 (@ (@ tptp.arrow_1865892024_mktop _let_5) tptp.e))) (=> _let_4 (and (=> _let_7 (@ _let_6 (@ (@ (@ tptp.arrow_452340254_above _let_5) tptp.c) tptp.e))) (=> (not _let_7) (@ _let_6 (@ (@ tptp.arrow_1717184938_mkbot _let_5) tptp.e)))))) (and (=> _let_3 (@ _let_1 tptp.lab)) (=> _let_4 (@ _let_1 tptp.lba)))))))))))))
% 40.88/41.43 (assert (not (= tptp.a tptp.b)))
% 40.88/41.43 (assert (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.b) tptp.a)) tptp.lba))
% 40.88/41.43 (assert (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.a) tptp.b)) tptp.lab))
% 40.88/41.43 (assert (not (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.a) tptp.b)) tptp.lba)))
% 40.88/41.43 (assert (not (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.b) tptp.a)) tptp.lab)))
% 40.88/41.43 (assert (forall ((X (-> tptp.produc1832616231le_alt Bool)) (Y (-> tptp.produc1832616231le_alt Bool))) (= (@ (@ (@ tptp.if_Pro399136856_alt_o true) X) Y) X)))
% 40.88/41.43 (assert (forall ((X (-> tptp.produc1832616231le_alt Bool)) (Y (-> tptp.produc1832616231le_alt Bool))) (= (@ (@ (@ tptp.if_Pro399136856_alt_o false) X) Y) Y)))
% 40.88/41.43 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 40.88/41.43 (assert (not (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.c) tptp.d)) (@ tptp.f tptp.p))))
% 40.88/41.43 (set-info :filename cvc5---1.0.5_16766)
% 40.88/41.43 (check-sat-assuming ( true ))
% 40.88/41.43 ------- get file name : TPTP file name is SCT171^1
% 40.88/41.43 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16766.smt2...
% 40.88/41.43 --- Run --ho-elim --full-saturate-quant at 10...
% 40.88/41.43 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 40.88/41.43 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 40.88/41.43 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 40.88/41.43 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 40.88/41.43 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 40.88/41.43 % SZS status Theorem for SCT171^1
% 40.88/41.43 % SZS output start Proof for SCT171^1
% 40.88/41.43 (
% 40.88/41.43 (let ((_let_1 (@ tptp.f tptp.p))) (let ((_let_2 (@ tptp.produc990411159le_alt tptp.c))) (let ((_let_3 (@ _let_2 tptp.d))) (let ((_let_4 (@ tptp.member545531028le_alt _let_3))) (let ((_let_5 (@ _let_4 _let_1))) (let ((_let_6 (not _let_5))) (let ((_let_7 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.b) tptp.a)))) (let ((_let_8 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.a) tptp.b)))) (let ((_let_9 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.e) tptp.d)))) (let ((_let_10 (= _let_5 (@ _let_4 (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0))))))))) (let ((_let_11 (@ _let_4 (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))))))) (let ((_let_12 (@ tptp.p k_14))) (let ((_let_13 (@ (@ tptp.arrow_1717184938_mkbot _let_12) tptp.e))) (let ((_let_14 (@ (@ (@ tptp.arrow_452340254_above _let_12) tptp.c) tptp.e))) (let ((_let_15 (@ (@ (@ tptp.if_Pro399136856_alt_o BOOLEAN_TERM_VARIABLE_18574) _let_14) _let_13))) (let ((_let_16 (@ (@ tptp.arrow_1865892024_mktop _let_12) tptp.e))) (let ((_let_17 (tptp.if_Pro399136856_alt_o BOOLEAN_TERM_VARIABLE_18581 _let_16 _let_15 k_15))) (let ((_let_18 (lambdaF_5 k_14 k_15))) (let ((_let_19 (= _let_18 _let_17))) (let ((_let_20 (forall ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (= (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= tptp.n _let_2)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0) (lambdaF_5 I __flatten_var_0))))))) (let ((_let_21 ((forall ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (= (lambdaF_5 I __flatten_var_0) (@ (@ (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat (@ tptp.h I)) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop (@ tptp.p I)) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= tptp.n (@ tptp.h I))) (@ (@ (@ tptp.arrow_452340254_above (@ tptp.p I)) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot (@ tptp.p I)) tptp.e))) __flatten_var_0)) I) __flatten_var_0)))))) (let ((_let_22 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_21) (REWRITE :args _let_21)))) (let ((_let_23 (=>))) (let ((_let_24 (=))) (let ((_let_25 (@))) (let ((_let_26 (@ tptp.h k_14))) (let ((_let_27 (REFL :args (tptp.if_Pro399136856_alt_o)))) (let ((_let_28 (TRANS (CONG (CONG (CONG (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (@ (@ tptp.ord_less_nat _let_26) tptp.n) BOOLEAN_TERM_VARIABLE_18581))) :args _let_25) (REFL :args (_let_16)) :args _let_25) (CONG (CONG (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (= tptp.n _let_26) BOOLEAN_TERM_VARIABLE_18574))) :args _let_25) (REFL :args (_let_14)) :args _let_25) (REFL :args (_let_13)) :args _let_25) :args _let_25) (REFL :args (k_15)) :args _let_25) (THEORY_PREPROCESS :args ((= (@ (@ (@ (@ tptp.if_Pro399136856_alt_o BOOLEAN_TERM_VARIABLE_18581) _let_16) _let_15) k_15) _let_17)))))) (let ((_let_29 (_let_20))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 :args (k_14 k_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_5 I __flatten_var_0)))) :args _let_29)) (CONG (REFL :args _let_29) (CONG (REFL :args (_let_18)) _let_28 :args _let_24) :args _let_23))) _let_22 :args (_let_19 false _let_20)))) (let ((_let_31 (lambdaF_4 k_14 k_15))) (let ((_let_32 (= _let_31 _let_18))) (let ((_let_33 (= lambdaF_4 lambdaF_5))) (let ((_let_34 (not _let_32))) (let ((_let_35 (@ tptp.f lambdaF_4))) (let ((_let_36 (tptp.produc990411159le_alt tptp.c tptp.d))) (let ((_let_37 (tptp.member545531028le_alt _let_36 _let_35))) (let ((_let_38 (@ tptp.f lambdaF_5))) (let ((_let_39 (tptp.member545531028le_alt _let_36 _let_38))) (let ((_let_40 (not _let_33))) (let ((_let_41 (@ tptp.member545531028le_alt _let_36))) (let ((_let_42 (REFL :args (tptp.f)))) (let ((_let_43 (CONG (REFL :args (tptp.member545531028le_alt)) (THEORY_PREPROCESS :args ((= _let_3 _let_36))) :args _let_25))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (TRANS (CONG _let_43 (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= tptp.n _let_2)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))) lambdaF_4))) :args _let_25) :args _let_25) (THEORY_PREPROCESS :args ((= (@ _let_41 _let_35) _let_37)))))))) (let ((_let_45 (tptp.member545531028le_alt _let_36 _let_1))) (let ((_let_46 (not _let_39))) (let ((_let_47 (not))) (let ((_let_48 (TRANS 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__flatten_var_0)))))) (@ (@ tptp.ord_less_nat tptp.n) (@ tptp.finite1907699781e_indi tptp.top_to527331954indi_o)) (@ (@ tptp.inj_on945046484di_nat tptp.h) tptp.top_to527331954indi_o) (forall ((A_24 tptp.arrow_1346734812le_alt) (B_14 tptp.arrow_1346734812le_alt) (A_23 tptp.arrow_1346734812le_alt) (B_13 tptp.arrow_1346734812le_alt)) (=> (= (@ (@ tptp.produc990411159le_alt A_24) B_14) (@ (@ tptp.produc990411159le_alt A_23) B_13)) (not (=> (= A_24 A_23) (not (= B_14 B_13)))))) (forall ((A_22 tptp.arrow_1346734812le_alt) (B_12 tptp.arrow_1346734812le_alt) (A_21 tptp.arrow_1346734812le_alt) (B_11 tptp.arrow_1346734812le_alt)) (= (= (@ (@ tptp.produc990411159le_alt A_22) B_12) (@ (@ tptp.produc990411159le_alt A_21) B_11)) (and (= A_22 A_21) (= B_12 B_11)))) (forall ((F (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (= (@ tptp.arrow_1724561858le_IIA F) (forall ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o X_1) tptp.arrow_1605628760e_Prof) (forall ((Xa (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o Xa) tptp.arrow_1605628760e_Prof) (forall ((A_5 tptp.arrow_1346734812le_alt) (B_4 tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)))) (=> (forall ((I tptp.arrow_1092341143e_indi)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)))) (= (@ _let_1 (@ X_1 I)) (@ _let_1 (@ Xa I))))) (= (@ _let_1 (@ F X_1)) (@ _let_1 (@ F Xa)))))))))))) (forall ((F (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (= (@ tptp.arrow_1889221221nimity F) (forall ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o X_1) tptp.arrow_1605628760e_Prof) (forall ((A_5 tptp.arrow_1346734812le_alt) (B_4 tptp.arrow_1346734812le_alt)) (=> (forall ((I tptp.arrow_1092341143e_indi)) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)) (@ X_1 I))) (@ (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt A_5) B_4)) (@ F X_1)))))))) (forall ((X_34 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1830848411lt_o_o X_34)) (forall ((X_34 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ tptp.top_to790289938lt_o_o X_34)) (forall ((X_34 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1049332548lt_o_o X_34)) (forall ((X_34 tptp.produc1832616231le_alt)) (@ tptp.top_to679332578_alt_o X_34)) (forall ((X_34 tptp.arrow_1092341143e_indi)) (@ tptp.top_to527331954indi_o X_34)) (forall ((X_33 Bool)) (@ (@ tptp.member_o X_33) tptp.top_top_o_o)) (forall ((X_33 tptp.arrow_1092341143e_indi)) (@ (@ tptp.member1714766084e_indi X_33) tptp.top_to527331954indi_o)) (forall ((X_33 tptp.produc1832616231le_alt)) (@ (@ tptp.member545531028le_alt X_33) tptp.top_to679332578_alt_o)) (forall ((X_33 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1561882372_alt_o X_33) tptp.top_to790289938lt_o_o)) (forall ((X_33 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member733327538_alt_o X_33) tptp.top_to1049332548lt_o_o)) (forall ((X_33 (-> tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1362619835_alt_o X_33) tptp.top_to1830848411lt_o_o)) (forall ((X_32 Bool)) (@ (@ tptp.member_o X_32) tptp.top_top_o_o)) (forall ((X_32 tptp.arrow_1092341143e_indi)) (@ (@ tptp.member1714766084e_indi X_32) tptp.top_to527331954indi_o)) (forall ((X_32 tptp.produc1832616231le_alt)) (@ (@ tptp.member545531028le_alt X_32) tptp.top_to679332578_alt_o)) (forall ((X_32 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1561882372_alt_o X_32) tptp.top_to790289938lt_o_o)) (forall ((X_32 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member733327538_alt_o X_32) tptp.top_to1049332548lt_o_o)) (forall ((X_32 (-> tptp.produc1832616231le_alt Bool))) (@ (@ tptp.member1362619835_alt_o X_32) tptp.top_to1830848411lt_o_o)) (forall ((X_31 (-> tptp.produc1832616231le_alt Bool))) (= (@ tptp.top_to1830848411lt_o_o X_31) tptp.top_top_o)) (forall ((X_31 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (= (@ tptp.top_to790289938lt_o_o X_31) tptp.top_top_o)) (forall ((X_31 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (= (@ tptp.top_to1049332548lt_o_o X_31) tptp.top_top_o)) (forall ((X_31 tptp.produc1832616231le_alt)) (= (@ tptp.top_to679332578_alt_o X_31) tptp.top_top_o)) (forall ((X_31 tptp.arrow_1092341143e_indi)) (= (@ tptp.top_to527331954indi_o X_31) tptp.top_top_o)) (forall ((A_20 (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (not (@ (@ tptp.ord_le898419007lt_o_o tptp.top_to1830848411lt_o_o) A_20))) (forall ((A_20 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (not (@ (@ tptp.ord_le972845494lt_o_o tptp.top_to790289938lt_o_o) A_20))) (forall ((A_20 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (not (@ (@ tptp.ord_le939309728lt_o_o tptp.top_to1049332548lt_o_o) A_20))) (forall ((A_20 Bool)) (not (@ (@ tptp.ord_less_o tptp.top_top_o) A_20))) (forall ((A_20 (-> tptp.produc1832616231le_alt Bool))) (not (@ (@ tptp.ord_le1973646398_alt_o tptp.top_to679332578_alt_o) A_20))) (forall ((A_20 (-> tptp.arrow_1092341143e_indi Bool))) (not (@ (@ tptp.ord_le316791758indi_o tptp.top_to527331954indi_o) A_20))) (forall ((X_30 tptp.nat) (Y_23 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X_30) Y_23)) (=> (not (= X_30 Y_23)) (@ (@ tptp.ord_less_nat Y_23) X_30)))) (forall ((X_29 (-> tptp.arrow_1092341143e_indi Bool)) (Y_22 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_29) Y_22) (not (@ (@ tptp.ord_le316791758indi_o Y_22) X_29)))) (forall ((X_29 tptp.nat) (Y_22 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_29) Y_22) (not (@ (@ tptp.ord_less_nat Y_22) X_29)))) (forall ((Z_1 (-> tptp.arrow_1092341143e_indi Bool)) (Y_21 (-> tptp.arrow_1092341143e_indi Bool)) (X_28 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o Z_1))) (=> (@ (@ tptp.ord_le316791758indi_o Y_21) X_28) (=> (@ _let_1 Y_21) (@ _let_1 X_28))))) (forall ((Z_1 tptp.nat) (Y_21 tptp.nat) (X_28 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z_1))) (=> (@ (@ tptp.ord_less_nat Y_21) X_28) (=> (@ _let_1 Y_21) (@ _let_1 X_28))))) (forall ((Z (-> tptp.arrow_1092341143e_indi Bool)) (X_27 (-> tptp.arrow_1092341143e_indi Bool)) (Y_20 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o X_27))) (=> (@ _let_1 Y_20) (=> (@ (@ tptp.ord_le316791758indi_o Y_20) Z) (@ _let_1 Z))))) (forall ((Z tptp.nat) (X_27 tptp.nat) (Y_20 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_27))) (=> (@ _let_1 Y_20) (=> (@ (@ tptp.ord_less_nat Y_20) Z) (@ _let_1 Z))))) (forall ((C_3 (-> tptp.arrow_1092341143e_indi Bool)) (B_10 (-> tptp.arrow_1092341143e_indi Bool)) (A_19 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o B_10) A_19) (=> (= B_10 C_3) (@ (@ tptp.ord_le316791758indi_o C_3) A_19)))) (forall ((C_3 tptp.nat) (B_10 tptp.nat) (A_19 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B_10) A_19) (=> (= B_10 C_3) (@ (@ tptp.ord_less_nat C_3) A_19)))) (forall ((C_2 (-> tptp.arrow_1092341143e_indi Bool)) (A_18 (-> tptp.arrow_1092341143e_indi Bool)) (B_9 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o A_18))) (=> (@ _let_1 B_9) (=> (= B_9 C_2) (@ _let_1 C_2))))) (forall ((C_2 tptp.nat) (A_18 tptp.nat) (B_9 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A_18))) (=> (@ _let_1 B_9) (=> (= B_9 C_2) (@ _let_1 C_2))))) (forall ((C_1 (-> tptp.arrow_1092341143e_indi Bool)) (A_17 (-> tptp.arrow_1092341143e_indi Bool)) (B_8 (-> tptp.arrow_1092341143e_indi Bool))) (let ((_let_1 (@ tptp.ord_le316791758indi_o C_1))) (=> (= A_17 B_8) (=> (@ _let_1 B_8) (@ _let_1 A_17))))) (forall ((C_1 tptp.nat) (A_17 tptp.nat) (B_8 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C_1))) (=> (= A_17 B_8) (=> (@ _let_1 B_8) (@ _let_1 A_17))))) (forall ((C (-> tptp.arrow_1092341143e_indi Bool)) (A_16 (-> tptp.arrow_1092341143e_indi Bool)) (B_7 (-> tptp.arrow_1092341143e_indi Bool))) (=> (= A_16 B_7) (=> (@ (@ tptp.ord_le316791758indi_o B_7) C) (@ (@ tptp.ord_le316791758indi_o A_16) C)))) (forall ((C tptp.nat) (A_16 tptp.nat) (B_7 tptp.nat)) (=> (= A_16 B_7) (=> (@ (@ tptp.ord_less_nat B_7) C) (@ (@ tptp.ord_less_nat A_16) C)))) (forall ((B_6 (-> tptp.arrow_1092341143e_indi Bool)) (A_15 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o B_6) A_15) (not (@ (@ tptp.ord_le316791758indi_o A_15) B_6)))) (forall ((B_6 tptp.nat) (A_15 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B_6) A_15) (not (@ (@ tptp.ord_less_nat A_15) B_6)))) (forall ((A_14 (-> tptp.arrow_1092341143e_indi Bool)) (B_5 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o A_14) B_5) (not (@ (@ tptp.ord_le316791758indi_o B_5) A_14)))) (forall ((A_14 tptp.nat) (B_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_14) B_5) (not (@ (@ tptp.ord_less_nat B_5) A_14)))) (forall ((P_3 Bool) (X_26 (-> tptp.arrow_1092341143e_indi Bool)) (Y_19 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_26) Y_19) (=> (@ (@ tptp.ord_le316791758indi_o Y_19) X_26) P_3))) (forall ((P_3 Bool) (X_26 tptp.nat) (Y_19 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_26) Y_19) (=> (@ (@ tptp.ord_less_nat Y_19) X_26) P_3))) (forall ((X_25 (-> tptp.arrow_1092341143e_indi Bool)) (Y_18 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_25) Y_18) (not (= Y_18 X_25)))) (forall ((X_25 tptp.nat) (Y_18 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_25) Y_18) (not (= Y_18 X_25)))) (forall ((X_24 (-> tptp.arrow_1092341143e_indi Bool)) (Y_17 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_24) Y_17) (not (= X_24 Y_17)))) (forall ((X_24 tptp.nat) (Y_17 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_24) Y_17) (not (= X_24 Y_17)))) (forall ((X_23 (-> tptp.arrow_1092341143e_indi Bool)) (Y_16 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_23) Y_16) (not (@ (@ tptp.ord_le316791758indi_o Y_16) X_23)))) (forall ((X_23 tptp.nat) (Y_16 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_23) Y_16) (not (@ (@ tptp.ord_less_nat Y_16) X_23)))) (forall ((X_22 (-> tptp.arrow_1092341143e_indi Bool)) (Y_15 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_22) Y_15) (not (@ (@ tptp.ord_le316791758indi_o Y_15) X_22)))) (forall ((X_22 tptp.nat) (Y_15 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_22) Y_15) (not (@ (@ tptp.ord_less_nat Y_15) X_22)))) (forall ((X_21 (-> tptp.arrow_1092341143e_indi Bool)) (Y_14 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.ord_le316791758indi_o X_21) Y_14) (not (= X_21 Y_14)))) (forall ((X_21 tptp.nat) (Y_14 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_21) Y_14) (not (= X_21 Y_14)))) (forall ((X_20 tptp.nat) (Y_13 tptp.nat)) (=> (not (= X_20 Y_13)) (=> (not (@ (@ tptp.ord_less_nat X_20) Y_13)) (@ (@ tptp.ord_less_nat Y_13) X_20)))) (forall ((Y_12 tptp.nat) (X_19 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y_12) X_19)) (= (not (@ (@ tptp.ord_less_nat X_19) Y_12)) (= X_19 Y_12)))) (forall ((X_18 tptp.nat) (Y_11 tptp.nat)) (or (@ (@ tptp.ord_less_nat X_18) Y_11) (= X_18 Y_11) (@ (@ tptp.ord_less_nat Y_11) X_18))) (forall ((X_17 tptp.nat) (Y_10 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X_17) Y_10)) (or (@ (@ tptp.ord_less_nat Y_10) X_17) (= X_17 Y_10)))) (forall ((X_16 tptp.nat) (Y_9 tptp.nat)) (= (not (= X_16 Y_9)) (or (@ (@ tptp.ord_less_nat X_16) Y_9) (@ (@ tptp.ord_less_nat Y_9) X_16)))) (forall ((X_15 (-> tptp.arrow_1092341143e_indi Bool))) (not (@ (@ tptp.ord_le316791758indi_o X_15) X_15))) (forall ((X_15 tptp.nat)) (not (@ (@ tptp.ord_less_nat X_15) X_15))) (= tptp.top_to1830848411lt_o_o (@ tptp.collec1079683069_alt_o (lambda ((X_1 (-> tptp.produc1832616231le_alt Bool))) true))) (= tptp.top_to790289938lt_o_o (@ tptp.collec1718651462_alt_o (lambda ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) true))) (= tptp.top_to1049332548lt_o_o (@ tptp.collec2125720304_alt_o (lambda ((X_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) true))) (= tptp.top_to679332578_alt_o (@ tptp.collec1201320914le_alt (lambda ((X_1 tptp.produc1832616231le_alt)) true))) (= tptp.top_to527331954indi_o (@ tptp.collec1832628290e_indi (lambda ((X_1 tptp.arrow_1092341143e_indi)) true))) (forall ((S (-> tptp.produc1832616231le_alt Bool)) (R (-> tptp.produc1832616231le_alt Bool))) (= (forall ((X_1 tptp.arrow_1346734812le_alt) (Xa tptp.arrow_1346734812le_alt)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt X_1) Xa)))) (= (@ _let_1 R) (@ _let_1 S)))) (= R S))) (forall ((A_13 (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (= (not (= A_13 tptp.top_to1830848411lt_o_o)) (@ (@ tptp.ord_le898419007lt_o_o A_13) tptp.top_to1830848411lt_o_o))) (forall ((A_13 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (= (not (= A_13 tptp.top_to790289938lt_o_o)) (@ (@ tptp.ord_le972845494lt_o_o A_13) tptp.top_to790289938lt_o_o))) (forall ((A_13 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (= (not (= A_13 tptp.top_to1049332548lt_o_o)) (@ (@ tptp.ord_le939309728lt_o_o A_13) tptp.top_to1049332548lt_o_o))) (forall ((A_13 Bool)) (= (not (= A_13 tptp.top_top_o)) (@ (@ tptp.ord_less_o A_13) tptp.top_top_o))) (forall ((A_13 (-> tptp.produc1832616231le_alt Bool))) (= (not (= A_13 tptp.top_to679332578_alt_o)) (@ (@ tptp.ord_le1973646398_alt_o A_13) tptp.top_to679332578_alt_o))) (forall ((A_13 (-> tptp.arrow_1092341143e_indi Bool))) (= (not (= A_13 tptp.top_to527331954indi_o)) (@ (@ tptp.ord_le316791758indi_o A_13) tptp.top_to527331954indi_o))) (forall ((X_14 tptp.arrow_1092341143e_indi) (Y_8 tptp.nat) (F_15 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_15) tptp.top_to527331954indi_o) (=> (= (@ F_15 X_14) Y_8) (= (@ (@ (@ tptp.hilber564731065di_nat tptp.top_to527331954indi_o) F_15) Y_8) X_14)))) (forall ((X_13 tptp.arrow_1092341143e_indi) (F_14 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_14) tptp.top_to527331954indi_o) (= (@ (@ (@ tptp.hilber564731065di_nat tptp.top_to527331954indi_o) F_14) (@ F_14 X_13)) X_13))) (forall ((X_12 tptp.arrow_1092341143e_indi) (F_13 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_12 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_13) A_12) (=> (@ (@ tptp.member1714766084e_indi X_12) A_12) (= (@ (@ (@ tptp.hilber564731065di_nat A_12) F_13) (@ F_13 X_12)) X_12)))) (forall ((Y_7 tptp.nat) (X_11 tptp.arrow_1092341143e_indi) (F_12 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_11 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_12) A_11) (=> (@ (@ tptp.member1714766084e_indi X_11) A_11) (=> (= (@ F_12 X_11) Y_7) (= (@ (@ (@ tptp.hilber564731065di_nat A_11) F_12) Y_7) X_11))))) (forall ((X_10 tptp.arrow_1092341143e_indi) (Y_6 tptp.arrow_1092341143e_indi) (F_11 (-> tptp.arrow_1092341143e_indi tptp.nat))) (=> (@ (@ tptp.inj_on945046484di_nat F_11) tptp.top_to527331954indi_o) (= (= (@ F_11 X_10) (@ F_11 Y_6)) (= X_10 Y_6)))) (forall ((F_10 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_10 (-> tptp.arrow_1092341143e_indi Bool))) (= (@ (@ tptp.inj_on945046484di_nat F_10) A_10) (forall ((X_1 tptp.arrow_1092341143e_indi)) (=> (@ (@ tptp.member1714766084e_indi X_1) A_10) (forall ((Xa tptp.arrow_1092341143e_indi)) (=> (@ (@ tptp.member1714766084e_indi Xa) A_10) (=> (= (@ F_10 X_1) (@ F_10 Xa)) (= X_1 Xa)))))))) (forall ((X_9 tptp.arrow_1092341143e_indi) (Y_5 tptp.arrow_1092341143e_indi) (F_9 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_9 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_9) A_9) (=> (not (= X_9 Y_5)) (=> (@ (@ tptp.member1714766084e_indi X_9) A_9) (=> (@ (@ tptp.member1714766084e_indi Y_5) A_9) (not (= (@ F_9 X_9) (@ F_9 Y_5)))))))) (forall ((Y_4 tptp.arrow_1092341143e_indi) (X_8 tptp.arrow_1092341143e_indi) (F_8 (-> tptp.arrow_1092341143e_indi tptp.nat)) (A_8 (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.inj_on945046484di_nat F_8) A_8) (=> (@ (@ tptp.member1714766084e_indi X_8) A_8) (=> (@ (@ tptp.member1714766084e_indi Y_4) A_8) (= (= (@ F_8 X_8) (@ F_8 Y_4)) (= X_8 Y_4)))))) (forall ((X_7 tptp.arrow_1092341143e_indi) (Y_3 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Bool) Bool)) (A_1 (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool)) (B (-> Bool Bool))) (=> (@ (@ tptp.member903234717lt_o_o F_1) (@ (@ tptp.pi_Arr1422400881lt_o_o A_1) (lambda ((Uu (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (__flatten_var_0 Bool)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member733327538_alt_o X_2) A_1) (@ (@ tptp.member_o (@ F_1 X_2)) B)))) (forall ((X_2 (-> tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.produc1832616231le_alt Bool) tptp.arrow_1092341143e_indi)) (A_1 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B (-> tptp.arrow_1092341143e_indi Bool))) (=> (@ (@ tptp.member1255309082e_indi F_1) (@ (@ tptp.pi_Pro1340600692e_indi A_1) (lambda ((Uu (-> tptp.produc1832616231le_alt Bool)) (__flatten_var_0 tptp.arrow_1092341143e_indi)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1362619835_alt_o X_2) A_1) (@ (@ tptp.member1714766084e_indi (@ F_1 X_2)) B)))) (forall ((X_2 (-> tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (A_1 (-> (-> tptp.produc1832616231le_alt Bool) Bool)) (B (-> Bool Bool))) (=> (@ (@ tptp.member1949484546lt_o_o F_1) (@ (@ tptp.pi_Pro410810898lt_o_o A_1) (lambda ((Uu (-> tptp.produc1832616231le_alt Bool)) (__flatten_var_0 Bool)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1362619835_alt_o X_2) A_1) (@ (@ tptp.member_o (@ F_1 X_2)) B)))) (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1621875105le_alt F_1) (@ (@ tptp.pi_Arr1055270199le_alt A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member545531028le_alt (@ F_1 X_2)) B)))) (forall ((X_2 Bool) (F_1 (-> Bool tptp.produc1832616231le_alt)) (A_1 (-> Bool Bool)) (B (-> tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1368218865le_alt F_1) (@ (@ tptp.pi_o_P988780107le_alt A_1) (lambda ((Uu Bool) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member545531028le_alt (@ F_1 X_2)) B)))) (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1079651021_alt_o F_1) (@ (@ tptp.pi_Arr651234977_alt_o A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member1561882372_alt_o (@ F_1 X_2)) B)))) (forall ((X_2 Bool) (F_1 (-> Bool tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_1 (-> Bool Bool)) (B (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member537117565_alt_o F_1) (@ (@ tptp.pi_o_A71242893_alt_o A_1) (lambda ((Uu Bool) (__flatten_var_0 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member1561882372_alt_o (@ F_1 X_2)) B)))) (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member24189887_alt_o F_1) (@ (@ tptp.pi_Arr1140519125_alt_o A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member733327538_alt_o (@ F_1 X_2)) B)))) (forall ((X_2 Bool) (F_1 (-> Bool (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_1 (-> Bool Bool)) (B (-> (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1710515983_alt_o F_1) (@ (@ tptp.pi_o_A1302557673_alt_o A_1) (lambda ((Uu Bool) (__flatten_var_0 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member733327538_alt_o (@ F_1 X_2)) B)))) (forall ((X_2 Bool) (F_1 (-> Bool tptp.produc1832616231le_alt Bool)) (A_1 (-> Bool Bool)) (B (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1099673524_alt_o F_1) (@ (@ tptp.pi_o_P1538584260_alt_o A_1) (lambda ((Uu Bool) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member_o X_2) A_1) (@ (@ tptp.member1362619835_alt_o (@ F_1 X_2)) B)))) (forall ((X_2 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (F_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (A_1 (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool)) (B (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member733327538_alt_o F_1) (@ (@ tptp.pi_Arr1021537730_alt_o A_1) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1561882372_alt_o X_2) A_1) (@ (@ tptp.member1362619835_alt_o (@ F_1 X_2)) B)))) (forall ((X_2 tptp.arrow_1092341143e_indi) (F_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (A_1 (-> tptp.arrow_1092341143e_indi Bool)) (B (-> (-> tptp.produc1832616231le_alt Bool) Bool))) (=> (@ (@ tptp.member1561882372_alt_o F_1) (@ (@ tptp.pi_Arr418143960_alt_o A_1) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ B __flatten_var_0)))) (=> (@ (@ tptp.member1714766084e_indi X_2) A_1) (@ (@ tptp.member1362619835_alt_o (@ F_1 X_2)) B)))) (forall ((F (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) tptp.produc1832616231le_alt Bool)) (I_1 tptp.arrow_1092341143e_indi)) (= (@ (@ tptp.arrow_1098709355ctator F) I_1) (forall ((X_1 (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool))) (=> (@ (@ tptp.member1561882372_alt_o X_1) tptp.arrow_1605628760e_Prof) (= (@ F X_1) (@ X_1 I_1)))))) (forall ((A (-> tptp.produc1832616231le_alt Bool))) (= (@ (@ tptp.pi_Pro539263375_alt_o A) (lambda ((Uu tptp.produc1832616231le_alt) (__flatten_var_0 Bool)) (@ tptp.top_top_o_o __flatten_var_0))) tptp.top_to1830848411lt_o_o)) (forall ((A (-> (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool) Bool))) (= (@ (@ tptp.pi_Arr1021537730_alt_o A) (lambda ((Uu (-> tptp.arrow_1092341143e_indi tptp.produc1832616231le_alt Bool)) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1830848411lt_o_o __flatten_var_0))) tptp.top_to1049332548lt_o_o)) (forall ((A (-> tptp.arrow_1092341143e_indi Bool))) (= (@ (@ tptp.pi_Arr418143960_alt_o A) (lambda ((Uu tptp.arrow_1092341143e_indi) (__flatten_var_0 (-> tptp.produc1832616231le_alt Bool))) (@ tptp.top_to1830848411lt_o_o __flatten_var_0))) tptp.top_to790289938lt_o_o)) (= (@ _let_9 (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (let ((_let_1 (@ tptp.p I))) (let ((_let_2 (@ tptp.h I))) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat _let_2) tptp.n)) (@ (@ tptp.arrow_1865892024_mktop _let_1) tptp.e)) (@ (@ (@ tptp.if_Pro399136856_alt_o (= _let_2 tptp.n)) (@ (@ (@ tptp.arrow_452340254_above _let_1) tptp.c) tptp.e)) (@ (@ tptp.arrow_1717184938_mkbot _let_1) tptp.e))) __flatten_var_0)))))) (@ _let_7 (@ tptp.f (lambda ((I tptp.arrow_1092341143e_indi) (__flatten_var_0 tptp.produc1832616231le_alt)) (@ (@ (@ (@ tptp.if_Pro399136856_alt_o (@ (@ tptp.ord_less_nat (@ tptp.h I)) tptp.n)) tptp.lab) tptp.lba) __flatten_var_0))))) (forall ((I tptp.arrow_1092341143e_indi)) (let ((_let_1 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.b) tptp.a)))) (let ((_let_2 (@ tptp.h I))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) tptp.n))) (let ((_let_4 (not _let_3))) (let ((_let_5 (@ tptp.p I))) (let ((_let_6 (@ tptp.member545531028le_alt (@ (@ tptp.produc990411159le_alt tptp.e) tptp.d)))) (let ((_let_7 (= _let_2 tptp.n))) (= (and (=> _let_3 (@ _let_6 (@ (@ tptp.arrow_1865892024_mktop _let_5) tptp.e))) (=> _let_4 (and (=> _let_7 (@ _let_6 (@ (@ (@ tptp.arrow_452340254_above _let_5) tptp.c) tptp.e))) (=> (not _let_7) (@ _let_6 (@ (@ tptp.arrow_1717184938_mkbot _let_5) tptp.e)))))) (and (=> _let_3 (@ _let_1 tptp.lab)) (=> _let_4 (@ _let_1 tptp.lba)))))))))))) (not (= tptp.a tptp.b)) (@ _let_7 tptp.lba) (@ _let_8 tptp.lab) (not (@ _let_8 tptp.lba)) (not (@ _let_7 tptp.lab)) (forall ((X (-> tptp.produc1832616231le_alt Bool)) (Y (-> tptp.produc1832616231le_alt Bool))) (= (@ (@ (@ tptp.if_Pro399136856_alt_o true) X) Y) X)) (forall ((X (-> tptp.produc1832616231le_alt Bool)) (Y (-> tptp.produc1832616231le_alt Bool))) (= (@ (@ (@ tptp.if_Pro399136856_alt_o false) X) Y) Y)) (forall ((P Bool)) (or (= P true) (= P false))) _let_6 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 40.88/41.44 )
% 40.88/41.44 % SZS output end Proof for SCT171^1
% 40.88/41.44 % cvc5---1.0.5 exiting
% 40.88/41.44 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------