TSTP Solution File: ITP157^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP157^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 03:18:43 EDT 2023
% Result : Theorem 0.55s 1.22s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : ITP157^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.20 % Command : do_cvc5 %s %d
% 0.20/0.40 % Computer : n022.cluster.edu
% 0.20/0.40 % Model : x86_64 x86_64
% 0.20/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.40 % Memory : 8042.1875MB
% 0.20/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 10:12:10 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.26/0.60 %----Proving TH0
% 0.26/0.61 %------------------------------------------------------------------------------
% 0.26/0.61 % File : ITP157^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.61 % Domain : Interactive Theorem Proving
% 0.26/0.61 % Problem : Sledgehammer Preferences problem prob_86__6247862_1
% 0.26/0.61 % Version : Especial.
% 0.26/0.61 % English :
% 0.26/0.61
% 0.26/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.61 % Source : [Des21]
% 0.26/0.61 % Names : Preferences/prob_86__6247862_1 [Des21]
% 0.26/0.61
% 0.26/0.61 % Status : Theorem
% 0.26/0.61 % Rating : 0.23 v8.1.0, 0.27 v7.5.0
% 0.26/0.61 % Syntax : Number of formulae : 527 ( 166 unt; 171 typ; 0 def)
% 0.26/0.61 % Number of atoms : 982 ( 312 equ; 0 cnn)
% 0.26/0.61 % Maximal formula atoms : 7 ( 2 avg)
% 0.26/0.61 % Number of connectives : 3250 ( 124 ~; 4 |; 110 &;2654 @)
% 0.26/0.61 % ( 0 <=>; 358 =>; 0 <=; 0 <~>)
% 0.26/0.61 % Maximal formula depth : 15 ( 7 avg)
% 0.26/0.61 % Number of types : 31 ( 30 usr)
% 0.26/0.61 % Number of type conns : 530 ( 530 >; 0 *; 0 +; 0 <<)
% 0.26/0.61 % Number of symbols : 142 ( 141 usr; 10 con; 0-3 aty)
% 0.26/0.61 % Number of variables : 1291 ( 171 ^;1096 !; 24 ?;1291 :)
% 0.26/0.61 % SPC : TH0_THM_EQU_NAR
% 0.26/0.61
% 0.26/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:43:15.680
% 0.26/0.61 %------------------------------------------------------------------------------
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% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
% 0.26/0.61 member122808528od_a_a: produc772425383od_a_a > set_Pr1194146439od_a_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.26/0.61 member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mtf__a_J,type,
% 0.26/0.61 member1403138919_a_a_a: produc1016684094_a_a_a > set_Pr1689873822_a_a_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
% 0.26/0.61 member448091577od_a_a: produc1555800720od_a_a > set_Pr195866352od_a_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.26/0.61 member160619001od_a_a: produc1921647824od_a_a > set_Pr681306928od_a_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.26/0.61 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001tf__a,type,
% 0.26/0.61 member_a: a > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_B,type,
% 0.26/0.61 b: set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_Pr,type,
% 0.26/0.61 pr: set_Product_prod_a_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_y,type,
% 0.26/0.61 y: a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_z,type,
% 0.26/0.61 z: a ).
% 0.26/0.61
% 0.26/0.61 % Relevant facts (355)
% 0.26/0.61 thf(fact_0_assms,axiom,
% 0.26/0.61 member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ) ).
% 0.26/0.61
% 0.26/0.61 % assms
% 0.26/0.61 thf(fact_1_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: produc2010915495od_a_a,Y: produc2010915495od_a_a,B: set_Pr231806599od_a_a,Pr: set_Pr532616391od_a_a] :
% 0.26/0.61 ( ( member1361298640od_a_a @ X @ ( prefer468349667od_a_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member180906768od_a_a @ ( produc539587415od_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_2_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: produc772425383od_a_a,Y: produc772425383od_a_a,B: set_Pr1194146439od_a_a,Pr: set_Pr2081559751od_a_a] :
% 0.26/0.61 ( ( member122808528od_a_a @ X @ ( prefer1377343203od_a_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member547056400od_a_a @ ( produc852390743od_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_3_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: produc1016684094_a_a_a,Y: produc1016684094_a_a_a,B: set_Pr1689873822_a_a_a,Pr: set_Pr729215751_a_a_a] :
% 0.26/0.61 ( ( member1403138919_a_a_a @ X @ ( prefer1944486522_a_a_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member470802768_a_a_a @ ( produc2054708503_a_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_4_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: produc1555800720od_a_a,Y: produc1555800720od_a_a,B: set_Pr195866352od_a_a,Pr: set_Pr660101255od_a_a] :
% 0.26/0.61 ( ( member448091577od_a_a @ X @ ( prefer445484748od_a_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member1424209616od_a_a @ ( produc1573596055od_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_5_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: produc1921647824od_a_a,Y: produc1921647824od_a_a,B: set_Pr681306928od_a_a,Pr: set_Pr231806599od_a_a] :
% 0.26/0.61 ( ( member160619001od_a_a @ X @ ( prefer701966604od_a_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member1361298640od_a_a @ ( produc563767703od_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_6_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,Y: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,Pr: set_Pr1295299783od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X @ ( prefer55414563od_a_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_7_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,Y: product_prod_a_a,B: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X @ ( prefer477097315od_a_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_8_at__lst__asgd__ge,axiom,
% 0.26/0.61 ! [X: a,Y: a,B: set_a,Pr: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member_a @ X @ ( prefer161218362good_a @ Y @ B @ Pr ) )
% 0.26/0.61 => ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Pr ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_lst_asgd_ge
% 0.26/0.61 thf(fact_9_prod_Oinject,axiom,
% 0.26/0.61 ! [X1: produc1921647824od_a_a,X2: produc1921647824od_a_a,Y1: produc1921647824od_a_a,Y2: produc1921647824od_a_a] :
% 0.26/0.61 ( ( ( produc563767703od_a_a @ X1 @ X2 )
% 0.26/0.61 = ( produc563767703od_a_a @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X2 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.inject
% 0.26/0.61 thf(fact_10_prod_Oinject,axiom,
% 0.26/0.61 ! [X1: product_prod_a_a,X2: produc1572603623od_a_a,Y1: product_prod_a_a,Y2: produc1572603623od_a_a] :
% 0.26/0.61 ( ( ( produc1555606807od_a_a @ X1 @ X2 )
% 0.26/0.61 = ( produc1555606807od_a_a @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X2 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.inject
% 0.26/0.61 thf(fact_11_prod_Oinject,axiom,
% 0.26/0.61 ! [X1: product_prod_a_a,X2: a,Y1: product_prod_a_a,Y2: a] :
% 0.26/0.61 ( ( ( produc2061588782_a_a_a @ X1 @ X2 )
% 0.26/0.61 = ( produc2061588782_a_a_a @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X2 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.inject
% 0.26/0.61 thf(fact_12_prod_Oinject,axiom,
% 0.26/0.61 ! [X1: a,X2: produc1572603623od_a_a,Y1: a,Y2: produc1572603623od_a_a] :
% 0.26/0.61 ( ( ( produc1095491584od_a_a @ X1 @ X2 )
% 0.26/0.61 = ( produc1095491584od_a_a @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X2 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.inject
% 0.26/0.61 thf(fact_13_prod_Oinject,axiom,
% 0.26/0.61 ! [X1: a,X2: product_prod_a_a,Y1: a,Y2: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc1299253312od_a_a @ X1 @ X2 )
% 0.26/0.61 = ( produc1299253312od_a_a @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X2 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.inject
% 0.26/0.61 thf(fact_14_prod_Oinject,axiom,
% 0.26/0.61 ! [X1: product_prod_a_a,X2: product_prod_a_a,Y1: product_prod_a_a,Y2: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc1474507607od_a_a @ X1 @ X2 )
% 0.26/0.61 = ( produc1474507607od_a_a @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X2 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.inject
% 0.26/0.61 thf(fact_15_prod_Oinject,axiom,
% 0.26/0.61 ! [X1: a,X2: a,Y1: a,Y2: a] :
% 0.26/0.61 ( ( ( product_Pair_a_a @ X1 @ X2 )
% 0.26/0.61 = ( product_Pair_a_a @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X2 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.inject
% 0.26/0.61 thf(fact_16_old_Oprod_Oinject,axiom,
% 0.26/0.61 ! [A: produc1921647824od_a_a,B2: produc1921647824od_a_a,A2: produc1921647824od_a_a,B3: produc1921647824od_a_a] :
% 0.26/0.61 ( ( ( produc563767703od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc563767703od_a_a @ A2 @ B3 ) )
% 0.26/0.61 = ( ( A = A2 )
% 0.26/0.61 & ( B2 = B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inject
% 0.26/0.61 thf(fact_17_old_Oprod_Oinject,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: produc1572603623od_a_a,A2: product_prod_a_a,B3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( ( produc1555606807od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1555606807od_a_a @ A2 @ B3 ) )
% 0.26/0.61 = ( ( A = A2 )
% 0.26/0.61 & ( B2 = B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inject
% 0.26/0.61 thf(fact_18_old_Oprod_Oinject,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: a,A2: product_prod_a_a,B3: a] :
% 0.26/0.61 ( ( ( produc2061588782_a_a_a @ A @ B2 )
% 0.26/0.61 = ( produc2061588782_a_a_a @ A2 @ B3 ) )
% 0.26/0.61 = ( ( A = A2 )
% 0.26/0.61 & ( B2 = B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inject
% 0.26/0.61 thf(fact_19_old_Oprod_Oinject,axiom,
% 0.26/0.61 ! [A: a,B2: produc1572603623od_a_a,A2: a,B3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( ( produc1095491584od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1095491584od_a_a @ A2 @ B3 ) )
% 0.26/0.61 = ( ( A = A2 )
% 0.26/0.61 & ( B2 = B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inject
% 0.26/0.61 thf(fact_20_old_Oprod_Oinject,axiom,
% 0.26/0.61 ! [A: a,B2: product_prod_a_a,A2: a,B3: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc1299253312od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1299253312od_a_a @ A2 @ B3 ) )
% 0.26/0.61 = ( ( A = A2 )
% 0.26/0.61 & ( B2 = B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inject
% 0.26/0.61 thf(fact_21_old_Oprod_Oinject,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: product_prod_a_a,A2: product_prod_a_a,B3: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc1474507607od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1474507607od_a_a @ A2 @ B3 ) )
% 0.26/0.61 = ( ( A = A2 )
% 0.26/0.61 & ( B2 = B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inject
% 0.26/0.61 thf(fact_22_old_Oprod_Oinject,axiom,
% 0.26/0.61 ! [A: a,B2: a,A2: a,B3: a] :
% 0.26/0.61 ( ( ( product_Pair_a_a @ A @ B2 )
% 0.26/0.61 = ( product_Pair_a_a @ A2 @ B3 ) )
% 0.26/0.61 = ( ( A = A2 )
% 0.26/0.61 & ( B2 = B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inject
% 0.26/0.61 thf(fact_23_surj__pair,axiom,
% 0.26/0.61 ! [P: produc2010915495od_a_a] :
% 0.26/0.61 ? [X3: produc1921647824od_a_a,Y3: produc1921647824od_a_a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc563767703od_a_a @ X3 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % surj_pair
% 0.26/0.61 thf(fact_24_surj__pair,axiom,
% 0.26/0.61 ! [P: produc772425383od_a_a] :
% 0.26/0.61 ? [X3: product_prod_a_a,Y3: produc1572603623od_a_a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc1555606807od_a_a @ X3 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % surj_pair
% 0.26/0.61 thf(fact_25_surj__pair,axiom,
% 0.26/0.61 ! [P: produc1016684094_a_a_a] :
% 0.26/0.61 ? [X3: product_prod_a_a,Y3: a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc2061588782_a_a_a @ X3 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % surj_pair
% 0.26/0.61 thf(fact_26_surj__pair,axiom,
% 0.26/0.61 ! [P: produc1555800720od_a_a] :
% 0.26/0.61 ? [X3: a,Y3: produc1572603623od_a_a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc1095491584od_a_a @ X3 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % surj_pair
% 0.26/0.61 thf(fact_27_surj__pair,axiom,
% 0.26/0.61 ! [P: produc1921647824od_a_a] :
% 0.26/0.61 ? [X3: a,Y3: product_prod_a_a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc1299253312od_a_a @ X3 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % surj_pair
% 0.26/0.61 thf(fact_28_surj__pair,axiom,
% 0.26/0.61 ! [P: produc1572603623od_a_a] :
% 0.26/0.61 ? [X3: product_prod_a_a,Y3: product_prod_a_a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc1474507607od_a_a @ X3 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % surj_pair
% 0.26/0.61 thf(fact_29_surj__pair,axiom,
% 0.26/0.61 ! [P: product_prod_a_a] :
% 0.26/0.61 ? [X3: a,Y3: a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( product_Pair_a_a @ X3 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % surj_pair
% 0.26/0.61 thf(fact_30_prod__cases,axiom,
% 0.26/0.61 ! [P2: produc2010915495od_a_a > $o,P: produc2010915495od_a_a] :
% 0.26/0.61 ( ! [A3: produc1921647824od_a_a,B4: produc1921647824od_a_a] : ( P2 @ ( produc563767703od_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ P ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases
% 0.26/0.61 thf(fact_31_prod__cases,axiom,
% 0.26/0.61 ! [P2: produc772425383od_a_a > $o,P: produc772425383od_a_a] :
% 0.26/0.61 ( ! [A3: product_prod_a_a,B4: produc1572603623od_a_a] : ( P2 @ ( produc1555606807od_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ P ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases
% 0.26/0.61 thf(fact_32_prod__cases,axiom,
% 0.26/0.61 ! [P2: produc1016684094_a_a_a > $o,P: produc1016684094_a_a_a] :
% 0.26/0.61 ( ! [A3: product_prod_a_a,B4: a] : ( P2 @ ( produc2061588782_a_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ P ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases
% 0.26/0.61 thf(fact_33_prod__cases,axiom,
% 0.26/0.61 ! [P2: produc1555800720od_a_a > $o,P: produc1555800720od_a_a] :
% 0.26/0.61 ( ! [A3: a,B4: produc1572603623od_a_a] : ( P2 @ ( produc1095491584od_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ P ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases
% 0.26/0.61 thf(fact_34_prod__cases,axiom,
% 0.26/0.61 ! [P2: produc1921647824od_a_a > $o,P: produc1921647824od_a_a] :
% 0.26/0.61 ( ! [A3: a,B4: product_prod_a_a] : ( P2 @ ( produc1299253312od_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ P ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases
% 0.26/0.61 thf(fact_35_prod__cases,axiom,
% 0.26/0.61 ! [P2: produc1572603623od_a_a > $o,P: produc1572603623od_a_a] :
% 0.26/0.61 ( ! [A3: product_prod_a_a,B4: product_prod_a_a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ P ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases
% 0.26/0.61 thf(fact_36_prod__cases,axiom,
% 0.26/0.61 ! [P2: product_prod_a_a > $o,P: product_prod_a_a] :
% 0.26/0.61 ( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ P ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases
% 0.26/0.61 thf(fact_37_Pair__inject,axiom,
% 0.26/0.61 ! [A: produc1921647824od_a_a,B2: produc1921647824od_a_a,A2: produc1921647824od_a_a,B3: produc1921647824od_a_a] :
% 0.26/0.61 ( ( ( produc563767703od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc563767703od_a_a @ A2 @ B3 ) )
% 0.26/0.61 => ~ ( ( A = A2 )
% 0.26/0.61 => ( B2 != B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Pair_inject
% 0.26/0.61 thf(fact_38_Pair__inject,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: produc1572603623od_a_a,A2: product_prod_a_a,B3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( ( produc1555606807od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1555606807od_a_a @ A2 @ B3 ) )
% 0.26/0.61 => ~ ( ( A = A2 )
% 0.26/0.61 => ( B2 != B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Pair_inject
% 0.26/0.61 thf(fact_39_Pair__inject,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: a,A2: product_prod_a_a,B3: a] :
% 0.26/0.61 ( ( ( produc2061588782_a_a_a @ A @ B2 )
% 0.26/0.61 = ( produc2061588782_a_a_a @ A2 @ B3 ) )
% 0.26/0.61 => ~ ( ( A = A2 )
% 0.26/0.61 => ( B2 != B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Pair_inject
% 0.26/0.61 thf(fact_40_Pair__inject,axiom,
% 0.26/0.61 ! [A: a,B2: produc1572603623od_a_a,A2: a,B3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( ( produc1095491584od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1095491584od_a_a @ A2 @ B3 ) )
% 0.26/0.61 => ~ ( ( A = A2 )
% 0.26/0.61 => ( B2 != B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Pair_inject
% 0.26/0.61 thf(fact_41_Pair__inject,axiom,
% 0.26/0.61 ! [A: a,B2: product_prod_a_a,A2: a,B3: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc1299253312od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1299253312od_a_a @ A2 @ B3 ) )
% 0.26/0.61 => ~ ( ( A = A2 )
% 0.26/0.61 => ( B2 != B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Pair_inject
% 0.26/0.61 thf(fact_42_Pair__inject,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: product_prod_a_a,A2: product_prod_a_a,B3: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc1474507607od_a_a @ A @ B2 )
% 0.26/0.61 = ( produc1474507607od_a_a @ A2 @ B3 ) )
% 0.26/0.61 => ~ ( ( A = A2 )
% 0.26/0.61 => ( B2 != B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Pair_inject
% 0.26/0.61 thf(fact_43_Pair__inject,axiom,
% 0.26/0.61 ! [A: a,B2: a,A2: a,B3: a] :
% 0.26/0.61 ( ( ( product_Pair_a_a @ A @ B2 )
% 0.26/0.61 = ( product_Pair_a_a @ A2 @ B3 ) )
% 0.26/0.61 => ~ ( ( A = A2 )
% 0.26/0.61 => ( B2 != B3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Pair_inject
% 0.26/0.61 thf(fact_44_prod__cases3,axiom,
% 0.26/0.61 ! [Y: produc772425383od_a_a] :
% 0.26/0.61 ~ ! [A3: product_prod_a_a,B4: product_prod_a_a,C: product_prod_a_a] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( produc1555606807od_a_a @ A3 @ ( produc1474507607od_a_a @ B4 @ C ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases3
% 0.26/0.61 thf(fact_45_prod__cases3,axiom,
% 0.26/0.61 ! [Y: produc1555800720od_a_a] :
% 0.26/0.61 ~ ! [A3: a,B4: product_prod_a_a,C: product_prod_a_a] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( produc1095491584od_a_a @ A3 @ ( produc1474507607od_a_a @ B4 @ C ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases3
% 0.26/0.61 thf(fact_46_prod__cases3,axiom,
% 0.26/0.61 ! [Y: produc1921647824od_a_a] :
% 0.26/0.61 ~ ! [A3: a,B4: a,C: a] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( produc1299253312od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases3
% 0.26/0.61 thf(fact_47_prod__cases3,axiom,
% 0.26/0.61 ! [Y: produc1572603623od_a_a] :
% 0.26/0.61 ~ ! [A3: product_prod_a_a,B4: a,C: a] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_cases3
% 0.26/0.61 thf(fact_48_prod__induct3,axiom,
% 0.26/0.61 ! [P2: produc1572603623od_a_a > $o,X: produc1572603623od_a_a] :
% 0.26/0.61 ( ! [A3: product_prod_a_a,B4: a,C: a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) )
% 0.26/0.61 => ( P2 @ X ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_induct3
% 0.26/0.61 thf(fact_49_old_Oprod_Oinducts,axiom,
% 0.26/0.61 ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
% 0.26/0.61 ( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ Prod ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inducts
% 0.26/0.61 thf(fact_50_old_Oprod_Oinducts,axiom,
% 0.26/0.61 ! [P2: produc1572603623od_a_a > $o,Prod: produc1572603623od_a_a] :
% 0.26/0.61 ( ! [A3: product_prod_a_a,B4: product_prod_a_a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ B4 ) )
% 0.26/0.61 => ( P2 @ Prod ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.inducts
% 0.26/0.61 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 0.26/0.61 ! [Y: product_prod_a_a] :
% 0.26/0.61 ~ ! [A3: a,B4: a] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( product_Pair_a_a @ A3 @ B4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.exhaust
% 0.26/0.61 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 0.26/0.61 ! [Y: produc1572603623od_a_a] :
% 0.26/0.61 ~ ! [A3: product_prod_a_a,B4: product_prod_a_a] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( produc1474507607od_a_a @ A3 @ B4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.prod.exhaust
% 0.26/0.61 thf(fact_53_at__least__as__good__def,axiom,
% 0.26/0.61 ( prefer55414563od_a_a
% 0.26/0.61 = ( ^ [X4: produc1572603623od_a_a,B5: set_Pr1948701895od_a_a,P3: set_Pr1295299783od_a_a] :
% 0.26/0.61 ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [Y4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ Y4 @ B5 )
% 0.26/0.61 & ( member1899387664od_a_a @ ( produc1935643479od_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_least_as_good_def
% 0.26/0.61 thf(fact_54_at__least__as__good__def,axiom,
% 0.26/0.61 ( prefer161218362good_a
% 0.26/0.61 = ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
% 0.26/0.61 ( collect_a
% 0.26/0.61 @ ^ [Y4: a] :
% 0.26/0.61 ( ( member_a @ Y4 @ B5 )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_least_as_good_def
% 0.26/0.61 thf(fact_55_at__least__as__good__def,axiom,
% 0.26/0.61 ( prefer477097315od_a_a
% 0.26/0.61 = ( ^ [X4: product_prod_a_a,B5: set_Product_prod_a_a,P3: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( collec645855634od_a_a
% 0.26/0.61 @ ^ [Y4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ Y4 @ B5 )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % at_least_as_good_def
% 0.26/0.61 thf(fact_56_ssubst__Pair__rhs,axiom,
% 0.26/0.61 ! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
% 0.26/0.61 => ( ( S2 = S )
% 0.26/0.61 => ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ssubst_Pair_rhs
% 0.26/0.61 thf(fact_57_ssubst__Pair__rhs,axiom,
% 0.26/0.61 ! [R: product_prod_a_a,S: product_prod_a_a,R2: set_Pr1948701895od_a_a,S2: product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ R @ S ) @ R2 )
% 0.26/0.61 => ( ( S2 = S )
% 0.26/0.61 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ssubst_Pair_rhs
% 0.26/0.61 thf(fact_58_curryI,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > $o,A: a,B2: a] :
% 0.26/0.61 ( ( F @ ( product_Pair_a_a @ A @ B2 ) )
% 0.26/0.61 => ( product_curry_a_a_o @ F @ A @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % curryI
% 0.26/0.61 thf(fact_59_curryI,axiom,
% 0.26/0.61 ! [F: produc1572603623od_a_a > $o,A: product_prod_a_a,B2: product_prod_a_a] :
% 0.26/0.61 ( ( F @ ( produc1474507607od_a_a @ A @ B2 ) )
% 0.26/0.61 => ( produc94438221_a_a_o @ F @ A @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % curryI
% 0.26/0.61 thf(fact_60_preference_Oindiff__trans,axiom,
% 0.26/0.61 ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a,Z: a] :
% 0.26/0.61 ( ( prefer1292084992ence_a @ Carrier @ Relation )
% 0.26/0.61 => ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) )
% 0.26/0.61 => ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ Relation )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ Relation ) )
% 0.26/0.61 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ Relation )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ Relation ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.indiff_trans
% 0.26/0.61 thf(fact_61_preference_Oindiff__trans,axiom,
% 0.26/0.61 ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a,Z: product_prod_a_a] :
% 0.26/0.61 ( ( prefer1338892073od_a_a @ Carrier @ Relation )
% 0.26/0.61 => ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Relation ) )
% 0.26/0.61 => ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ Z ) @ Relation )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Z @ Y ) @ Relation ) )
% 0.26/0.61 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Z ) @ Relation )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Z @ X ) @ Relation ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.indiff_trans
% 0.26/0.61 thf(fact_62_preference_Onot__outside,axiom,
% 0.26/0.61 ! [Carrier: set_Pr1948701895od_a_a,Relation: set_Pr1295299783od_a_a,X: produc1572603623od_a_a,Y: produc1572603623od_a_a] :
% 0.26/0.61 ( ( prefer1409946857od_a_a @ Carrier @ Relation )
% 0.26/0.61 => ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X @ Y ) @ Relation )
% 0.26/0.61 => ( member2057358096od_a_a @ X @ Carrier ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.not_outside
% 0.26/0.61 thf(fact_63_preference_Onot__outside,axiom,
% 0.26/0.61 ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
% 0.26/0.61 ( ( prefer1292084992ence_a @ Carrier @ Relation )
% 0.26/0.61 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
% 0.26/0.61 => ( member_a @ X @ Carrier ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.not_outside
% 0.26/0.61 thf(fact_64_preference_Onot__outside,axiom,
% 0.26/0.61 ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
% 0.26/0.61 ( ( prefer1338892073od_a_a @ Carrier @ Relation )
% 0.26/0.61 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
% 0.26/0.61 => ( member449909584od_a_a @ X @ Carrier ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.not_outside
% 0.26/0.61 thf(fact_65_swap__simp,axiom,
% 0.26/0.61 ! [X: a,Y: a] :
% 0.26/0.61 ( ( product_swap_a_a @ ( product_Pair_a_a @ X @ Y ) )
% 0.26/0.61 = ( product_Pair_a_a @ Y @ X ) ) ).
% 0.26/0.61
% 0.26/0.61 % swap_simp
% 0.26/0.61 thf(fact_66_swap__simp,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,Y: product_prod_a_a] :
% 0.26/0.61 ( ( produc1641853175od_a_a @ ( produc1474507607od_a_a @ X @ Y ) )
% 0.26/0.61 = ( produc1474507607od_a_a @ Y @ X ) ) ).
% 0.26/0.61
% 0.26/0.61 % swap_simp
% 0.26/0.61 thf(fact_67_curryD,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > $o,A: a,B2: a] :
% 0.26/0.61 ( ( product_curry_a_a_o @ F @ A @ B2 )
% 0.26/0.61 => ( F @ ( product_Pair_a_a @ A @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % curryD
% 0.26/0.61 thf(fact_68_curryD,axiom,
% 0.26/0.61 ! [F: produc1572603623od_a_a > $o,A: product_prod_a_a,B2: product_prod_a_a] :
% 0.26/0.61 ( ( produc94438221_a_a_o @ F @ A @ B2 )
% 0.26/0.61 => ( F @ ( produc1474507607od_a_a @ A @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % curryD
% 0.26/0.61 thf(fact_69_curryE,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > $o,A: a,B2: a] :
% 0.26/0.61 ( ( product_curry_a_a_o @ F @ A @ B2 )
% 0.26/0.61 => ( F @ ( product_Pair_a_a @ A @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % curryE
% 0.26/0.61 thf(fact_70_curryE,axiom,
% 0.26/0.61 ! [F: produc1572603623od_a_a > $o,A: product_prod_a_a,B2: product_prod_a_a] :
% 0.26/0.61 ( ( produc94438221_a_a_o @ F @ A @ B2 )
% 0.26/0.61 => ( F @ ( produc1474507607od_a_a @ A @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % curryE
% 0.26/0.61 thf(fact_71_no__better__than__def,axiom,
% 0.26/0.61 ( prefer926864306od_a_a
% 0.26/0.61 = ( ^ [X4: produc1572603623od_a_a,B5: set_Pr1948701895od_a_a,P3: set_Pr1295299783od_a_a] :
% 0.26/0.61 ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [Y4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ Y4 @ B5 )
% 0.26/0.61 & ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X4 @ Y4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % no_better_than_def
% 0.26/0.61 thf(fact_72_no__better__than__def,axiom,
% 0.26/0.61 ( prefer1676310729than_a
% 0.26/0.61 = ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
% 0.26/0.61 ( collect_a
% 0.26/0.61 @ ^ [Y4: a] :
% 0.26/0.61 ( ( member_a @ Y4 @ B5 )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % no_better_than_def
% 0.26/0.61 thf(fact_73_no__better__than__def,axiom,
% 0.26/0.61 ( prefer1498087410od_a_a
% 0.26/0.61 = ( ^ [X4: product_prod_a_a,B5: set_Product_prod_a_a,P3: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( collec645855634od_a_a
% 0.26/0.61 @ ^ [Y4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ Y4 @ B5 )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % no_better_than_def
% 0.26/0.61 thf(fact_74_as__good__as__def,axiom,
% 0.26/0.61 ( prefer1867335523od_a_a
% 0.26/0.61 = ( ^ [X4: produc1572603623od_a_a,B5: set_Pr1948701895od_a_a,P3: set_Pr1295299783od_a_a] :
% 0.26/0.61 ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [Y4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ Y4 @ B5 )
% 0.26/0.61 & ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X4 @ Y4 ) @ P3 )
% 0.26/0.61 & ( member1899387664od_a_a @ ( produc1935643479od_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % as_good_as_def
% 0.26/0.61 thf(fact_75_as__good__as__def,axiom,
% 0.26/0.61 ( prefer436369274d_as_a
% 0.26/0.61 = ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
% 0.26/0.61 ( collect_a
% 0.26/0.61 @ ^ [Y4: a] :
% 0.26/0.61 ( ( member_a @ Y4 @ B5 )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % as_good_as_def
% 0.26/0.61 thf(fact_76_as__good__as__def,axiom,
% 0.26/0.61 ( prefer74720675od_a_a
% 0.26/0.61 = ( ^ [X4: product_prod_a_a,B5: set_Product_prod_a_a,P3: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( collec645855634od_a_a
% 0.26/0.61 @ ^ [Y4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ Y4 @ B5 )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ P3 )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % as_good_as_def
% 0.26/0.61 thf(fact_77_pred__equals__eq2,axiom,
% 0.26/0.61 ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
% 0.26/0.61 ( ( ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 ) )
% 0.26/0.61 = ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) ) )
% 0.26/0.61 = ( R2 = S3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % pred_equals_eq2
% 0.26/0.61 thf(fact_78_pred__equals__eq2,axiom,
% 0.26/0.61 ! [R2: set_Pr1948701895od_a_a,S3: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( ( ^ [X4: product_prod_a_a,Y4: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R2 ) )
% 0.26/0.61 = ( ^ [X4: product_prod_a_a,Y4: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ S3 ) ) )
% 0.26/0.61 = ( R2 = S3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % pred_equals_eq2
% 0.26/0.61 thf(fact_79_preference__def,axiom,
% 0.26/0.61 ( prefer1409946857od_a_a
% 0.26/0.61 = ( ^ [Carrier2: set_Pr1948701895od_a_a,Relation2: set_Pr1295299783od_a_a] :
% 0.26/0.61 ( ! [X4: produc1572603623od_a_a,Y4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X4 @ Y4 ) @ Relation2 )
% 0.26/0.61 => ( member2057358096od_a_a @ X4 @ Carrier2 ) )
% 0.26/0.61 & ! [X4: produc1572603623od_a_a,Y4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X4 @ Y4 ) @ Relation2 )
% 0.26/0.61 => ( member2057358096od_a_a @ Y4 @ Carrier2 ) )
% 0.26/0.61 & ( order_491428350od_a_a @ Carrier2 @ Relation2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference_def
% 0.26/0.61 thf(fact_80_preference__def,axiom,
% 0.26/0.61 ( prefer1292084992ence_a
% 0.26/0.61 = ( ^ [Carrier2: set_a,Relation2: set_Product_prod_a_a] :
% 0.26/0.61 ( ! [X4: a,Y4: a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
% 0.26/0.61 => ( member_a @ X4 @ Carrier2 ) )
% 0.26/0.61 & ! [X4: a,Y4: a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
% 0.26/0.61 => ( member_a @ Y4 @ Carrier2 ) )
% 0.26/0.61 & ( order_preorder_on_a @ Carrier2 @ Relation2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference_def
% 0.26/0.61 thf(fact_81_preference__def,axiom,
% 0.26/0.61 ( prefer1338892073od_a_a
% 0.26/0.61 = ( ^ [Carrier2: set_Product_prod_a_a,Relation2: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ! [X4: product_prod_a_a,Y4: product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ Relation2 )
% 0.26/0.61 => ( member449909584od_a_a @ X4 @ Carrier2 ) )
% 0.26/0.61 & ! [X4: product_prod_a_a,Y4: product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ Relation2 )
% 0.26/0.61 => ( member449909584od_a_a @ Y4 @ Carrier2 ) )
% 0.26/0.61 & ( order_359341630od_a_a @ Carrier2 @ Relation2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference_def
% 0.26/0.61 thf(fact_82_preference_Ointro,axiom,
% 0.26/0.61 ! [Relation: set_Pr1295299783od_a_a,Carrier: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ! [X3: produc1572603623od_a_a,Y3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ Relation )
% 0.26/0.61 => ( member2057358096od_a_a @ X3 @ Carrier ) )
% 0.26/0.61 => ( ! [X3: produc1572603623od_a_a,Y3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ Relation )
% 0.26/0.61 => ( member2057358096od_a_a @ Y3 @ Carrier ) )
% 0.26/0.61 => ( ( order_491428350od_a_a @ Carrier @ Relation )
% 0.26/0.61 => ( prefer1409946857od_a_a @ Carrier @ Relation ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.intro
% 0.26/0.61 thf(fact_83_preference_Ointro,axiom,
% 0.26/0.61 ! [Relation: set_Product_prod_a_a,Carrier: set_a] :
% 0.26/0.61 ( ! [X3: a,Y3: a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
% 0.26/0.61 => ( member_a @ X3 @ Carrier ) )
% 0.26/0.61 => ( ! [X3: a,Y3: a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
% 0.26/0.61 => ( member_a @ Y3 @ Carrier ) )
% 0.26/0.61 => ( ( order_preorder_on_a @ Carrier @ Relation )
% 0.26/0.61 => ( prefer1292084992ence_a @ Carrier @ Relation ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.intro
% 0.26/0.61 thf(fact_84_preference_Ointro,axiom,
% 0.26/0.61 ! [Relation: set_Pr1948701895od_a_a,Carrier: set_Product_prod_a_a] :
% 0.26/0.61 ( ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ Relation )
% 0.26/0.61 => ( member449909584od_a_a @ X3 @ Carrier ) )
% 0.26/0.61 => ( ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ Relation )
% 0.26/0.61 => ( member449909584od_a_a @ Y3 @ Carrier ) )
% 0.26/0.61 => ( ( order_359341630od_a_a @ Carrier @ Relation )
% 0.26/0.61 => ( prefer1338892073od_a_a @ Carrier @ Relation ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % preference.intro
% 0.26/0.61 thf(fact_85_pair__in__swap__image,axiom,
% 0.26/0.61 ! [Y: a,X: a,A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( image_794773445od_a_a @ product_swap_a_a @ A4 ) )
% 0.26/0.61 = ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % pair_in_swap_image
% 0.26/0.61 thf(fact_86_pair__in__swap__image,axiom,
% 0.26/0.61 ! [Y: product_prod_a_a,X: product_prod_a_a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ ( image_236793797od_a_a @ produc1641853175od_a_a @ A4 ) )
% 0.26/0.61 = ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % pair_in_swap_image
% 0.26/0.61 thf(fact_87_strict__contour__is__diff,axiom,
% 0.26/0.61 ! [B: set_Pr1948701895od_a_a,Y: produc1572603623od_a_a,Pr: set_Pr1295299783od_a_a] :
% 0.26/0.61 ( ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [A5: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ A5 @ B )
% 0.26/0.61 & ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A5 @ Y ) @ Pr )
% 0.26/0.61 & ~ ( member1899387664od_a_a @ ( produc1935643479od_a_a @ Y @ A5 ) @ Pr ) ) )
% 0.26/0.61 = ( minus_1034916142od_a_a @ ( prefer55414563od_a_a @ Y @ B @ Pr ) @ ( prefer1867335523od_a_a @ Y @ B @ Pr ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % strict_contour_is_diff
% 0.26/0.61 thf(fact_88_strict__contour__is__diff,axiom,
% 0.26/0.61 ! [B: set_a,Y: a,Pr: set_Product_prod_a_a] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [A5: a] :
% 0.26/0.61 ( ( member_a @ A5 @ B )
% 0.26/0.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ A5 @ Y ) @ Pr )
% 0.26/0.61 & ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ A5 ) @ Pr ) ) )
% 0.26/0.61 = ( minus_minus_set_a @ ( prefer161218362good_a @ Y @ B @ Pr ) @ ( prefer436369274d_as_a @ Y @ B @ Pr ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % strict_contour_is_diff
% 0.26/0.61 thf(fact_89_strict__contour__is__diff,axiom,
% 0.26/0.61 ! [B: set_Product_prod_a_a,Y: product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( collec645855634od_a_a
% 0.26/0.61 @ ^ [A5: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ A5 @ B )
% 0.26/0.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A5 @ Y ) @ Pr )
% 0.26/0.61 & ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ A5 ) @ Pr ) ) )
% 0.26/0.61 = ( minus_1507102574od_a_a @ ( prefer477097315od_a_a @ Y @ B @ Pr ) @ ( prefer74720675od_a_a @ Y @ B @ Pr ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % strict_contour_is_diff
% 0.26/0.61 thf(fact_90_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.26/0.61 ( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_91_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: a,P2: a > $o] :
% 0.26/0.61 ( ( member_a @ A @ ( collect_a @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_92_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: produc1572603623od_a_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.61 ( ( member2057358096od_a_a @ A @ ( collec1635618130od_a_a @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_93_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
% 0.26/0.61 = A4 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_94_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A4: set_a] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [X4: a] : ( member_a @ X4 @ A4 ) )
% 0.26/0.61 = A4 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_95_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ A4 ) )
% 0.26/0.61 = A4 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_96_DiffI,axiom,
% 0.26/0.61 ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ C2 @ A4 )
% 0.26/0.61 => ( ~ ( member449909584od_a_a @ C2 @ B )
% 0.26/0.61 => ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffI
% 0.26/0.61 thf(fact_97_DiffI,axiom,
% 0.26/0.61 ! [C2: a,A4: set_a,B: set_a] :
% 0.26/0.61 ( ( member_a @ C2 @ A4 )
% 0.26/0.61 => ( ~ ( member_a @ C2 @ B )
% 0.26/0.61 => ( member_a @ C2 @ ( minus_minus_set_a @ A4 @ B ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffI
% 0.26/0.61 thf(fact_98_DiffI,axiom,
% 0.26/0.61 ! [C2: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ C2 @ A4 )
% 0.26/0.61 => ( ~ ( member2057358096od_a_a @ C2 @ B )
% 0.26/0.61 => ( member2057358096od_a_a @ C2 @ ( minus_1034916142od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffI
% 0.26/0.61 thf(fact_99_image__eqI,axiom,
% 0.26/0.61 ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_100_image__eqI,axiom,
% 0.26/0.61 ! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_101_image__eqI,axiom,
% 0.26/0.61 ! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_102_image__eqI,axiom,
% 0.26/0.61 ! [B2: product_prod_a_a,F: a > product_prod_a_a,X: a,A4: set_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_103_image__eqI,axiom,
% 0.26/0.61 ! [B2: a,F: a > a,X: a,A4: set_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( member_a @ B2 @ ( image_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_104_image__eqI,axiom,
% 0.26/0.61 ! [B2: produc1572603623od_a_a,F: a > produc1572603623od_a_a,X: a,A4: set_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( member2057358096od_a_a @ B2 @ ( image_1763923566od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_105_image__eqI,axiom,
% 0.26/0.61 ! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_106_image__eqI,axiom,
% 0.26/0.61 ! [B2: a,F: produc1572603623od_a_a > a,X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( member_a @ B2 @ ( image_1105229276_a_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_107_image__eqI,axiom,
% 0.26/0.61 ! [B2: produc1572603623od_a_a,F: produc1572603623od_a_a > produc1572603623od_a_a,X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( member2057358096od_a_a @ B2 @ ( image_236793797od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_108_Diff__iff,axiom,
% 0.26/0.61 ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
% 0.26/0.61 = ( ( member449909584od_a_a @ C2 @ A4 )
% 0.26/0.61 & ~ ( member449909584od_a_a @ C2 @ B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_iff
% 0.26/0.61 thf(fact_109_Diff__iff,axiom,
% 0.26/0.61 ! [C2: a,A4: set_a,B: set_a] :
% 0.26/0.61 ( ( member_a @ C2 @ ( minus_minus_set_a @ A4 @ B ) )
% 0.26/0.61 = ( ( member_a @ C2 @ A4 )
% 0.26/0.61 & ~ ( member_a @ C2 @ B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_iff
% 0.26/0.61 thf(fact_110_Diff__iff,axiom,
% 0.26/0.61 ! [C2: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ C2 @ ( minus_1034916142od_a_a @ A4 @ B ) )
% 0.26/0.61 = ( ( member2057358096od_a_a @ C2 @ A4 )
% 0.26/0.61 & ~ ( member2057358096od_a_a @ C2 @ B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_iff
% 0.26/0.61 thf(fact_111_minus__set__def,axiom,
% 0.26/0.61 ( minus_1507102574od_a_a
% 0.26/0.61 = ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
% 0.26/0.61 ( collec645855634od_a_a
% 0.26/0.61 @ ( minus_1797478127_a_a_o
% 0.26/0.61 @ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
% 0.26/0.61 @ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % minus_set_def
% 0.26/0.61 thf(fact_112_minus__set__def,axiom,
% 0.26/0.61 ( minus_minus_set_a
% 0.26/0.61 = ( ^ [A6: set_a,B5: set_a] :
% 0.26/0.61 ( collect_a
% 0.26/0.61 @ ( minus_minus_a_o
% 0.26/0.61 @ ^ [X4: a] : ( member_a @ X4 @ A6 )
% 0.26/0.61 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % minus_set_def
% 0.26/0.61 thf(fact_113_minus__set__def,axiom,
% 0.26/0.61 ( minus_1034916142od_a_a
% 0.26/0.61 = ( ^ [A6: set_Pr1948701895od_a_a,B5: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( collec1635618130od_a_a
% 0.26/0.61 @ ( minus_107310383_a_a_o
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ A6 )
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ B5 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % minus_set_def
% 0.26/0.61 thf(fact_114_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_115_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: a,F: product_prod_a_a > a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_116_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_117_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: a,A4: set_a,B2: product_prod_a_a,F: a > product_prod_a_a] :
% 0.26/0.61 ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_118_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: a,A4: set_a,B2: a,F: a > a] :
% 0.26/0.61 ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member_a @ B2 @ ( image_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_119_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: a,A4: set_a,B2: produc1572603623od_a_a,F: a > produc1572603623od_a_a] :
% 0.26/0.61 ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member2057358096od_a_a @ B2 @ ( image_1763923566od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_120_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_121_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: a,F: produc1572603623od_a_a > a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member_a @ B2 @ ( image_1105229276_a_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_122_rev__image__eqI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: produc1572603623od_a_a,F: produc1572603623od_a_a > produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( ( B2
% 0.26/0.61 = ( F @ X ) )
% 0.26/0.61 => ( member2057358096od_a_a @ B2 @ ( image_236793797od_a_a @ F @ A4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_123_imageI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( member449909584od_a_a @ ( F @ X ) @ ( image_794773445od_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_124_imageI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( member_a @ ( F @ X ) @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_125_imageI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.61 => ( member2057358096od_a_a @ ( F @ X ) @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_126_imageI,axiom,
% 0.26/0.61 ! [X: a,A4: set_a,F: a > product_prod_a_a] :
% 0.26/0.61 ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( member449909584od_a_a @ ( F @ X ) @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_127_imageI,axiom,
% 0.26/0.61 ! [X: a,A4: set_a,F: a > a] :
% 0.26/0.61 ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( member_a @ ( F @ X ) @ ( image_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_128_imageI,axiom,
% 0.26/0.61 ! [X: a,A4: set_a,F: a > produc1572603623od_a_a] :
% 0.26/0.61 ( ( member_a @ X @ A4 )
% 0.26/0.61 => ( member2057358096od_a_a @ ( F @ X ) @ ( image_1763923566od_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_129_imageI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( member449909584od_a_a @ ( F @ X ) @ ( image_734753285od_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_130_imageI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( member_a @ ( F @ X ) @ ( image_1105229276_a_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_131_imageI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.61 => ( member2057358096od_a_a @ ( F @ X ) @ ( image_236793797od_a_a @ F @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_132_DiffD2,axiom,
% 0.26/0.61 ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
% 0.26/0.61 => ~ ( member449909584od_a_a @ C2 @ B ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffD2
% 0.26/0.61 thf(fact_133_DiffD2,axiom,
% 0.26/0.61 ! [C2: a,A4: set_a,B: set_a] :
% 0.26/0.61 ( ( member_a @ C2 @ ( minus_minus_set_a @ A4 @ B ) )
% 0.26/0.61 => ~ ( member_a @ C2 @ B ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffD2
% 0.26/0.61 thf(fact_134_DiffD2,axiom,
% 0.26/0.61 ! [C2: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ C2 @ ( minus_1034916142od_a_a @ A4 @ B ) )
% 0.26/0.61 => ~ ( member2057358096od_a_a @ C2 @ B ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffD2
% 0.26/0.61 thf(fact_135_DiffD1,axiom,
% 0.26/0.61 ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
% 0.26/0.61 => ( member449909584od_a_a @ C2 @ A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffD1
% 0.26/0.61 thf(fact_136_DiffD1,axiom,
% 0.26/0.61 ! [C2: a,A4: set_a,B: set_a] :
% 0.26/0.61 ( ( member_a @ C2 @ ( minus_minus_set_a @ A4 @ B ) )
% 0.26/0.61 => ( member_a @ C2 @ A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffD1
% 0.26/0.61 thf(fact_137_DiffD1,axiom,
% 0.26/0.61 ! [C2: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ C2 @ ( minus_1034916142od_a_a @ A4 @ B ) )
% 0.26/0.61 => ( member2057358096od_a_a @ C2 @ A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffD1
% 0.26/0.61 thf(fact_138_DiffE,axiom,
% 0.26/0.61 ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
% 0.26/0.61 => ~ ( ( member449909584od_a_a @ C2 @ A4 )
% 0.26/0.61 => ( member449909584od_a_a @ C2 @ B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffE
% 0.26/0.61 thf(fact_139_DiffE,axiom,
% 0.26/0.61 ! [C2: a,A4: set_a,B: set_a] :
% 0.26/0.61 ( ( member_a @ C2 @ ( minus_minus_set_a @ A4 @ B ) )
% 0.26/0.61 => ~ ( ( member_a @ C2 @ A4 )
% 0.26/0.61 => ( member_a @ C2 @ B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffE
% 0.26/0.61 thf(fact_140_DiffE,axiom,
% 0.26/0.61 ! [C2: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ C2 @ ( minus_1034916142od_a_a @ A4 @ B ) )
% 0.26/0.61 => ~ ( ( member2057358096od_a_a @ C2 @ A4 )
% 0.26/0.61 => ( member2057358096od_a_a @ C2 @ B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % DiffE
% 0.26/0.61 thf(fact_141_imageE,axiom,
% 0.26/0.61 ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: product_prod_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_142_imageE,axiom,
% 0.26/0.61 ! [B2: product_prod_a_a,F: a > product_prod_a_a,A4: set_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_143_imageE,axiom,
% 0.26/0.61 ! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member2057358096od_a_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_144_imageE,axiom,
% 0.26/0.61 ! [B2: a,F: product_prod_a_a > a,A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: product_prod_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_145_imageE,axiom,
% 0.26/0.61 ! [B2: a,F: a > a,A4: set_a] :
% 0.26/0.61 ( ( member_a @ B2 @ ( image_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_146_imageE,axiom,
% 0.26/0.61 ! [B2: a,F: produc1572603623od_a_a > a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member_a @ B2 @ ( image_1105229276_a_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member2057358096od_a_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_147_imageE,axiom,
% 0.26/0.61 ! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: product_prod_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_148_imageE,axiom,
% 0.26/0.61 ! [B2: produc1572603623od_a_a,F: a > produc1572603623od_a_a,A4: set_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ B2 @ ( image_1763923566od_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_149_imageE,axiom,
% 0.26/0.61 ! [B2: produc1572603623od_a_a,F: produc1572603623od_a_a > produc1572603623od_a_a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ B2 @ ( image_236793797od_a_a @ F @ A4 ) )
% 0.26/0.61 => ~ ! [X3: produc1572603623od_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( F @ X3 ) )
% 0.26/0.61 => ~ ( member2057358096od_a_a @ X3 @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageE
% 0.26/0.61 thf(fact_150_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.26/0.61 ( ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X4 @ ( image_794773445od_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_794773445od_a_a @ F
% 0.26/0.61 @ ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_151_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: a > product_prod_a_a,A4: set_a,P2: product_prod_a_a > $o] :
% 0.26/0.61 ( ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X4 @ ( image_1725938350od_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_1725938350od_a_a @ F
% 0.26/0.61 @ ( collect_a
% 0.26/0.61 @ ^ [X4: a] :
% 0.26/0.61 ( ( member_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_152_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: produc1572603623od_a_a > product_prod_a_a,A4: set_Pr1948701895od_a_a,P2: product_prod_a_a > $o] :
% 0.26/0.61 ( ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X4 @ ( image_734753285od_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_734753285od_a_a @ F
% 0.26/0.61 @ ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_153_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > a,A4: set_Product_prod_a_a,P2: a > $o] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [X4: a] :
% 0.26/0.61 ( ( member_a @ X4 @ ( image_340790172_a_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_340790172_a_a_a @ F
% 0.26/0.61 @ ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_154_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: a > a,A4: set_a,P2: a > $o] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [X4: a] :
% 0.26/0.61 ( ( member_a @ X4 @ ( image_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_a_a @ F
% 0.26/0.61 @ ( collect_a
% 0.26/0.61 @ ^ [X4: a] :
% 0.26/0.61 ( ( member_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_155_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: produc1572603623od_a_a > a,A4: set_Pr1948701895od_a_a,P2: a > $o] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [X4: a] :
% 0.26/0.61 ( ( member_a @ X4 @ ( image_1105229276_a_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_1105229276_a_a_a @ F
% 0.26/0.61 @ ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_156_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > produc1572603623od_a_a,A4: set_Product_prod_a_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.61 ( ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X4 @ ( image_1765377413od_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_1765377413od_a_a @ F
% 0.26/0.61 @ ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_157_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: a > produc1572603623od_a_a,A4: set_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.61 ( ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X4 @ ( image_1763923566od_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_1763923566od_a_a @ F
% 0.26/0.61 @ ( collect_a
% 0.26/0.61 @ ^ [X4: a] :
% 0.26/0.61 ( ( member_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_158_Compr__image__eq,axiom,
% 0.26/0.61 ! [F: produc1572603623od_a_a > produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.61 ( ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X4 @ ( image_236793797od_a_a @ F @ A4 ) )
% 0.26/0.61 & ( P2 @ X4 ) ) )
% 0.26/0.61 = ( image_236793797od_a_a @ F
% 0.26/0.61 @ ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X4 @ A4 )
% 0.26/0.61 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Compr_image_eq
% 0.26/0.61 thf(fact_159_set__diff__eq,axiom,
% 0.26/0.61 ( minus_1507102574od_a_a
% 0.26/0.61 = ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
% 0.26/0.61 ( collec645855634od_a_a
% 0.26/0.61 @ ^ [X4: product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ X4 @ A6 )
% 0.26/0.61 & ~ ( member449909584od_a_a @ X4 @ B5 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_diff_eq
% 0.26/0.61 thf(fact_160_set__diff__eq,axiom,
% 0.26/0.61 ( minus_minus_set_a
% 0.26/0.61 = ( ^ [A6: set_a,B5: set_a] :
% 0.26/0.61 ( collect_a
% 0.26/0.61 @ ^ [X4: a] :
% 0.26/0.61 ( ( member_a @ X4 @ A6 )
% 0.26/0.61 & ~ ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_diff_eq
% 0.26/0.61 thf(fact_161_set__diff__eq,axiom,
% 0.26/0.61 ( minus_1034916142od_a_a
% 0.26/0.61 = ( ^ [A6: set_Pr1948701895od_a_a,B5: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( collec1635618130od_a_a
% 0.26/0.61 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ X4 @ A6 )
% 0.26/0.61 & ~ ( member2057358096od_a_a @ X4 @ B5 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_diff_eq
% 0.26/0.61 thf(fact_162_UNIV__I,axiom,
% 0.26/0.61 ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_I
% 0.26/0.61 thf(fact_163_UNIV__I,axiom,
% 0.26/0.61 ! [X: a] : ( member_a @ X @ top_top_set_a ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_I
% 0.26/0.61 thf(fact_164_UNIV__I,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a] : ( member2057358096od_a_a @ X @ top_to52711959od_a_a ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_I
% 0.26/0.61 thf(fact_165_UNIV__witness,axiom,
% 0.26/0.61 ? [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ top_to398455383od_a_a ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_witness
% 0.26/0.61 thf(fact_166_UNIV__witness,axiom,
% 0.26/0.61 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_witness
% 0.26/0.61 thf(fact_167_UNIV__witness,axiom,
% 0.26/0.61 ? [X3: produc1572603623od_a_a] : ( member2057358096od_a_a @ X3 @ top_to52711959od_a_a ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_witness
% 0.26/0.61 thf(fact_168_UNIV__eq__I,axiom,
% 0.26/0.61 ! [A4: set_Product_prod_a_a] :
% 0.26/0.61 ( ! [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.61 => ( top_to398455383od_a_a = A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_eq_I
% 0.26/0.61 thf(fact_169_UNIV__eq__I,axiom,
% 0.26/0.61 ! [A4: set_a] :
% 0.26/0.61 ( ! [X3: a] : ( member_a @ X3 @ A4 )
% 0.26/0.61 => ( top_top_set_a = A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_eq_I
% 0.26/0.61 thf(fact_170_UNIV__eq__I,axiom,
% 0.26/0.61 ! [A4: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ! [X3: produc1572603623od_a_a] : ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.61 => ( top_to52711959od_a_a = A4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % UNIV_eq_I
% 0.26/0.61 thf(fact_171_iso__tuple__UNIV__I,axiom,
% 0.26/0.61 ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ) ).
% 0.26/0.61
% 0.26/0.61 % iso_tuple_UNIV_I
% 0.26/0.61 thf(fact_172_iso__tuple__UNIV__I,axiom,
% 0.26/0.61 ! [X: a] : ( member_a @ X @ top_top_set_a ) ).
% 0.26/0.61
% 0.26/0.61 % iso_tuple_UNIV_I
% 0.26/0.61 thf(fact_173_iso__tuple__UNIV__I,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a] : ( member2057358096od_a_a @ X @ top_to52711959od_a_a ) ).
% 0.26/0.61
% 0.26/0.61 % iso_tuple_UNIV_I
% 0.26/0.61 thf(fact_174_same__fstI,axiom,
% 0.26/0.61 ! [P2: a > $o,X: a,Y5: a,Y: a,R2: a > set_Product_prod_a_a] :
% 0.26/0.61 ( ( P2 @ X )
% 0.26/0.61 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y5 @ Y ) @ ( R2 @ X ) )
% 0.26/0.61 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ X @ Y5 ) @ ( product_Pair_a_a @ X @ Y ) ) @ ( same_fst_a_a @ P2 @ R2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % same_fstI
% 0.26/0.61 thf(fact_175_same__fstI,axiom,
% 0.26/0.61 ! [P2: product_prod_a_a > $o,X: product_prod_a_a,Y5: product_prod_a_a,Y: product_prod_a_a,R2: product_prod_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( P2 @ X )
% 0.26/0.61 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y5 @ Y ) @ ( R2 @ X ) )
% 0.26/0.61 => ( member1899387664od_a_a @ ( produc1935643479od_a_a @ ( produc1474507607od_a_a @ X @ Y5 ) @ ( produc1474507607od_a_a @ X @ Y ) ) @ ( same_f1138477100od_a_a @ P2 @ R2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % same_fstI
% 0.26/0.61 thf(fact_176_map__prod__simp,axiom,
% 0.26/0.61 ! [F: a > a,G: a > a,A: a,B2: a] :
% 0.26/0.61 ( ( produc700022774_a_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
% 0.26/0.61 = ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_simp
% 0.26/0.61 thf(fact_177_map__prod__simp,axiom,
% 0.26/0.61 ! [F: a > product_prod_a_a,G: a > product_prod_a_a,A: a,B2: a] :
% 0.26/0.61 ( ( produc2012818120od_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
% 0.26/0.61 = ( produc1474507607od_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_simp
% 0.26/0.61 thf(fact_178_map__prod__simp,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > a,G: product_prod_a_a > a,A: product_prod_a_a,B2: product_prod_a_a] :
% 0.26/0.61 ( ( produc363290532_a_a_a @ F @ G @ ( produc1474507607od_a_a @ A @ B2 ) )
% 0.26/0.61 = ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_simp
% 0.26/0.61 thf(fact_179_map__prod__simp,axiom,
% 0.26/0.61 ! [F: product_prod_a_a > product_prod_a_a,G: product_prod_a_a > product_prod_a_a,A: product_prod_a_a,B2: product_prod_a_a] :
% 0.26/0.61 ( ( produc1779756150od_a_a @ F @ G @ ( produc1474507607od_a_a @ A @ B2 ) )
% 0.26/0.61 = ( produc1474507607od_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_simp
% 0.26/0.61 thf(fact_180_map__prod__imageI,axiom,
% 0.26/0.61 ! [A: a,B2: a,R2: set_Product_prod_a_a,F: a > a,G: a > a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ R2 )
% 0.26/0.61 => ( member449909584od_a_a @ ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_imageI
% 0.26/0.61 thf(fact_181_map__prod__imageI,axiom,
% 0.26/0.61 ! [A: a,B2: a,R2: set_Product_prod_a_a,F: a > product_prod_a_a,G: a > product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ R2 )
% 0.26/0.61 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( F @ A ) @ ( G @ B2 ) ) @ ( image_1765377413od_a_a @ ( produc2012818120od_a_a @ F @ G ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_imageI
% 0.26/0.61 thf(fact_182_map__prod__imageI,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: product_prod_a_a,R2: set_Pr1948701895od_a_a,F: product_prod_a_a > a,G: product_prod_a_a > a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ R2 )
% 0.26/0.61 => ( member449909584od_a_a @ ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) @ ( image_734753285od_a_a @ ( produc363290532_a_a_a @ F @ G ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_imageI
% 0.26/0.61 thf(fact_183_map__prod__imageI,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,B2: product_prod_a_a,R2: set_Pr1948701895od_a_a,F: product_prod_a_a > product_prod_a_a,G: product_prod_a_a > product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ R2 )
% 0.26/0.61 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( F @ A ) @ ( G @ B2 ) ) @ ( image_236793797od_a_a @ ( produc1779756150od_a_a @ F @ G ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % map_prod_imageI
% 0.26/0.61 thf(fact_184_top__empty__eq,axiom,
% 0.26/0.61 ( top_to1483957574_a_a_o
% 0.26/0.61 = ( ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ top_to398455383od_a_a ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % top_empty_eq
% 0.26/0.61 thf(fact_185_top__empty__eq,axiom,
% 0.26/0.61 ( top_top_a_o
% 0.26/0.61 = ( ^ [X4: a] : ( member_a @ X4 @ top_top_set_a ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % top_empty_eq
% 0.26/0.61 thf(fact_186_top__empty__eq,axiom,
% 0.26/0.61 ( top_to2011536774_a_a_o
% 0.26/0.61 = ( ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ top_to52711959od_a_a ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % top_empty_eq
% 0.26/0.61 thf(fact_187_fst__eqD,axiom,
% 0.26/0.61 ! [X: a,Y: a,A: a] :
% 0.26/0.61 ( ( ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) )
% 0.26/0.61 = A )
% 0.26/0.61 => ( X = A ) ) ).
% 0.26/0.61
% 0.26/0.61 % fst_eqD
% 0.26/0.61 thf(fact_188_fst__eqD,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,Y: product_prod_a_a,A: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ X @ Y ) )
% 0.26/0.61 = A )
% 0.26/0.61 => ( X = A ) ) ).
% 0.26/0.61
% 0.26/0.61 % fst_eqD
% 0.26/0.61 thf(fact_189_fst__conv,axiom,
% 0.26/0.61 ! [X1: a,X2: a] :
% 0.26/0.61 ( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
% 0.26/0.61 = X1 ) ).
% 0.26/0.61
% 0.26/0.61 % fst_conv
% 0.26/0.61 thf(fact_190_fst__conv,axiom,
% 0.26/0.61 ! [X1: product_prod_a_a,X2: product_prod_a_a] :
% 0.26/0.61 ( ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ X1 @ X2 ) )
% 0.26/0.61 = X1 ) ).
% 0.26/0.61
% 0.26/0.61 % fst_conv
% 0.26/0.61 thf(fact_191_prod__fun__imageE,axiom,
% 0.26/0.61 ! [C2: product_prod_a_a,F: a > a,G: a > a,R2: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ C2 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) )
% 0.26/0.61 => ~ ! [X3: a,Y3: a] :
% 0.26/0.61 ( ( C2
% 0.26/0.61 = ( product_Pair_a_a @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.26/0.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_fun_imageE
% 0.26/0.61 thf(fact_192_prod__fun__imageE,axiom,
% 0.26/0.61 ! [C2: product_prod_a_a,F: product_prod_a_a > a,G: product_prod_a_a > a,R2: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member449909584od_a_a @ C2 @ ( image_734753285od_a_a @ ( produc363290532_a_a_a @ F @ G ) @ R2 ) )
% 0.26/0.61 => ~ ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
% 0.26/0.61 ( ( C2
% 0.26/0.61 = ( product_Pair_a_a @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.26/0.61 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_fun_imageE
% 0.26/0.61 thf(fact_193_prod__fun__imageE,axiom,
% 0.26/0.61 ! [C2: produc1572603623od_a_a,F: a > product_prod_a_a,G: a > product_prod_a_a,R2: set_Product_prod_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ C2 @ ( image_1765377413od_a_a @ ( produc2012818120od_a_a @ F @ G ) @ R2 ) )
% 0.26/0.61 => ~ ! [X3: a,Y3: a] :
% 0.26/0.61 ( ( C2
% 0.26/0.61 = ( produc1474507607od_a_a @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.26/0.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_fun_imageE
% 0.26/0.61 thf(fact_194_prod__fun__imageE,axiom,
% 0.26/0.61 ! [C2: produc1572603623od_a_a,F: product_prod_a_a > product_prod_a_a,G: product_prod_a_a > product_prod_a_a,R2: set_Pr1948701895od_a_a] :
% 0.26/0.61 ( ( member2057358096od_a_a @ C2 @ ( image_236793797od_a_a @ ( produc1779756150od_a_a @ F @ G ) @ R2 ) )
% 0.26/0.61 => ~ ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
% 0.26/0.61 ( ( C2
% 0.26/0.61 = ( produc1474507607od_a_a @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.26/0.61 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod_fun_imageE
% 0.26/0.61 thf(fact_195_top__empty__eq2,axiom,
% 0.26/0.61 ( top_top_a_a_o
% 0.26/0.61 = ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ top_to398455383od_a_a ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % top_empty_eq2
% 0.26/0.61 thf(fact_196_top__empty__eq2,axiom,
% 0.26/0.61 ( top_to993969022_a_a_o
% 0.26/0.61 = ( ^ [X4: product_prod_a_a,Y4: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ top_to52711959od_a_a ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % top_empty_eq2
% 0.26/0.61 thf(fact_197_eq__fst__iff,axiom,
% 0.26/0.61 ! [A: a,P: product_prod_a_a] :
% 0.26/0.61 ( ( A
% 0.26/0.61 = ( product_fst_a_a @ P ) )
% 0.26/0.61 = ( ? [B6: a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( product_Pair_a_a @ A @ B6 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % eq_fst_iff
% 0.26/0.61 thf(fact_198_eq__fst__iff,axiom,
% 0.26/0.61 ! [A: product_prod_a_a,P: produc1572603623od_a_a] :
% 0.26/0.61 ( ( A
% 0.26/0.61 = ( produc2115494211od_a_a @ P ) )
% 0.26/0.61 = ( ? [B6: product_prod_a_a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc1474507607od_a_a @ A @ B6 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % eq_fst_iff
% 0.26/0.61 thf(fact_199_fstI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,Y: a,Z: a] :
% 0.26/0.61 ( ( X
% 0.26/0.61 = ( product_Pair_a_a @ Y @ Z ) )
% 0.26/0.61 => ( ( product_fst_a_a @ X )
% 0.26/0.61 = Y ) ) ).
% 0.26/0.61
% 0.26/0.61 % fstI
% 0.26/0.61 thf(fact_200_fstI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,Y: product_prod_a_a,Z: product_prod_a_a] :
% 0.26/0.61 ( ( X
% 0.26/0.61 = ( produc1474507607od_a_a @ Y @ Z ) )
% 0.26/0.61 => ( ( produc2115494211od_a_a @ X )
% 0.26/0.61 = Y ) ) ).
% 0.26/0.61
% 0.26/0.61 % fstI
% 0.26/0.61 thf(fact_201_prod_Ocollapse,axiom,
% 0.26/0.61 ! [Prod: product_prod_a_a] :
% 0.26/0.61 ( ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) )
% 0.26/0.61 = Prod ) ).
% 0.26/0.61
% 0.26/0.61 % prod.collapse
% 0.26/0.61 thf(fact_202_prod_Ocollapse,axiom,
% 0.26/0.61 ! [Prod: produc1572603623od_a_a] :
% 0.26/0.61 ( ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ Prod ) @ ( produc368344197od_a_a @ Prod ) )
% 0.26/0.61 = Prod ) ).
% 0.26/0.61
% 0.26/0.61 % prod.collapse
% 0.26/0.61 thf(fact_203_eq__snd__iff,axiom,
% 0.26/0.61 ! [B2: a,P: product_prod_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( product_snd_a_a @ P ) )
% 0.26/0.61 = ( ? [A5: a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( product_Pair_a_a @ A5 @ B2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % eq_snd_iff
% 0.26/0.61 thf(fact_204_eq__snd__iff,axiom,
% 0.26/0.61 ! [B2: product_prod_a_a,P: produc1572603623od_a_a] :
% 0.26/0.61 ( ( B2
% 0.26/0.61 = ( produc368344197od_a_a @ P ) )
% 0.26/0.61 = ( ? [A5: product_prod_a_a] :
% 0.26/0.61 ( P
% 0.26/0.61 = ( produc1474507607od_a_a @ A5 @ B2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % eq_snd_iff
% 0.26/0.61 thf(fact_205_sndI,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,Y: a,Z: a] :
% 0.26/0.61 ( ( X
% 0.26/0.61 = ( product_Pair_a_a @ Y @ Z ) )
% 0.26/0.61 => ( ( product_snd_a_a @ X )
% 0.26/0.61 = Z ) ) ).
% 0.26/0.61
% 0.26/0.61 % sndI
% 0.26/0.61 thf(fact_206_sndI,axiom,
% 0.26/0.61 ! [X: produc1572603623od_a_a,Y: product_prod_a_a,Z: product_prod_a_a] :
% 0.26/0.61 ( ( X
% 0.26/0.61 = ( produc1474507607od_a_a @ Y @ Z ) )
% 0.26/0.61 => ( ( produc368344197od_a_a @ X )
% 0.26/0.61 = Z ) ) ).
% 0.26/0.61
% 0.26/0.61 % sndI
% 0.26/0.61 thf(fact_207_snd__eqD,axiom,
% 0.26/0.61 ! [X: a,Y: a,A: a] :
% 0.26/0.61 ( ( ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) )
% 0.26/0.61 = A )
% 0.26/0.61 => ( Y = A ) ) ).
% 0.26/0.61
% 0.26/0.61 % snd_eqD
% 0.26/0.61 thf(fact_208_snd__eqD,axiom,
% 0.26/0.61 ! [X: product_prod_a_a,Y: product_prod_a_a,A: product_prod_a_a] :
% 0.26/0.61 ( ( ( produc368344197od_a_a @ ( produc1474507607od_a_a @ X @ Y ) )
% 0.26/0.61 = A )
% 0.26/0.61 => ( Y = A ) ) ).
% 0.26/0.61
% 0.26/0.61 % snd_eqD
% 0.26/0.61 thf(fact_209_snd__conv,axiom,
% 0.26/0.61 ! [X1: a,X2: a] :
% 0.26/0.61 ( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % snd_conv
% 0.26/0.61 thf(fact_210_snd__conv,axiom,
% 0.26/0.61 ! [X1: product_prod_a_a,X2: product_prod_a_a] :
% 0.26/0.61 ( ( produc368344197od_a_a @ ( produc1474507607od_a_a @ X1 @ X2 ) )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % snd_conv
% 0.26/0.61 thf(fact_211_surjective__pairing,axiom,
% 0.26/0.61 ! [T: product_prod_a_a] :
% 0.26/0.61 ( T
% 0.26/0.61 = ( product_Pair_a_a @ ( product_fst_a_a @ T ) @ ( product_snd_a_a @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % surjective_pairing
% 0.26/0.61 thf(fact_212_surjective__pairing,axiom,
% 0.26/0.61 ! [T: produc1572603623od_a_a] :
% 0.26/0.61 ( T
% 0.26/0.61 = ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ T ) @ ( produc368344197od_a_a @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % surjective_pairing
% 0.26/0.61 thf(fact_213_prod_Oexhaust__sel,axiom,
% 0.26/0.61 ! [Prod: product_prod_a_a] :
% 0.26/0.61 ( Prod
% 0.26/0.61 = ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.exhaust_sel
% 0.26/0.61 thf(fact_214_prod_Oexhaust__sel,axiom,
% 0.26/0.61 ! [Prod: produc1572603623od_a_a] :
% 0.26/0.61 ( Prod
% 0.26/0.61 = ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ Prod ) @ ( produc368344197od_a_a @ Prod ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.exhaust_sel
% 0.26/0.61 thf(fact_215_prod_Oswap__def,axiom,
% 0.26/0.61 ( product_swap_a_a
% 0.26/0.61 = ( ^ [P4: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P4 ) @ ( product_fst_a_a @ P4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.swap_def
% 0.26/0.61 thf(fact_216_prod_Oswap__def,axiom,
% 0.26/0.61 ( produc1641853175od_a_a
% 0.26/0.61 = ( ^ [P4: produc1572603623od_a_a] : ( produc1474507607od_a_a @ ( produc368344197od_a_a @ P4 ) @ ( produc2115494211od_a_a @ P4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % prod.swap_def
% 0.26/0.61 thf(fact_217_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.61 ! [P2: a > a > $o,X: a,Y: a,A: product_prod_a_a] :
% 0.26/0.61 ( ( P2 @ X @ Y )
% 0.26/0.61 => ( ( A
% 0.26/0.61 = ( product_Pair_a_a @ X @ Y ) )
% 0.26/0.61 => ( P2 @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.61 thf(fact_218_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.26/0.61 ! [P2: product_prod_a_a > product_prod_a_a > $o,X: product_prod_a_a,Y: product_prod_a_a,A: produc1572603623od_a_a] :
% 0.26/0.62 ( ( P2 @ X @ Y )
% 0.26/0.62 => ( ( A
% 0.26/0.62 = ( produc1474507607od_a_a @ X @ Y ) )
% 0.26/0.62 => ( P2 @ ( produc2115494211od_a_a @ A ) @ ( produc368344197od_a_a @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % BNF_Greatest_Fixpoint.subst_Pair
% 0.26/0.62 thf(fact_219_conjI__realizer,axiom,
% 0.26/0.62 ! [P2: a > $o,P: a,Q: a > $o,Q2: a] :
% 0.26/0.62 ( ( P2 @ P )
% 0.26/0.62 => ( ( Q @ Q2 )
% 0.26/0.62 => ( ( P2 @ ( product_fst_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) )
% 0.26/0.62 & ( Q @ ( product_snd_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % conjI_realizer
% 0.26/0.62 thf(fact_220_conjI__realizer,axiom,
% 0.26/0.62 ! [P2: product_prod_a_a > $o,P: product_prod_a_a,Q: product_prod_a_a > $o,Q2: product_prod_a_a] :
% 0.26/0.62 ( ( P2 @ P )
% 0.26/0.62 => ( ( Q @ Q2 )
% 0.26/0.62 => ( ( P2 @ ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ P @ Q2 ) ) )
% 0.26/0.62 & ( Q @ ( produc368344197od_a_a @ ( produc1474507607od_a_a @ P @ Q2 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % conjI_realizer
% 0.26/0.62 thf(fact_221_exI__realizer,axiom,
% 0.26/0.62 ! [P2: a > a > $o,Y: a,X: a] :
% 0.26/0.62 ( ( P2 @ Y @ X )
% 0.26/0.62 => ( P2 @ ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % exI_realizer
% 0.26/0.62 thf(fact_222_exI__realizer,axiom,
% 0.26/0.62 ! [P2: product_prod_a_a > product_prod_a_a > $o,Y: product_prod_a_a,X: product_prod_a_a] :
% 0.26/0.62 ( ( P2 @ Y @ X )
% 0.26/0.62 => ( P2 @ ( produc368344197od_a_a @ ( produc1474507607od_a_a @ X @ Y ) ) @ ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ X @ Y ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % exI_realizer
% 0.26/0.62 thf(fact_223_image2__eqI,axiom,
% 0.26/0.62 ! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,C2: a,G: product_prod_a_a > a,A4: set_Product_prod_a_a] :
% 0.26/0.62 ( ( B2
% 0.26/0.62 = ( F @ X ) )
% 0.26/0.62 => ( ( C2
% 0.26/0.62 = ( G @ X ) )
% 0.26/0.62 => ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr1853143117_a_a_a @ A4 @ F @ G ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % image2_eqI
% 0.26/0.62 thf(fact_224_image2__eqI,axiom,
% 0.26/0.62 ! [B2: a,F: a > a,X: a,C2: a,G: a > a,A4: set_a] :
% 0.26/0.62 ( ( B2
% 0.26/0.62 = ( F @ X ) )
% 0.26/0.62 => ( ( C2
% 0.26/0.62 = ( G @ X ) )
% 0.26/0.62 => ( ( member_a @ X @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr423046308_a_a_a @ A4 @ F @ G ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % image2_eqI
% 0.26/0.62 thf(fact_225_image2__eqI,axiom,
% 0.26/0.62 ! [B2: a,F: produc1572603623od_a_a > a,X: produc1572603623od_a_a,C2: a,G: produc1572603623od_a_a > a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( B2
% 0.26/0.62 = ( F @ X ) )
% 0.26/0.62 => ( ( C2
% 0.26/0.62 = ( G @ X ) )
% 0.26/0.62 => ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr356189709_a_a_a @ A4 @ F @ G ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % image2_eqI
% 0.26/0.62 thf(fact_226_image2__eqI,axiom,
% 0.26/0.62 ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,C2: product_prod_a_a,G: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
% 0.26/0.62 ( ( B2
% 0.26/0.62 = ( F @ X ) )
% 0.26/0.62 => ( ( C2
% 0.26/0.62 = ( G @ X ) )
% 0.26/0.62 => ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ C2 ) @ ( bNF_Gr200450189od_a_a @ A4 @ F @ G ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % image2_eqI
% 0.26/0.62 thf(fact_227_image2__eqI,axiom,
% 0.26/0.62 ! [B2: product_prod_a_a,F: a > product_prod_a_a,X: a,C2: product_prod_a_a,G: a > product_prod_a_a,A4: set_a] :
% 0.26/0.62 ( ( B2
% 0.26/0.62 = ( F @ X ) )
% 0.26/0.62 => ( ( C2
% 0.26/0.62 = ( G @ X ) )
% 0.26/0.62 => ( ( member_a @ X @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ C2 ) @ ( bNF_Gr1715025636od_a_a @ A4 @ F @ G ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % image2_eqI
% 0.26/0.62 thf(fact_228_image2__eqI,axiom,
% 0.26/0.62 ! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,X: produc1572603623od_a_a,C2: product_prod_a_a,G: produc1572603623od_a_a > product_prod_a_a,A4: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( B2
% 0.26/0.62 = ( F @ X ) )
% 0.26/0.62 => ( ( C2
% 0.26/0.62 = ( G @ X ) )
% 0.26/0.62 => ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ C2 ) @ ( bNF_Gr533818957od_a_a @ A4 @ F @ G ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % image2_eqI
% 0.26/0.62 thf(fact_229_in__lex__prod,axiom,
% 0.26/0.62 ! [A: a,B2: product_prod_a_a,A2: a,B3: product_prod_a_a,R: set_Product_prod_a_a,S: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member1361298640od_a_a @ ( produc563767703od_a_a @ ( produc1299253312od_a_a @ A @ B2 ) @ ( produc1299253312od_a_a @ A2 @ B3 ) ) @ ( lex_pr1321960536od_a_a @ R @ S ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R )
% 0.26/0.62 | ( ( A = A2 )
% 0.26/0.62 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ B3 ) @ S ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_lex_prod
% 0.26/0.62 thf(fact_230_in__lex__prod,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: a,A2: product_prod_a_a,B3: a,R: set_Pr1948701895od_a_a,S: set_Product_prod_a_a] :
% 0.26/0.62 ( ( member470802768_a_a_a @ ( produc2054708503_a_a_a @ ( produc2061588782_a_a_a @ A @ B2 ) @ ( produc2061588782_a_a_a @ A2 @ B3 ) ) @ ( lex_pr2084296006_a_a_a @ R @ S ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ A2 ) @ R )
% 0.26/0.62 | ( ( A = A2 )
% 0.26/0.62 & ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ B3 ) @ S ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_lex_prod
% 0.26/0.62 thf(fact_231_in__lex__prod,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: product_prod_a_a,A2: product_prod_a_a,B3: product_prod_a_a,R: set_Pr1948701895od_a_a,S: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc1474507607od_a_a @ A2 @ B3 ) ) @ ( lex_pr942790511od_a_a @ R @ S ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ A2 ) @ R )
% 0.26/0.62 | ( ( A = A2 )
% 0.26/0.62 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ B3 ) @ S ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_lex_prod
% 0.26/0.62 thf(fact_232_in__lex__prod,axiom,
% 0.26/0.62 ! [A: a,B2: a,A2: a,B3: a,R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Pair_a_a @ A2 @ B3 ) ) @ ( lex_prod_a_a @ R @ S ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R )
% 0.26/0.62 | ( ( A = A2 )
% 0.26/0.62 & ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ B3 ) @ S ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_lex_prod
% 0.26/0.62 thf(fact_233_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_a] :
% 0.26/0.62 ( ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ B2 ) @ ( produc1282482655_a_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 & ( member_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_234_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ B2 ) @ ( produc1227942600od_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 & ( member2057358096od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_235_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: a,B2: product_prod_a_a,A4: set_a,B: a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ B2 ) @ ( produc520147185od_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member_a @ A @ A4 )
% 0.26/0.62 & ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_236_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: a,B2: produc1572603623od_a_a,A4: set_a,B: a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ B2 ) @ ( produc663418545od_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member_a @ A @ A4 )
% 0.26/0.62 & ( member2057358096od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_237_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,B2: product_prod_a_a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ B2 ) @ ( produc197318472od_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 & ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_238_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,B2: a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_a] :
% 0.26/0.62 ( ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ B2 ) @ ( produc4724255_a_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 & ( member_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_239_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,B2: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B2 ) @ ( produc1460477704od_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 & ( member2057358096od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_240_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: a,B2: a,A4: set_a,B: a > set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member_a @ A @ A4 )
% 0.26/0.62 & ( member_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_241_mem__Sigma__iff,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 & ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Sigma_iff
% 0.26/0.62 thf(fact_242_SigmaI,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,A4: set_Product_prod_a_a,B2: a,B: product_prod_a_a > set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 => ( ( member_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ B2 ) @ ( produc1282482655_a_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_243_SigmaI,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,A4: set_Product_prod_a_a,B2: produc1572603623od_a_a,B: product_prod_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 => ( ( member2057358096od_a_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ B2 ) @ ( produc1227942600od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_244_SigmaI,axiom,
% 0.26/0.62 ! [A: a,A4: set_a,B2: product_prod_a_a,B: a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member_a @ A @ A4 )
% 0.26/0.62 => ( ( member449909584od_a_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ B2 ) @ ( produc520147185od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_245_SigmaI,axiom,
% 0.26/0.62 ! [A: a,A4: set_a,B2: produc1572603623od_a_a,B: a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member_a @ A @ A4 )
% 0.26/0.62 => ( ( member2057358096od_a_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ B2 ) @ ( produc663418545od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_246_SigmaI,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: product_prod_a_a,B: produc1572603623od_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 => ( ( member449909584od_a_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ B2 ) @ ( produc197318472od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_247_SigmaI,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: a,B: produc1572603623od_a_a > set_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 => ( ( member_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ B2 ) @ ( produc4724255_a_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_248_SigmaI,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: produc1572603623od_a_a,B: produc1572603623od_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 => ( ( member2057358096od_a_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B2 ) @ ( produc1460477704od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_249_SigmaI,axiom,
% 0.26/0.62 ! [A: a,A4: set_a,B2: a,B: a > set_a] :
% 0.26/0.62 ( ( member_a @ A @ A4 )
% 0.26/0.62 => ( ( member_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_250_SigmaI,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 => ( ( member449909584od_a_a @ B2 @ ( B @ A ) )
% 0.26/0.62 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaI
% 0.26/0.62 thf(fact_251_SigmaE2,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_a] :
% 0.26/0.62 ( ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ B2 ) @ ( produc1282482655_a_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 => ~ ( member_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_252_SigmaE2,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ B2 ) @ ( produc1227942600od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 => ~ ( member2057358096od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_253_SigmaE2,axiom,
% 0.26/0.62 ! [A: a,B2: product_prod_a_a,A4: set_a,B: a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ B2 ) @ ( produc520147185od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member_a @ A @ A4 )
% 0.26/0.62 => ~ ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_254_SigmaE2,axiom,
% 0.26/0.62 ! [A: a,B2: produc1572603623od_a_a,A4: set_a,B: a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ B2 ) @ ( produc663418545od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member_a @ A @ A4 )
% 0.26/0.62 => ~ ( member2057358096od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_255_SigmaE2,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,B2: product_prod_a_a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ B2 ) @ ( produc197318472od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 => ~ ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_256_SigmaE2,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,B2: a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_a] :
% 0.26/0.62 ( ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ B2 ) @ ( produc4724255_a_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 => ~ ( member_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_257_SigmaE2,axiom,
% 0.26/0.62 ! [A: produc1572603623od_a_a,B2: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B2 ) @ ( produc1460477704od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member2057358096od_a_a @ A @ A4 )
% 0.26/0.62 => ~ ( member2057358096od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_258_SigmaE2,axiom,
% 0.26/0.62 ! [A: a,B2: a,A4: set_a,B: a > set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member_a @ A @ A4 )
% 0.26/0.62 => ~ ( member_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_259_SigmaE2,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ( ( member449909584od_a_a @ A @ A4 )
% 0.26/0.62 => ~ ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE2
% 0.26/0.62 thf(fact_260_SigmaD2,axiom,
% 0.26/0.62 ! [A: a,B2: a,A4: set_a,B: a > set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
% 0.26/0.62 => ( member_a @ B2 @ ( B @ A ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaD2
% 0.26/0.62 thf(fact_261_SigmaD2,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
% 0.26/0.62 => ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaD2
% 0.26/0.62 thf(fact_262_SigmaD1,axiom,
% 0.26/0.62 ! [A: a,B2: a,A4: set_a,B: a > set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
% 0.26/0.62 => ( member_a @ A @ A4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaD1
% 0.26/0.62 thf(fact_263_SigmaD1,axiom,
% 0.26/0.62 ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
% 0.26/0.62 => ( member449909584od_a_a @ A @ A4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaD1
% 0.26/0.62 thf(fact_264_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc1016684094_a_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_a] :
% 0.26/0.62 ( ( member1403138919_a_a_a @ C2 @ ( produc1282482655_a_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: a] :
% 0.26/0.62 ( ( member_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc2061588782_a_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_265_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc772425383od_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member122808528od_a_a @ C2 @ ( produc1227942600od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc1555606807od_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_266_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc1921647824od_a_a,A4: set_a,B: a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member160619001od_a_a @ C2 @ ( produc520147185od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc1299253312od_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_267_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc1555800720od_a_a,A4: set_a,B: a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member448091577od_a_a @ C2 @ ( produc663418545od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc1095491584od_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_268_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc47586087od_a_a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member1545452880od_a_a @ C2 @ ( produc197318472od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc524982679od_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_269_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc1683075710_a_a_a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_a] :
% 0.26/0.62 ( ( member575366567_a_a_a @ C2 @ ( produc4724255_a_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: a] :
% 0.26/0.62 ( ( member_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc436797294_a_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_270_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc1990712039od_a_a,A4: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member1899387664od_a_a @ C2 @ ( produc1460477704od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc1935643479od_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_271_SigmaE,axiom,
% 0.26/0.62 ! [C2: product_prod_a_a,A4: set_a,B: a > set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ C2 @ ( product_Sigma_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: a] :
% 0.26/0.62 ( ( member_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( product_Pair_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_272_SigmaE,axiom,
% 0.26/0.62 ! [C2: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ C2 @ ( produc304751368od_a_a @ A4 @ B ) )
% 0.26/0.62 => ~ ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.62 => ! [Y3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ Y3 @ ( B @ X3 ) )
% 0.26/0.62 => ( C2
% 0.26/0.62 != ( produc1474507607od_a_a @ X3 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % SigmaE
% 0.26/0.62 thf(fact_273_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc1016684094_a_a_a,A4: set_Product_prod_a_a,B: set_a] :
% 0.26/0.62 ( ( member1403138919_a_a_a @ X
% 0.26/0.62 @ ( produc1282482655_a_a_a @ A4
% 0.26/0.62 @ ^ [Uu: product_prod_a_a] : B ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ ( produc1805832986_a_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member_a @ ( produc1954021468_a_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_274_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc772425383od_a_a,A4: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member122808528od_a_a @ X
% 0.26/0.62 @ ( produc1227942600od_a_a @ A4
% 0.26/0.62 @ ^ [Uu: product_prod_a_a] : B ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ ( produc1775747843od_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member2057358096od_a_a @ ( produc1055472197od_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_275_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc1921647824od_a_a,A4: set_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ( member160619001od_a_a @ X
% 0.26/0.62 @ ( produc520147185od_a_a @ A4
% 0.26/0.62 @ ^ [Uu: a] : B ) )
% 0.26/0.62 = ( ( member_a @ ( produc1043497516od_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member449909584od_a_a @ ( produc1191685998od_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_276_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc1555800720od_a_a,A4: set_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member448091577od_a_a @ X
% 0.26/0.62 @ ( produc663418545od_a_a @ A4
% 0.26/0.62 @ ^ [Uu: a] : B ) )
% 0.26/0.62 = ( ( member_a @ ( produc530563564od_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member2057358096od_a_a @ ( produc921029422od_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_277_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc47586087od_a_a,A4: set_Pr1948701895od_a_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ( member1545452880od_a_a @ X
% 0.26/0.62 @ ( produc197318472od_a_a @ A4
% 0.26/0.62 @ ^ [Uu: produc1572603623od_a_a] : B ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ ( produc745123715od_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member449909584od_a_a @ ( produc24848069od_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_278_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc1683075710_a_a_a,A4: set_Pr1948701895od_a_a,B: set_a] :
% 0.26/0.62 ( ( member575366567_a_a_a @ X
% 0.26/0.62 @ ( produc4724255_a_a_a @ A4
% 0.26/0.62 @ ^ [Uu: produc1572603623od_a_a] : B ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ ( produc2019352922_a_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member_a @ ( produc262335132_a_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_279_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc1990712039od_a_a,A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( member1899387664od_a_a @ X
% 0.26/0.62 @ ( produc1460477704od_a_a @ A4
% 0.26/0.62 @ ^ [Uu: produc1572603623od_a_a] : B ) )
% 0.26/0.62 = ( ( member2057358096od_a_a @ ( produc303632707od_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member2057358096od_a_a @ ( produc1441227909od_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_280_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: product_prod_a_a,A4: set_a,B: set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X
% 0.26/0.62 @ ( product_Sigma_a_a @ A4
% 0.26/0.62 @ ^ [Uu: a] : B ) )
% 0.26/0.62 = ( ( member_a @ ( product_fst_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member_a @ ( product_snd_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_281_mem__Times__iff,axiom,
% 0.26/0.62 ! [X: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X
% 0.26/0.62 @ ( produc304751368od_a_a @ A4
% 0.26/0.62 @ ^ [Uu: product_prod_a_a] : B ) )
% 0.26/0.62 = ( ( member449909584od_a_a @ ( produc2115494211od_a_a @ X ) @ A4 )
% 0.26/0.62 & ( member449909584od_a_a @ ( produc368344197od_a_a @ X ) @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Times_iff
% 0.26/0.62 thf(fact_282_member__product,axiom,
% 0.26/0.62 ! [X: product_prod_a_a,A4: set_a,B: set_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X @ ( product_product_a_a @ A4 @ B ) )
% 0.26/0.62 = ( member449909584od_a_a @ X
% 0.26/0.62 @ ( product_Sigma_a_a @ A4
% 0.26/0.62 @ ^ [Uu: a] : B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % member_product
% 0.26/0.62 thf(fact_283_member__product,axiom,
% 0.26/0.62 ! [X: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X @ ( produc905674258od_a_a @ A4 @ B ) )
% 0.26/0.62 = ( member2057358096od_a_a @ X
% 0.26/0.62 @ ( produc304751368od_a_a @ A4
% 0.26/0.62 @ ^ [Uu: product_prod_a_a] : B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % member_product
% 0.26/0.62 thf(fact_284_subsetI,axiom,
% 0.26/0.62 ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ X3 @ B ) )
% 0.26/0.62 => ( ord_le1824328871od_a_a @ A4 @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_285_subsetI,axiom,
% 0.26/0.62 ! [A4: set_a,B: set_a] :
% 0.26/0.62 ( ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ A4 )
% 0.26/0.62 => ( member_a @ X3 @ B ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ A4 @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_286_subsetI,axiom,
% 0.26/0.62 ! [A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ X3 @ B ) )
% 0.26/0.62 => ( ord_le456379495od_a_a @ A4 @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_287_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_288_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_Product_prod_a_a,F: product_prod_a_a > a,B: set_a] :
% 0.26/0.62 ( ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_289_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_290_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_a,F: a > product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_291_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_a,F: a > a,B: set_a] :
% 0.26/0.62 ( ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ A4 )
% 0.26/0.62 => ( member_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ ( image_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_292_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_a,F: a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_le456379495od_a_a @ ( image_1763923566od_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_293_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.62 ( ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_294_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > a,B: set_a] :
% 0.26/0.62 ( ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ ( image_1105229276_a_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_295_image__subsetI,axiom,
% 0.26/0.62 ! [A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ ( F @ X3 ) @ B ) )
% 0.26/0.62 => ( ord_le456379495od_a_a @ ( image_236793797od_a_a @ F @ A4 ) @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_296_subrelI,axiom,
% 0.26/0.62 ! [R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
% 0.26/0.62 ( ! [X3: a,Y3: a] :
% 0.26/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.26/0.62 => ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ S ) )
% 0.26/0.62 => ( ord_le1824328871od_a_a @ R @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % subrelI
% 0.26/0.62 thf(fact_297_subrelI,axiom,
% 0.26/0.62 ! [R: set_Pr1948701895od_a_a,S: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.26/0.62 => ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ S ) )
% 0.26/0.62 => ( ord_le456379495od_a_a @ R @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % subrelI
% 0.26/0.62 thf(fact_298_subset__iff,axiom,
% 0.26/0.62 ( ord_le1824328871od_a_a
% 0.26/0.62 = ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
% 0.26/0.62 ! [T2: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ T2 @ A6 )
% 0.26/0.62 => ( member449909584od_a_a @ T2 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_299_subset__iff,axiom,
% 0.26/0.62 ( ord_less_eq_set_a
% 0.26/0.62 = ( ^ [A6: set_a,B5: set_a] :
% 0.26/0.62 ! [T2: a] :
% 0.26/0.62 ( ( member_a @ T2 @ A6 )
% 0.26/0.62 => ( member_a @ T2 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_300_subset__iff,axiom,
% 0.26/0.62 ( ord_le456379495od_a_a
% 0.26/0.62 = ( ^ [A6: set_Pr1948701895od_a_a,B5: set_Pr1948701895od_a_a] :
% 0.26/0.62 ! [T2: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ T2 @ A6 )
% 0.26/0.62 => ( member2057358096od_a_a @ T2 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_301_subset__eq,axiom,
% 0.26/0.62 ( ord_le1824328871od_a_a
% 0.26/0.62 = ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
% 0.26/0.62 ! [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ A6 )
% 0.26/0.62 => ( member449909584od_a_a @ X4 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_302_subset__eq,axiom,
% 0.26/0.62 ( ord_less_eq_set_a
% 0.26/0.62 = ( ^ [A6: set_a,B5: set_a] :
% 0.26/0.62 ! [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ A6 )
% 0.26/0.62 => ( member_a @ X4 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_303_subset__eq,axiom,
% 0.26/0.62 ( ord_le456379495od_a_a
% 0.26/0.62 = ( ^ [A6: set_Pr1948701895od_a_a,B5: set_Pr1948701895od_a_a] :
% 0.26/0.62 ! [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ A6 )
% 0.26/0.62 => ( member2057358096od_a_a @ X4 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_304_subsetD,axiom,
% 0.26/0.62 ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,C2: product_prod_a_a] :
% 0.26/0.62 ( ( ord_le1824328871od_a_a @ A4 @ B )
% 0.26/0.62 => ( ( member449909584od_a_a @ C2 @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ C2 @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_305_subsetD,axiom,
% 0.26/0.62 ! [A4: set_a,B: set_a,C2: a] :
% 0.26/0.62 ( ( ord_less_eq_set_a @ A4 @ B )
% 0.26/0.62 => ( ( member_a @ C2 @ A4 )
% 0.26/0.62 => ( member_a @ C2 @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_306_subsetD,axiom,
% 0.26/0.62 ! [A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C2: produc1572603623od_a_a] :
% 0.26/0.62 ( ( ord_le456379495od_a_a @ A4 @ B )
% 0.26/0.62 => ( ( member2057358096od_a_a @ C2 @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ C2 @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_307_in__mono,axiom,
% 0.26/0.62 ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,X: product_prod_a_a] :
% 0.26/0.62 ( ( ord_le1824328871od_a_a @ A4 @ B )
% 0.26/0.62 => ( ( member449909584od_a_a @ X @ A4 )
% 0.26/0.62 => ( member449909584od_a_a @ X @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_308_in__mono,axiom,
% 0.26/0.62 ! [A4: set_a,B: set_a,X: a] :
% 0.26/0.62 ( ( ord_less_eq_set_a @ A4 @ B )
% 0.26/0.62 => ( ( member_a @ X @ A4 )
% 0.26/0.62 => ( member_a @ X @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_309_in__mono,axiom,
% 0.26/0.62 ! [A4: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,X: produc1572603623od_a_a] :
% 0.26/0.62 ( ( ord_le456379495od_a_a @ A4 @ B )
% 0.26/0.62 => ( ( member2057358096od_a_a @ X @ A4 )
% 0.26/0.62 => ( member2057358096od_a_a @ X @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_310_prop__restrict,axiom,
% 0.26/0.62 ! [X: product_prod_a_a,Z2: set_Product_prod_a_a,X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.26/0.62 ( ( member449909584od_a_a @ X @ Z2 )
% 0.26/0.62 => ( ( ord_le1824328871od_a_a @ Z2
% 0.26/0.62 @ ( collec645855634od_a_a
% 0.26/0.62 @ ^ [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ X5 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) )
% 0.26/0.62 => ( P2 @ X ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prop_restrict
% 0.26/0.62 thf(fact_311_prop__restrict,axiom,
% 0.26/0.62 ! [X: a,Z2: set_a,X5: set_a,P2: a > $o] :
% 0.26/0.62 ( ( member_a @ X @ Z2 )
% 0.26/0.62 => ( ( ord_less_eq_set_a @ Z2
% 0.26/0.62 @ ( collect_a
% 0.26/0.62 @ ^ [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ X5 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) )
% 0.26/0.62 => ( P2 @ X ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prop_restrict
% 0.26/0.62 thf(fact_312_prop__restrict,axiom,
% 0.26/0.62 ! [X: produc1572603623od_a_a,Z2: set_Pr1948701895od_a_a,X5: set_Pr1948701895od_a_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X @ Z2 )
% 0.26/0.62 => ( ( ord_le456379495od_a_a @ Z2
% 0.26/0.62 @ ( collec1635618130od_a_a
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ X5 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) )
% 0.26/0.62 => ( P2 @ X ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % prop_restrict
% 0.26/0.62 thf(fact_313_Collect__restrict,axiom,
% 0.26/0.62 ! [X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.26/0.62 ( ord_le1824328871od_a_a
% 0.26/0.62 @ ( collec645855634od_a_a
% 0.26/0.62 @ ^ [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ X5 )
% 0.26/0.62 & ( P2 @ X4 ) ) )
% 0.26/0.62 @ X5 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_restrict
% 0.26/0.62 thf(fact_314_Collect__restrict,axiom,
% 0.26/0.62 ! [X5: set_a,P2: a > $o] :
% 0.26/0.62 ( ord_less_eq_set_a
% 0.26/0.62 @ ( collect_a
% 0.26/0.62 @ ^ [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ X5 )
% 0.26/0.62 & ( P2 @ X4 ) ) )
% 0.26/0.62 @ X5 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_restrict
% 0.26/0.62 thf(fact_315_Collect__restrict,axiom,
% 0.26/0.62 ! [X5: set_Pr1948701895od_a_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.62 ( ord_le456379495od_a_a
% 0.26/0.62 @ ( collec1635618130od_a_a
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ X5 )
% 0.26/0.62 & ( P2 @ X4 ) ) )
% 0.26/0.62 @ X5 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_restrict
% 0.26/0.62 thf(fact_316_Collect__subset,axiom,
% 0.26/0.62 ! [A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.26/0.62 ( ord_le1824328871od_a_a
% 0.26/0.62 @ ( collec645855634od_a_a
% 0.26/0.62 @ ^ [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) )
% 0.26/0.62 @ A4 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_subset
% 0.26/0.62 thf(fact_317_Collect__subset,axiom,
% 0.26/0.62 ! [A4: set_a,P2: a > $o] :
% 0.26/0.62 ( ord_less_eq_set_a
% 0.26/0.62 @ ( collect_a
% 0.26/0.62 @ ^ [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) )
% 0.26/0.62 @ A4 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_subset
% 0.26/0.62 thf(fact_318_Collect__subset,axiom,
% 0.26/0.62 ! [A4: set_Pr1948701895od_a_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.62 ( ord_le456379495od_a_a
% 0.26/0.62 @ ( collec1635618130od_a_a
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) )
% 0.26/0.62 @ A4 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_subset
% 0.26/0.62 thf(fact_319_subset__Collect__iff,axiom,
% 0.26/0.62 ! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.26/0.62 ( ( ord_le1824328871od_a_a @ B @ A4 )
% 0.26/0.62 => ( ( ord_le1824328871od_a_a @ B
% 0.26/0.62 @ ( collec645855634od_a_a
% 0.26/0.62 @ ^ [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) )
% 0.26/0.62 = ( ! [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ B )
% 0.26/0.62 => ( P2 @ X4 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_Collect_iff
% 0.26/0.62 thf(fact_320_subset__Collect__iff,axiom,
% 0.26/0.62 ! [B: set_a,A4: set_a,P2: a > $o] :
% 0.26/0.62 ( ( ord_less_eq_set_a @ B @ A4 )
% 0.26/0.62 => ( ( ord_less_eq_set_a @ B
% 0.26/0.62 @ ( collect_a
% 0.26/0.62 @ ^ [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) )
% 0.26/0.62 = ( ! [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ B )
% 0.26/0.62 => ( P2 @ X4 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_Collect_iff
% 0.26/0.62 thf(fact_321_subset__Collect__iff,axiom,
% 0.26/0.62 ! [B: set_Pr1948701895od_a_a,A4: set_Pr1948701895od_a_a,P2: produc1572603623od_a_a > $o] :
% 0.26/0.62 ( ( ord_le456379495od_a_a @ B @ A4 )
% 0.26/0.62 => ( ( ord_le456379495od_a_a @ B
% 0.26/0.62 @ ( collec1635618130od_a_a
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) )
% 0.26/0.62 = ( ! [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ B )
% 0.26/0.62 => ( P2 @ X4 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_Collect_iff
% 0.26/0.62 thf(fact_322_subset__CollectI,axiom,
% 0.26/0.62 ! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,Q: product_prod_a_a > $o,P2: product_prod_a_a > $o] :
% 0.26/0.62 ( ( ord_le1824328871od_a_a @ B @ A4 )
% 0.26/0.62 => ( ! [X3: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X3 @ B )
% 0.26/0.62 => ( ( Q @ X3 )
% 0.26/0.62 => ( P2 @ X3 ) ) )
% 0.26/0.62 => ( ord_le1824328871od_a_a
% 0.26/0.62 @ ( collec645855634od_a_a
% 0.26/0.62 @ ^ [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ B )
% 0.26/0.62 & ( Q @ X4 ) ) )
% 0.26/0.62 @ ( collec645855634od_a_a
% 0.26/0.62 @ ^ [X4: product_prod_a_a] :
% 0.26/0.62 ( ( member449909584od_a_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_CollectI
% 0.26/0.62 thf(fact_323_subset__CollectI,axiom,
% 0.26/0.62 ! [B: set_a,A4: set_a,Q: a > $o,P2: a > $o] :
% 0.26/0.62 ( ( ord_less_eq_set_a @ B @ A4 )
% 0.26/0.62 => ( ! [X3: a] :
% 0.26/0.62 ( ( member_a @ X3 @ B )
% 0.26/0.62 => ( ( Q @ X3 )
% 0.26/0.62 => ( P2 @ X3 ) ) )
% 0.26/0.62 => ( ord_less_eq_set_a
% 0.26/0.62 @ ( collect_a
% 0.26/0.62 @ ^ [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ B )
% 0.26/0.62 & ( Q @ X4 ) ) )
% 0.26/0.62 @ ( collect_a
% 0.26/0.62 @ ^ [X4: a] :
% 0.26/0.62 ( ( member_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_CollectI
% 0.26/0.62 thf(fact_324_subset__CollectI,axiom,
% 0.26/0.62 ! [B: set_Pr1948701895od_a_a,A4: set_Pr1948701895od_a_a,Q: produc1572603623od_a_a > $o,P2: produc1572603623od_a_a > $o] :
% 0.26/0.62 ( ( ord_le456379495od_a_a @ B @ A4 )
% 0.26/0.62 => ( ! [X3: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X3 @ B )
% 0.26/0.62 => ( ( Q @ X3 )
% 0.26/0.62 => ( P2 @ X3 ) ) )
% 0.26/0.62 => ( ord_le456379495od_a_a
% 0.26/0.62 @ ( collec1635618130od_a_a
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ B )
% 0.26/0.62 & ( Q @ X4 ) ) )
% 0.26/0.62 @ ( collec1635618130od_a_a
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] :
% 0.26/0.62 ( ( member2057358096od_a_a @ X4 @ A4 )
% 0.26/0.62 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_CollectI
% 0.26/0.62 thf(fact_325_pred__subset__eq,axiom,
% 0.26/0.62 ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
% 0.26/0.62 ( ( ord_le1347718902_a_a_o
% 0.26/0.62 @ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ R2 )
% 0.26/0.62 @ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ S3 ) )
% 0.26/0.62 = ( ord_le1824328871od_a_a @ R2 @ S3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % pred_subset_eq
% 0.26/0.62 thf(fact_326_pred__subset__eq,axiom,
% 0.26/0.62 ! [R2: set_a,S3: set_a] :
% 0.26/0.62 ( ( ord_less_eq_a_o
% 0.26/0.62 @ ^ [X4: a] : ( member_a @ X4 @ R2 )
% 0.26/0.62 @ ^ [X4: a] : ( member_a @ X4 @ S3 ) )
% 0.26/0.62 = ( ord_less_eq_set_a @ R2 @ S3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % pred_subset_eq
% 0.26/0.62 thf(fact_327_pred__subset__eq,axiom,
% 0.26/0.62 ! [R2: set_Pr1948701895od_a_a,S3: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( ord_le1525442358_a_a_o
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ R2 )
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ S3 ) )
% 0.26/0.62 = ( ord_le456379495od_a_a @ R2 @ S3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % pred_subset_eq
% 0.26/0.62 thf(fact_328_less__eq__set__def,axiom,
% 0.26/0.62 ( ord_le1824328871od_a_a
% 0.26/0.62 = ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
% 0.26/0.62 ( ord_le1347718902_a_a_o
% 0.26/0.62 @ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
% 0.26/0.62 @ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_eq_set_def
% 0.26/0.62 thf(fact_329_less__eq__set__def,axiom,
% 0.26/0.62 ( ord_less_eq_set_a
% 0.26/0.62 = ( ^ [A6: set_a,B5: set_a] :
% 0.26/0.62 ( ord_less_eq_a_o
% 0.26/0.62 @ ^ [X4: a] : ( member_a @ X4 @ A6 )
% 0.26/0.62 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_eq_set_def
% 0.26/0.62 thf(fact_330_less__eq__set__def,axiom,
% 0.26/0.62 ( ord_le456379495od_a_a
% 0.26/0.62 = ( ^ [A6: set_Pr1948701895od_a_a,B5: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ord_le1525442358_a_a_o
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ A6 )
% 0.26/0.62 @ ^ [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_eq_set_def
% 0.26/0.62 thf(fact_331_pred__subset__eq2,axiom,
% 0.26/0.62 ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
% 0.26/0.62 ( ( ord_less_eq_a_a_o
% 0.26/0.62 @ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 )
% 0.26/0.62 @ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) )
% 0.26/0.62 = ( ord_le1824328871od_a_a @ R2 @ S3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % pred_subset_eq2
% 0.26/0.62 thf(fact_332_pred__subset__eq2,axiom,
% 0.26/0.62 ! [R2: set_Pr1948701895od_a_a,S3: set_Pr1948701895od_a_a] :
% 0.26/0.62 ( ( ord_le252190158_a_a_o
% 0.26/0.62 @ ^ [X4: product_prod_a_a,Y4: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R2 )
% 0.26/0.62 @ ^ [X4: product_prod_a_a,Y4: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ S3 ) )
% 0.26/0.62 = ( ord_le456379495od_a_a @ R2 @ S3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % pred_subset_eq2
% 0.26/0.62 thf(fact_333_GrD1,axiom,
% 0.26/0.62 ! [X: a,Fx: a,A4: set_a,F: a > a] :
% 0.26/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
% 0.26/0.62 => ( member_a @ X @ A4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % GrD1
% 0.26/0.62 thf(fact_334_GrD1,axiom,
% 0.26/0.62 ! [X: product_prod_a_a,Fx: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
% 0.26/0.71 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Fx ) @ ( bNF_Gr1372473186od_a_a @ A4 @ F ) )
% 0.26/0.71 => ( member449909584od_a_a @ X @ A4 ) ) ).
% 0.26/0.71
% 0.26/0.71 % GrD1
% 0.26/0.71 thf(fact_335_GrD2,axiom,
% 0.26/0.71 ! [X: a,Fx: a,A4: set_a,F: a > a] :
% 0.26/0.71 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
% 0.26/0.71 => ( ( F @ X )
% 0.26/0.71 = Fx ) ) ).
% 0.26/0.71
% 0.26/0.71 % GrD2
% 0.26/0.71 thf(fact_336_GrD2,axiom,
% 0.26/0.71 ! [X: product_prod_a_a,Fx: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
% 0.26/0.71 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Fx ) @ ( bNF_Gr1372473186od_a_a @ A4 @ F ) )
% 0.26/0.71 => ( ( F @ X )
% 0.26/0.71 = Fx ) ) ).
% 0.26/0.71
% 0.26/0.71 % GrD2
% 0.26/0.71 thf(fact_337_all__not__in__conv,axiom,
% 0.26/0.71 ! [A4: set_Product_prod_a_a] :
% 0.26/0.71 ( ( ! [X4: product_prod_a_a] :
% 0.26/0.71 ~ ( member449909584od_a_a @ X4 @ A4 ) )
% 0.26/0.71 = ( A4 = bot_bo2131659635od_a_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % all_not_in_conv
% 0.26/0.71 thf(fact_338_all__not__in__conv,axiom,
% 0.26/0.71 ! [A4: set_a] :
% 0.26/0.71 ( ( ! [X4: a] :
% 0.26/0.71 ~ ( member_a @ X4 @ A4 ) )
% 0.26/0.71 = ( A4 = bot_bot_set_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % all_not_in_conv
% 0.26/0.71 thf(fact_339_all__not__in__conv,axiom,
% 0.26/0.71 ! [A4: set_Pr1948701895od_a_a] :
% 0.26/0.71 ( ( ! [X4: produc1572603623od_a_a] :
% 0.26/0.71 ~ ( member2057358096od_a_a @ X4 @ A4 ) )
% 0.26/0.71 = ( A4 = bot_bo1116205875od_a_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % all_not_in_conv
% 0.26/0.71 thf(fact_340_empty__iff,axiom,
% 0.26/0.71 ! [C2: product_prod_a_a] :
% 0.26/0.71 ~ ( member449909584od_a_a @ C2 @ bot_bo2131659635od_a_a ) ).
% 0.26/0.71
% 0.26/0.71 % empty_iff
% 0.26/0.71 thf(fact_341_empty__iff,axiom,
% 0.26/0.71 ! [C2: a] :
% 0.26/0.71 ~ ( member_a @ C2 @ bot_bot_set_a ) ).
% 0.26/0.71
% 0.26/0.71 % empty_iff
% 0.26/0.71 thf(fact_342_empty__iff,axiom,
% 0.26/0.71 ! [C2: produc1572603623od_a_a] :
% 0.26/0.71 ~ ( member2057358096od_a_a @ C2 @ bot_bo1116205875od_a_a ) ).
% 0.26/0.71
% 0.26/0.71 % empty_iff
% 0.26/0.71 thf(fact_343_ex__in__conv,axiom,
% 0.26/0.71 ! [A4: set_Product_prod_a_a] :
% 0.26/0.71 ( ( ? [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
% 0.26/0.71 = ( A4 != bot_bo2131659635od_a_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % ex_in_conv
% 0.26/0.71 thf(fact_344_ex__in__conv,axiom,
% 0.26/0.71 ! [A4: set_a] :
% 0.26/0.71 ( ( ? [X4: a] : ( member_a @ X4 @ A4 ) )
% 0.26/0.71 = ( A4 != bot_bot_set_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % ex_in_conv
% 0.26/0.71 thf(fact_345_ex__in__conv,axiom,
% 0.26/0.71 ! [A4: set_Pr1948701895od_a_a] :
% 0.26/0.71 ( ( ? [X4: produc1572603623od_a_a] : ( member2057358096od_a_a @ X4 @ A4 ) )
% 0.26/0.71 = ( A4 != bot_bo1116205875od_a_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % ex_in_conv
% 0.26/0.71 thf(fact_346_equals0I,axiom,
% 0.26/0.71 ! [A4: set_Product_prod_a_a] :
% 0.26/0.71 ( ! [Y3: product_prod_a_a] :
% 0.26/0.71 ~ ( member449909584od_a_a @ Y3 @ A4 )
% 0.26/0.71 => ( A4 = bot_bo2131659635od_a_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % equals0I
% 0.26/0.71 thf(fact_347_equals0I,axiom,
% 0.26/0.71 ! [A4: set_a] :
% 0.26/0.71 ( ! [Y3: a] :
% 0.26/0.71 ~ ( member_a @ Y3 @ A4 )
% 0.26/0.71 => ( A4 = bot_bot_set_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % equals0I
% 0.26/0.71 thf(fact_348_equals0I,axiom,
% 0.26/0.71 ! [A4: set_Pr1948701895od_a_a] :
% 0.26/0.71 ( ! [Y3: produc1572603623od_a_a] :
% 0.26/0.71 ~ ( member2057358096od_a_a @ Y3 @ A4 )
% 0.26/0.71 => ( A4 = bot_bo1116205875od_a_a ) ) ).
% 0.26/0.71
% 0.26/0.71 % equals0I
% 0.26/0.71 thf(fact_349_equals0D,axiom,
% 0.26/0.71 ! [A4: set_Product_prod_a_a,A: product_prod_a_a] :
% 0.26/0.71 ( ( A4 = bot_bo2131659635od_a_a )
% 0.26/0.71 => ~ ( member449909584od_a_a @ A @ A4 ) ) ).
% 0.26/0.71
% 0.26/0.71 % equals0D
% 0.26/0.71 thf(fact_350_equals0D,axiom,
% 0.26/0.71 ! [A4: set_a,A: a] :
% 0.26/0.71 ( ( A4 = bot_bot_set_a )
% 0.26/0.71 => ~ ( member_a @ A @ A4 ) ) ).
% 0.26/0.71
% 0.26/0.71 % equals0D
% 0.26/0.71 thf(fact_351_equals0D,axiom,
% 0.26/0.71 ! [A4: set_Pr1948701895od_a_a,A: produc1572603623od_a_a] :
% 0.26/0.71 ( ( A4 = bot_bo1116205875od_a_a )
% 0.26/0.71 => ~ ( member2057358096od_a_a @ A @ A4 ) ) ).
% 0.26/0.71
% 0.26/0.71 % equals0D
% 0.26/0.71 thf(fact_352_emptyE,axiom,
% 0.26/0.71 ! [A: product_prod_a_a] :
% 0.26/0.71 ~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ) ).
% 0.26/0.71
% 0.26/0.71 % emptyE
% 0.26/0.71 thf(fact_353_emptyE,axiom,
% 0.26/0.71 ! [A: a] :
% 0.26/0.71 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 0.26/0.71
% 0.26/0.71 % emptyE
% 0.26/0.71 thf(fact_354_emptyE,axiom,
% 0.26/0.71 ! [A: produc1572603623od_a_a] :
% 0.26/0.71 ~ ( member2057358096od_a_a @ A @ bot_bo1116205875od_a_a ) ).
% 0.26/0.71
% 0.26/0.71 % emptyE
% 0.26/0.71
% 0.26/0.71 % Conjectures (1)
% 0.26/0.71 thf(conj_0,conjecture,
% 0.26/0.71 member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ).
% 0.26/0.71
% 0.26/0.71 %------------------------------------------------------------------------------
% 0.26/0.71 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wjGbg5LVSI/cvc5---1.0.5_1472.p...
% 0.26/0.71 (declare-sort $$unsorted 0)
% 0.26/0.71 (declare-sort tptp.set_Pr2081559751od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr532616391od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1423126247od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1056976615od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr660101255od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1546279079od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr1295299783od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1990712039od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr1194146439od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr231806599od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr729215751_a_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr173461255od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc772425383od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc2010915495od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1120419623_a_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc47586087od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr195866352od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr6137822_a_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1555800720od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1683075710_a_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr1948701895od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1572603623od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr681306928od_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Pr1689873822_a_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1921647824od_a_a 0)
% 0.26/0.71 (declare-sort tptp.produc1016684094_a_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_Product_prod_a_a 0)
% 0.26/0.71 (declare-sort tptp.product_prod_a_a 0)
% 0.26/0.71 (declare-sort tptp.set_a 0)
% 0.26/0.71 (declare-sort tptp.a 0)
% 0.26/0.71 (declare-fun tptp.bNF_Gr1372473186od_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.product_prod_a_a)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.bNF_Gr_a_a (tptp.set_a (-> tptp.a tptp.a)) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.bNF_Gr533818957od_a_a (tptp.set_Pr1948701895od_a_a (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a) (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.bNF_Gr356189709_a_a_a (tptp.set_Pr1948701895od_a_a (-> tptp.produc1572603623od_a_a tptp.a) (-> tptp.produc1572603623od_a_a tptp.a)) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.bNF_Gr200450189od_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.product_prod_a_a) (-> tptp.product_prod_a_a tptp.product_prod_a_a)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.bNF_Gr1853143117_a_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.a) (-> tptp.product_prod_a_a tptp.a)) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.bNF_Gr1715025636od_a_a (tptp.set_a (-> tptp.a tptp.product_prod_a_a) (-> tptp.a tptp.product_prod_a_a)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.bNF_Gr423046308_a_a_a (tptp.set_a (-> tptp.a tptp.a) (-> tptp.a tptp.a)) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.minus_107310383_a_a_o ((-> tptp.produc1572603623od_a_a Bool) (-> tptp.produc1572603623od_a_a Bool) tptp.produc1572603623od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.minus_1797478127_a_a_o ((-> tptp.product_prod_a_a Bool) (-> tptp.product_prod_a_a Bool) tptp.product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.minus_minus_a_o ((-> tptp.a Bool) (-> tptp.a Bool) tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.minus_1034916142od_a_a (tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.minus_1507102574od_a_a (tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.minus_minus_set_a (tptp.set_a tptp.set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.order_491428350od_a_a (tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.order_359341630od_a_a (tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.order_preorder_on_a (tptp.set_a tptp.set_Product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.bot_bo1116205875od_a_a () tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.bot_bo2131659635od_a_a () tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.bot_bot_set_a () tptp.set_a)
% 0.26/0.71 (declare-fun tptp.ord_le1525442358_a_a_o ((-> tptp.produc1572603623od_a_a Bool) (-> tptp.produc1572603623od_a_a Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le252190158_a_a_o ((-> tptp.product_prod_a_a tptp.product_prod_a_a Bool) (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1347718902_a_a_o ((-> tptp.product_prod_a_a Bool) (-> tptp.product_prod_a_a Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_a_a_o ((-> tptp.a tptp.a Bool) (-> tptp.a tptp.a Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_a_o ((-> tptp.a Bool) (-> tptp.a Bool)) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le456379495od_a_a (tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1824328871od_a_a (tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.top_to2011536774_a_a_o (tptp.produc1572603623od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.top_to993969022_a_a_o (tptp.product_prod_a_a tptp.product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.top_to1483957574_a_a_o (tptp.product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.top_top_a_a_o (tptp.a tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.top_top_a_o (tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.top_to52711959od_a_a () tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.top_to398455383od_a_a () tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.top_top_set_a () tptp.set_a)
% 0.26/0.71 (declare-fun tptp.prefer1867335523od_a_a (tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.prefer74720675od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.prefer436369274d_as_a (tptp.a tptp.set_a tptp.set_Product_prod_a_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.prefer468349667od_a_a (tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a) tptp.set_Pr231806599od_a_a)
% 0.26/0.71 (declare-fun tptp.prefer1377343203od_a_a (tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a) tptp.set_Pr1194146439od_a_a)
% 0.26/0.71 (declare-fun tptp.prefer55414563od_a_a (tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.prefer1944486522_a_a_a (tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a) tptp.set_Pr1689873822_a_a_a)
% 0.26/0.71 (declare-fun tptp.prefer445484748od_a_a (tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a) tptp.set_Pr195866352od_a_a)
% 0.26/0.71 (declare-fun tptp.prefer701966604od_a_a (tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a) tptp.set_Pr681306928od_a_a)
% 0.26/0.71 (declare-fun tptp.prefer477097315od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.prefer161218362good_a (tptp.a tptp.set_a tptp.set_Product_prod_a_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.prefer926864306od_a_a (tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.prefer1498087410od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.prefer1676310729than_a (tptp.a tptp.set_a tptp.set_Product_prod_a_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.prefer1409946857od_a_a (tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.prefer1338892073od_a_a (tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.prefer1292084992ence_a (tptp.set_a tptp.set_Product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.produc539587415od_a_a (tptp.produc2010915495od_a_a tptp.produc2010915495od_a_a) tptp.produc1056976615od_a_a)
% 0.26/0.71 (declare-fun tptp.produc852390743od_a_a (tptp.produc772425383od_a_a tptp.produc772425383od_a_a) tptp.produc1423126247od_a_a)
% 0.26/0.71 (declare-fun tptp.produc1935643479od_a_a (tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a) tptp.produc1990712039od_a_a)
% 0.26/0.71 (declare-fun tptp.produc524982679od_a_a (tptp.produc1572603623od_a_a tptp.product_prod_a_a) tptp.produc47586087od_a_a)
% 0.26/0.71 (declare-fun tptp.produc436797294_a_a_a (tptp.produc1572603623od_a_a tptp.a) tptp.produc1683075710_a_a_a)
% 0.26/0.71 (declare-fun tptp.produc2054708503_a_a_a (tptp.produc1016684094_a_a_a tptp.produc1016684094_a_a_a) tptp.produc1120419623_a_a_a)
% 0.26/0.71 (declare-fun tptp.produc1573596055od_a_a (tptp.produc1555800720od_a_a tptp.produc1555800720od_a_a) tptp.produc1546279079od_a_a)
% 0.26/0.71 (declare-fun tptp.produc563767703od_a_a (tptp.produc1921647824od_a_a tptp.produc1921647824od_a_a) tptp.produc2010915495od_a_a)
% 0.26/0.71 (declare-fun tptp.produc1555606807od_a_a (tptp.product_prod_a_a tptp.produc1572603623od_a_a) tptp.produc772425383od_a_a)
% 0.26/0.71 (declare-fun tptp.produc1474507607od_a_a (tptp.product_prod_a_a tptp.product_prod_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc2061588782_a_a_a (tptp.product_prod_a_a tptp.a) tptp.produc1016684094_a_a_a)
% 0.26/0.71 (declare-fun tptp.produc1095491584od_a_a (tptp.a tptp.produc1572603623od_a_a) tptp.produc1555800720od_a_a)
% 0.26/0.71 (declare-fun tptp.produc1299253312od_a_a (tptp.a tptp.product_prod_a_a) tptp.produc1921647824od_a_a)
% 0.26/0.71 (declare-fun tptp.product_Pair_a_a (tptp.a tptp.a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc1460477704od_a_a (tptp.set_Pr1948701895od_a_a (-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)) tptp.set_Pr1295299783od_a_a)
% 0.26/0.71 (declare-fun tptp.produc197318472od_a_a (tptp.set_Pr1948701895od_a_a (-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)) tptp.set_Pr173461255od_a_a)
% 0.26/0.71 (declare-fun tptp.produc4724255_a_a_a (tptp.set_Pr1948701895od_a_a (-> tptp.produc1572603623od_a_a tptp.set_a)) tptp.set_Pr6137822_a_a_a)
% 0.26/0.71 (declare-fun tptp.produc1227942600od_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)) tptp.set_Pr1194146439od_a_a)
% 0.26/0.71 (declare-fun tptp.produc304751368od_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.produc1282482655_a_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.set_a)) tptp.set_Pr1689873822_a_a_a)
% 0.26/0.71 (declare-fun tptp.produc663418545od_a_a (tptp.set_a (-> tptp.a tptp.set_Pr1948701895od_a_a)) tptp.set_Pr195866352od_a_a)
% 0.26/0.71 (declare-fun tptp.produc520147185od_a_a (tptp.set_a (-> tptp.a tptp.set_Product_prod_a_a)) tptp.set_Pr681306928od_a_a)
% 0.26/0.71 (declare-fun tptp.product_Sigma_a_a (tptp.set_a (-> tptp.a tptp.set_a)) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc94438221_a_a_o ((-> tptp.produc1572603623od_a_a Bool) tptp.product_prod_a_a tptp.product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.product_curry_a_a_o ((-> tptp.product_prod_a_a Bool) tptp.a tptp.a) Bool)
% 0.26/0.71 (declare-fun tptp.produc1779756150od_a_a ((-> tptp.product_prod_a_a tptp.product_prod_a_a) (-> tptp.product_prod_a_a tptp.product_prod_a_a) tptp.produc1572603623od_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc363290532_a_a_a ((-> tptp.product_prod_a_a tptp.a) (-> tptp.product_prod_a_a tptp.a) tptp.produc1572603623od_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc2012818120od_a_a ((-> tptp.a tptp.product_prod_a_a) (-> tptp.a tptp.product_prod_a_a) tptp.product_prod_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc700022774_a_a_a ((-> tptp.a tptp.a) (-> tptp.a tptp.a) tptp.product_prod_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc303632707od_a_a (tptp.produc1990712039od_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc745123715od_a_a (tptp.produc47586087od_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc2019352922_a_a_a (tptp.produc1683075710_a_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc1775747843od_a_a (tptp.produc772425383od_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc2115494211od_a_a (tptp.produc1572603623od_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc1805832986_a_a_a (tptp.produc1016684094_a_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc530563564od_a_a (tptp.produc1555800720od_a_a) tptp.a)
% 0.26/0.71 (declare-fun tptp.produc1043497516od_a_a (tptp.produc1921647824od_a_a) tptp.a)
% 0.26/0.71 (declare-fun tptp.product_fst_a_a (tptp.product_prod_a_a) tptp.a)
% 0.26/0.71 (declare-fun tptp.produc1441227909od_a_a (tptp.produc1990712039od_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc24848069od_a_a (tptp.produc47586087od_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc262335132_a_a_a (tptp.produc1683075710_a_a_a) tptp.a)
% 0.26/0.71 (declare-fun tptp.produc1055472197od_a_a (tptp.produc772425383od_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc368344197od_a_a (tptp.produc1572603623od_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc1954021468_a_a_a (tptp.produc1016684094_a_a_a) tptp.a)
% 0.26/0.71 (declare-fun tptp.produc921029422od_a_a (tptp.produc1555800720od_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.produc1191685998od_a_a (tptp.produc1921647824od_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.product_snd_a_a (tptp.product_prod_a_a) tptp.a)
% 0.26/0.71 (declare-fun tptp.produc1641853175od_a_a (tptp.produc1572603623od_a_a) tptp.produc1572603623od_a_a)
% 0.26/0.71 (declare-fun tptp.product_swap_a_a (tptp.product_prod_a_a) tptp.product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.produc905674258od_a_a (tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.product_product_a_a (tptp.set_a tptp.set_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.collec1635618130od_a_a ((-> tptp.produc1572603623od_a_a Bool)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.collec645855634od_a_a ((-> tptp.product_prod_a_a Bool)) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.image_236793797od_a_a ((-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a) tptp.set_Pr1948701895od_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.image_734753285od_a_a ((-> tptp.produc1572603623od_a_a tptp.product_prod_a_a) tptp.set_Pr1948701895od_a_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.image_1105229276_a_a_a ((-> tptp.produc1572603623od_a_a tptp.a) tptp.set_Pr1948701895od_a_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.image_1765377413od_a_a ((-> tptp.product_prod_a_a tptp.produc1572603623od_a_a) tptp.set_Product_prod_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.image_794773445od_a_a ((-> tptp.product_prod_a_a tptp.product_prod_a_a) tptp.set_Product_prod_a_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.image_340790172_a_a_a ((-> tptp.product_prod_a_a tptp.a) tptp.set_Product_prod_a_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.image_1763923566od_a_a ((-> tptp.a tptp.produc1572603623od_a_a) tptp.set_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.image_1725938350od_a_a ((-> tptp.a tptp.product_prod_a_a) tptp.set_a) tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.image_a_a ((-> tptp.a tptp.a) tptp.set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.lex_pr942790511od_a_a (tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a) tptp.set_Pr1295299783od_a_a)
% 0.26/0.71 (declare-fun tptp.lex_pr2084296006_a_a_a (tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a) tptp.set_Pr729215751_a_a_a)
% 0.26/0.71 (declare-fun tptp.lex_pr1321960536od_a_a (tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a) tptp.set_Pr231806599od_a_a)
% 0.26/0.71 (declare-fun tptp.lex_prod_a_a (tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.same_f1138477100od_a_a ((-> tptp.product_prod_a_a Bool) (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)) tptp.set_Pr1295299783od_a_a)
% 0.26/0.71 (declare-fun tptp.same_fst_a_a ((-> tptp.a Bool) (-> tptp.a tptp.set_Product_prod_a_a)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.71 (declare-fun tptp.member180906768od_a_a (tptp.produc1056976615od_a_a tptp.set_Pr532616391od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member547056400od_a_a (tptp.produc1423126247od_a_a tptp.set_Pr2081559751od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member1899387664od_a_a (tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member1545452880od_a_a (tptp.produc47586087od_a_a tptp.set_Pr173461255od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member575366567_a_a_a (tptp.produc1683075710_a_a_a tptp.set_Pr6137822_a_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member470802768_a_a_a (tptp.produc1120419623_a_a_a tptp.set_Pr729215751_a_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member1424209616od_a_a (tptp.produc1546279079od_a_a tptp.set_Pr660101255od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member1361298640od_a_a (tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member122808528od_a_a (tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member2057358096od_a_a (tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member1403138919_a_a_a (tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member448091577od_a_a (tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member160619001od_a_a (tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member449909584od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 0.26/0.71 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.b () tptp.set_a)
% 0.26/0.71 (declare-fun tptp.pr () tptp.set_Product_prod_a_a)
% 0.26/0.71 (declare-fun tptp.y () tptp.a)
% 0.26/0.71 (declare-fun tptp.z () tptp.a)
% 0.26/0.71 (assert (@ (@ tptp.member_a tptp.z) (@ (@ (@ tptp.prefer161218362good_a tptp.y) tptp.b) tptp.pr)))
% 0.26/0.71 (assert (forall ((X tptp.produc2010915495od_a_a) (Y tptp.produc2010915495od_a_a) (B tptp.set_Pr231806599od_a_a) (Pr tptp.set_Pr532616391od_a_a)) (=> (@ (@ tptp.member1361298640od_a_a X) (@ (@ (@ tptp.prefer468349667od_a_a Y) B) Pr)) (@ (@ tptp.member180906768od_a_a (@ (@ tptp.produc539587415od_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X tptp.produc772425383od_a_a) (Y tptp.produc772425383od_a_a) (B tptp.set_Pr1194146439od_a_a) (Pr tptp.set_Pr2081559751od_a_a)) (=> (@ (@ tptp.member122808528od_a_a X) (@ (@ (@ tptp.prefer1377343203od_a_a Y) B) Pr)) (@ (@ tptp.member547056400od_a_a (@ (@ tptp.produc852390743od_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X tptp.produc1016684094_a_a_a) (Y tptp.produc1016684094_a_a_a) (B tptp.set_Pr1689873822_a_a_a) (Pr tptp.set_Pr729215751_a_a_a)) (=> (@ (@ tptp.member1403138919_a_a_a X) (@ (@ (@ tptp.prefer1944486522_a_a_a Y) B) Pr)) (@ (@ tptp.member470802768_a_a_a (@ (@ tptp.produc2054708503_a_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X tptp.produc1555800720od_a_a) (Y tptp.produc1555800720od_a_a) (B tptp.set_Pr195866352od_a_a) (Pr tptp.set_Pr660101255od_a_a)) (=> (@ (@ tptp.member448091577od_a_a X) (@ (@ (@ tptp.prefer445484748od_a_a Y) B) Pr)) (@ (@ tptp.member1424209616od_a_a (@ (@ tptp.produc1573596055od_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X tptp.produc1921647824od_a_a) (Y tptp.produc1921647824od_a_a) (B tptp.set_Pr681306928od_a_a) (Pr tptp.set_Pr231806599od_a_a)) (=> (@ (@ tptp.member160619001od_a_a X) (@ (@ (@ tptp.prefer701966604od_a_a Y) B) Pr)) (@ (@ tptp.member1361298640od_a_a (@ (@ tptp.produc563767703od_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (Y tptp.produc1572603623od_a_a) (B tptp.set_Pr1948701895od_a_a) (Pr tptp.set_Pr1295299783od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X) (@ (@ (@ tptp.prefer55414563od_a_a Y) B) Pr)) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (B tptp.set_Product_prod_a_a) (Pr tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member449909584od_a_a X) (@ (@ (@ tptp.prefer477097315od_a_a Y) B) Pr)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X tptp.a) (Y tptp.a) (B tptp.set_a) (Pr tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.prefer161218362good_a Y) B) Pr)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) Pr))))
% 0.26/0.71 (assert (forall ((X1 tptp.produc1921647824od_a_a) (X2 tptp.produc1921647824od_a_a) (Y1 tptp.produc1921647824od_a_a) (Y2 tptp.produc1921647824od_a_a)) (= (= (@ (@ tptp.produc563767703od_a_a X1) X2) (@ (@ tptp.produc563767703od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.26/0.71 (assert (forall ((X1 tptp.product_prod_a_a) (X2 tptp.produc1572603623od_a_a) (Y1 tptp.product_prod_a_a) (Y2 tptp.produc1572603623od_a_a)) (= (= (@ (@ tptp.produc1555606807od_a_a X1) X2) (@ (@ tptp.produc1555606807od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.26/0.71 (assert (forall ((X1 tptp.product_prod_a_a) (X2 tptp.a) (Y1 tptp.product_prod_a_a) (Y2 tptp.a)) (= (= (@ (@ tptp.produc2061588782_a_a_a X1) X2) (@ (@ tptp.produc2061588782_a_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.26/0.71 (assert (forall ((X1 tptp.a) (X2 tptp.produc1572603623od_a_a) (Y1 tptp.a) (Y2 tptp.produc1572603623od_a_a)) (= (= (@ (@ tptp.produc1095491584od_a_a X1) X2) (@ (@ tptp.produc1095491584od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.26/0.71 (assert (forall ((X1 tptp.a) (X2 tptp.product_prod_a_a) (Y1 tptp.a) (Y2 tptp.product_prod_a_a)) (= (= (@ (@ tptp.produc1299253312od_a_a X1) X2) (@ (@ tptp.produc1299253312od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.26/0.71 (assert (forall ((X1 tptp.product_prod_a_a) (X2 tptp.product_prod_a_a) (Y1 tptp.product_prod_a_a) (Y2 tptp.product_prod_a_a)) (= (= (@ (@ tptp.produc1474507607od_a_a X1) X2) (@ (@ tptp.produc1474507607od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.26/0.71 (assert (forall ((X1 tptp.a) (X2 tptp.a) (Y1 tptp.a) (Y2 tptp.a)) (= (= (@ (@ tptp.product_Pair_a_a X1) X2) (@ (@ tptp.product_Pair_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.26/0.71 (assert (forall ((A tptp.produc1921647824od_a_a) (B2 tptp.produc1921647824od_a_a) (A2 tptp.produc1921647824od_a_a) (B3 tptp.produc1921647824od_a_a)) (= (= (@ (@ tptp.produc563767703od_a_a A) B2) (@ (@ tptp.produc563767703od_a_a A2) B3)) (and (= A A2) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.produc1572603623od_a_a) (A2 tptp.product_prod_a_a) (B3 tptp.produc1572603623od_a_a)) (= (= (@ (@ tptp.produc1555606807od_a_a A) B2) (@ (@ tptp.produc1555606807od_a_a A2) B3)) (and (= A A2) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.a) (A2 tptp.product_prod_a_a) (B3 tptp.a)) (= (= (@ (@ tptp.produc2061588782_a_a_a A) B2) (@ (@ tptp.produc2061588782_a_a_a A2) B3)) (and (= A A2) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.produc1572603623od_a_a) (A2 tptp.a) (B3 tptp.produc1572603623od_a_a)) (= (= (@ (@ tptp.produc1095491584od_a_a A) B2) (@ (@ tptp.produc1095491584od_a_a A2) B3)) (and (= A A2) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.product_prod_a_a) (A2 tptp.a) (B3 tptp.product_prod_a_a)) (= (= (@ (@ tptp.produc1299253312od_a_a A) B2) (@ (@ tptp.produc1299253312od_a_a A2) B3)) (and (= A A2) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (A2 tptp.product_prod_a_a) (B3 tptp.product_prod_a_a)) (= (= (@ (@ tptp.produc1474507607od_a_a A) B2) (@ (@ tptp.produc1474507607od_a_a A2) B3)) (and (= A A2) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (A2 tptp.a) (B3 tptp.a)) (= (= (@ (@ tptp.product_Pair_a_a A) B2) (@ (@ tptp.product_Pair_a_a A2) B3)) (and (= A A2) (= B2 B3)))))
% 0.26/0.71 (assert (forall ((P tptp.produc2010915495od_a_a)) (exists ((X3 tptp.produc1921647824od_a_a) (Y3 tptp.produc1921647824od_a_a)) (= P (@ (@ tptp.produc563767703od_a_a X3) Y3)))))
% 0.26/0.71 (assert (forall ((P tptp.produc772425383od_a_a)) (exists ((X3 tptp.product_prod_a_a) (Y3 tptp.produc1572603623od_a_a)) (= P (@ (@ tptp.produc1555606807od_a_a X3) Y3)))))
% 0.26/0.71 (assert (forall ((P tptp.produc1016684094_a_a_a)) (exists ((X3 tptp.product_prod_a_a) (Y3 tptp.a)) (= P (@ (@ tptp.produc2061588782_a_a_a X3) Y3)))))
% 0.26/0.71 (assert (forall ((P tptp.produc1555800720od_a_a)) (exists ((X3 tptp.a) (Y3 tptp.produc1572603623od_a_a)) (= P (@ (@ tptp.produc1095491584od_a_a X3) Y3)))))
% 0.26/0.71 (assert (forall ((P tptp.produc1921647824od_a_a)) (exists ((X3 tptp.a) (Y3 tptp.product_prod_a_a)) (= P (@ (@ tptp.produc1299253312od_a_a X3) Y3)))))
% 0.26/0.71 (assert (forall ((P tptp.produc1572603623od_a_a)) (exists ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (= P (@ (@ tptp.produc1474507607od_a_a X3) Y3)))))
% 0.26/0.71 (assert (forall ((P tptp.product_prod_a_a)) (exists ((X3 tptp.a) (Y3 tptp.a)) (= P (@ (@ tptp.product_Pair_a_a X3) Y3)))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc2010915495od_a_a Bool)) (P tptp.produc2010915495od_a_a)) (=> (forall ((A3 tptp.produc1921647824od_a_a) (B4 tptp.produc1921647824od_a_a)) (@ P2 (@ (@ tptp.produc563767703od_a_a A3) B4))) (@ P2 P))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc772425383od_a_a Bool)) (P tptp.produc772425383od_a_a)) (=> (forall ((A3 tptp.product_prod_a_a) (B4 tptp.produc1572603623od_a_a)) (@ P2 (@ (@ tptp.produc1555606807od_a_a A3) B4))) (@ P2 P))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc1016684094_a_a_a Bool)) (P tptp.produc1016684094_a_a_a)) (=> (forall ((A3 tptp.product_prod_a_a) (B4 tptp.a)) (@ P2 (@ (@ tptp.produc2061588782_a_a_a A3) B4))) (@ P2 P))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc1555800720od_a_a Bool)) (P tptp.produc1555800720od_a_a)) (=> (forall ((A3 tptp.a) (B4 tptp.produc1572603623od_a_a)) (@ P2 (@ (@ tptp.produc1095491584od_a_a A3) B4))) (@ P2 P))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc1921647824od_a_a Bool)) (P tptp.produc1921647824od_a_a)) (=> (forall ((A3 tptp.a) (B4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.produc1299253312od_a_a A3) B4))) (@ P2 P))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc1572603623od_a_a Bool)) (P tptp.produc1572603623od_a_a)) (=> (forall ((A3 tptp.product_prod_a_a) (B4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.produc1474507607od_a_a A3) B4))) (@ P2 P))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.product_prod_a_a Bool)) (P tptp.product_prod_a_a)) (=> (forall ((A3 tptp.a) (B4 tptp.a)) (@ P2 (@ (@ tptp.product_Pair_a_a A3) B4))) (@ P2 P))))
% 0.26/0.71 (assert (forall ((A tptp.produc1921647824od_a_a) (B2 tptp.produc1921647824od_a_a) (A2 tptp.produc1921647824od_a_a) (B3 tptp.produc1921647824od_a_a)) (=> (= (@ (@ tptp.produc563767703od_a_a A) B2) (@ (@ tptp.produc563767703od_a_a A2) B3)) (not (=> (= A A2) (not (= B2 B3)))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.produc1572603623od_a_a) (A2 tptp.product_prod_a_a) (B3 tptp.produc1572603623od_a_a)) (=> (= (@ (@ tptp.produc1555606807od_a_a A) B2) (@ (@ tptp.produc1555606807od_a_a A2) B3)) (not (=> (= A A2) (not (= B2 B3)))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.a) (A2 tptp.product_prod_a_a) (B3 tptp.a)) (=> (= (@ (@ tptp.produc2061588782_a_a_a A) B2) (@ (@ tptp.produc2061588782_a_a_a A2) B3)) (not (=> (= A A2) (not (= B2 B3)))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.produc1572603623od_a_a) (A2 tptp.a) (B3 tptp.produc1572603623od_a_a)) (=> (= (@ (@ tptp.produc1095491584od_a_a A) B2) (@ (@ tptp.produc1095491584od_a_a A2) B3)) (not (=> (= A A2) (not (= B2 B3)))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.product_prod_a_a) (A2 tptp.a) (B3 tptp.product_prod_a_a)) (=> (= (@ (@ tptp.produc1299253312od_a_a A) B2) (@ (@ tptp.produc1299253312od_a_a A2) B3)) (not (=> (= A A2) (not (= B2 B3)))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (A2 tptp.product_prod_a_a) (B3 tptp.product_prod_a_a)) (=> (= (@ (@ tptp.produc1474507607od_a_a A) B2) (@ (@ tptp.produc1474507607od_a_a A2) B3)) (not (=> (= A A2) (not (= B2 B3)))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (A2 tptp.a) (B3 tptp.a)) (=> (= (@ (@ tptp.product_Pair_a_a A) B2) (@ (@ tptp.product_Pair_a_a A2) B3)) (not (=> (= A A2) (not (= B2 B3)))))))
% 0.26/0.71 (assert (forall ((Y tptp.produc772425383od_a_a)) (not (forall ((A3 tptp.product_prod_a_a) (B4 tptp.product_prod_a_a) (C tptp.product_prod_a_a)) (not (= Y (@ (@ tptp.produc1555606807od_a_a A3) (@ (@ tptp.produc1474507607od_a_a B4) C))))))))
% 0.26/0.71 (assert (forall ((Y tptp.produc1555800720od_a_a)) (not (forall ((A3 tptp.a) (B4 tptp.product_prod_a_a) (C tptp.product_prod_a_a)) (not (= Y (@ (@ tptp.produc1095491584od_a_a A3) (@ (@ tptp.produc1474507607od_a_a B4) C))))))))
% 0.26/0.71 (assert (forall ((Y tptp.produc1921647824od_a_a)) (not (forall ((A3 tptp.a) (B4 tptp.a) (C tptp.a)) (not (= Y (@ (@ tptp.produc1299253312od_a_a A3) (@ (@ tptp.product_Pair_a_a B4) C))))))))
% 0.26/0.71 (assert (forall ((Y tptp.produc1572603623od_a_a)) (not (forall ((A3 tptp.product_prod_a_a) (B4 tptp.a) (C tptp.a)) (not (= Y (@ (@ tptp.produc1474507607od_a_a A3) (@ (@ tptp.product_Pair_a_a B4) C))))))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc1572603623od_a_a Bool)) (X tptp.produc1572603623od_a_a)) (=> (forall ((A3 tptp.product_prod_a_a) (B4 tptp.a) (C tptp.a)) (@ P2 (@ (@ tptp.produc1474507607od_a_a A3) (@ (@ tptp.product_Pair_a_a B4) C)))) (@ P2 X))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.product_prod_a_a Bool)) (Prod tptp.product_prod_a_a)) (=> (forall ((A3 tptp.a) (B4 tptp.a)) (@ P2 (@ (@ tptp.product_Pair_a_a A3) B4))) (@ P2 Prod))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.produc1572603623od_a_a Bool)) (Prod tptp.produc1572603623od_a_a)) (=> (forall ((A3 tptp.product_prod_a_a) (B4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.produc1474507607od_a_a A3) B4))) (@ P2 Prod))))
% 0.26/0.71 (assert (forall ((Y tptp.product_prod_a_a)) (not (forall ((A3 tptp.a) (B4 tptp.a)) (not (= Y (@ (@ tptp.product_Pair_a_a A3) B4)))))))
% 0.26/0.71 (assert (forall ((Y tptp.produc1572603623od_a_a)) (not (forall ((A3 tptp.product_prod_a_a) (B4 tptp.product_prod_a_a)) (not (= Y (@ (@ tptp.produc1474507607od_a_a A3) B4)))))))
% 0.26/0.71 (assert (= tptp.prefer55414563od_a_a (lambda ((X4 tptp.produc1572603623od_a_a) (B5 tptp.set_Pr1948701895od_a_a) (P3 tptp.set_Pr1295299783od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((Y4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a Y4) B5) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a Y4) X4)) P3)))))))
% 0.26/0.71 (assert (= tptp.prefer161218362good_a (lambda ((X4 tptp.a) (B5 tptp.set_a) (P3 tptp.set_Product_prod_a_a)) (@ tptp.collect_a (lambda ((Y4 tptp.a)) (and (@ (@ tptp.member_a Y4) B5) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y4) X4)) P3)))))))
% 0.26/0.71 (assert (= tptp.prefer477097315od_a_a (lambda ((X4 tptp.product_prod_a_a) (B5 tptp.set_Product_prod_a_a) (P3 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec645855634od_a_a (lambda ((Y4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Y4) B5) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y4) X4)) P3)))))))
% 0.26/0.71 (assert (forall ((R tptp.a) (S tptp.a) (R2 tptp.set_Product_prod_a_a) (S2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a R))) (=> (@ (@ tptp.member449909584od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member449909584od_a_a (@ _let_1 S2)) R2))))))
% 0.26/0.71 (assert (forall ((R tptp.product_prod_a_a) (S tptp.product_prod_a_a) (R2 tptp.set_Pr1948701895od_a_a) (S2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.produc1474507607od_a_a R))) (=> (@ (@ tptp.member2057358096od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member2057358096od_a_a (@ _let_1 S2)) R2))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a Bool)) (A tptp.a) (B2 tptp.a)) (=> (@ F (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ (@ tptp.product_curry_a_a_o F) A) B2))))
% 0.26/0.71 (assert (forall ((F (-> tptp.produc1572603623od_a_a Bool)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (=> (@ F (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ (@ tptp.produc94438221_a_a_o F) A) B2))))
% 0.26/0.71 (assert (forall ((Carrier tptp.set_a) (Relation tptp.set_Product_prod_a_a) (X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a Z))) (let ((_let_2 (@ tptp.product_Pair_a_a X))) (let ((_let_3 (@ tptp.product_Pair_a_a Y))) (=> (@ (@ tptp.prefer1292084992ence_a Carrier) Relation) (=> (and (@ (@ tptp.member449909584od_a_a (@ _let_2 Y)) Relation) (@ (@ tptp.member449909584od_a_a (@ _let_3 X)) Relation)) (=> (and (@ (@ tptp.member449909584od_a_a (@ _let_3 Z)) Relation) (@ (@ tptp.member449909584od_a_a (@ _let_1 Y)) Relation)) (and (@ (@ tptp.member449909584od_a_a (@ _let_2 Z)) Relation) (@ (@ tptp.member449909584od_a_a (@ _let_1 X)) Relation))))))))))
% 0.26/0.71 (assert (forall ((Carrier tptp.set_Product_prod_a_a) (Relation tptp.set_Pr1948701895od_a_a) (X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (Z tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.produc1474507607od_a_a Z))) (let ((_let_2 (@ tptp.produc1474507607od_a_a X))) (let ((_let_3 (@ tptp.produc1474507607od_a_a Y))) (=> (@ (@ tptp.prefer1338892073od_a_a Carrier) Relation) (=> (and (@ (@ tptp.member2057358096od_a_a (@ _let_2 Y)) Relation) (@ (@ tptp.member2057358096od_a_a (@ _let_3 X)) Relation)) (=> (and (@ (@ tptp.member2057358096od_a_a (@ _let_3 Z)) Relation) (@ (@ tptp.member2057358096od_a_a (@ _let_1 Y)) Relation)) (and (@ (@ tptp.member2057358096od_a_a (@ _let_2 Z)) Relation) (@ (@ tptp.member2057358096od_a_a (@ _let_1 X)) Relation))))))))))
% 0.26/0.71 (assert (forall ((Carrier tptp.set_Pr1948701895od_a_a) (Relation tptp.set_Pr1295299783od_a_a) (X tptp.produc1572603623od_a_a) (Y tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.prefer1409946857od_a_a Carrier) Relation) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X) Y)) Relation) (@ (@ tptp.member2057358096od_a_a X) Carrier)))))
% 0.26/0.71 (assert (forall ((Carrier tptp.set_a) (Relation tptp.set_Product_prod_a_a) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.prefer1292084992ence_a Carrier) Relation) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) Relation) (@ (@ tptp.member_a X) Carrier)))))
% 0.26/0.71 (assert (forall ((Carrier tptp.set_Product_prod_a_a) (Relation tptp.set_Pr1948701895od_a_a) (X tptp.product_prod_a_a) (Y tptp.product_prod_a_a)) (=> (@ (@ tptp.prefer1338892073od_a_a Carrier) Relation) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) Relation) (@ (@ tptp.member449909584od_a_a X) Carrier)))))
% 0.26/0.71 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ tptp.product_swap_a_a (@ (@ tptp.product_Pair_a_a X) Y)) (@ (@ tptp.product_Pair_a_a Y) X))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a)) (= (@ tptp.produc1641853175od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) (@ (@ tptp.produc1474507607od_a_a Y) X))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a Bool)) (A tptp.a) (B2 tptp.a)) (=> (@ (@ (@ tptp.product_curry_a_a_o F) A) B2) (@ F (@ (@ tptp.product_Pair_a_a A) B2)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.produc1572603623od_a_a Bool)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (=> (@ (@ (@ tptp.produc94438221_a_a_o F) A) B2) (@ F (@ (@ tptp.produc1474507607od_a_a A) B2)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a Bool)) (A tptp.a) (B2 tptp.a)) (=> (@ (@ (@ tptp.product_curry_a_a_o F) A) B2) (@ F (@ (@ tptp.product_Pair_a_a A) B2)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.produc1572603623od_a_a Bool)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (=> (@ (@ (@ tptp.produc94438221_a_a_o F) A) B2) (@ F (@ (@ tptp.produc1474507607od_a_a A) B2)))))
% 0.26/0.71 (assert (= tptp.prefer926864306od_a_a (lambda ((X4 tptp.produc1572603623od_a_a) (B5 tptp.set_Pr1948701895od_a_a) (P3 tptp.set_Pr1295299783od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((Y4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a Y4) B5) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) P3)))))))
% 0.26/0.71 (assert (= tptp.prefer1676310729than_a (lambda ((X4 tptp.a) (B5 tptp.set_a) (P3 tptp.set_Product_prod_a_a)) (@ tptp.collect_a (lambda ((Y4 tptp.a)) (and (@ (@ tptp.member_a Y4) B5) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) P3)))))))
% 0.26/0.71 (assert (= tptp.prefer1498087410od_a_a (lambda ((X4 tptp.product_prod_a_a) (B5 tptp.set_Product_prod_a_a) (P3 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec645855634od_a_a (lambda ((Y4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Y4) B5) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) P3)))))))
% 0.26/0.71 (assert (= tptp.prefer1867335523od_a_a (lambda ((X4 tptp.produc1572603623od_a_a) (B5 tptp.set_Pr1948701895od_a_a) (P3 tptp.set_Pr1295299783od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((Y4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a Y4) B5) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) P3) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a Y4) X4)) P3)))))))
% 0.26/0.71 (assert (= tptp.prefer436369274d_as_a (lambda ((X4 tptp.a) (B5 tptp.set_a) (P3 tptp.set_Product_prod_a_a)) (@ tptp.collect_a (lambda ((Y4 tptp.a)) (and (@ (@ tptp.member_a Y4) B5) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) P3) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y4) X4)) P3)))))))
% 0.26/0.71 (assert (= tptp.prefer74720675od_a_a (lambda ((X4 tptp.product_prod_a_a) (B5 tptp.set_Product_prod_a_a) (P3 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec645855634od_a_a (lambda ((Y4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Y4) B5) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) P3) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y4) X4)) P3)))))))
% 0.26/0.71 (assert (forall ((R2 tptp.set_Product_prod_a_a) (S3 tptp.set_Product_prod_a_a)) (= (= (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R2)) (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) S3))) (= R2 S3))))
% 0.26/0.71 (assert (forall ((R2 tptp.set_Pr1948701895od_a_a) (S3 tptp.set_Pr1948701895od_a_a)) (= (= (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R2)) (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) S3))) (= R2 S3))))
% 0.26/0.71 (assert (= tptp.prefer1409946857od_a_a (lambda ((Carrier2 tptp.set_Pr1948701895od_a_a) (Relation2 tptp.set_Pr1295299783od_a_a)) (and (forall ((X4 tptp.produc1572603623od_a_a) (Y4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) Relation2) (@ (@ tptp.member2057358096od_a_a X4) Carrier2))) (forall ((X4 tptp.produc1572603623od_a_a) (Y4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) Relation2) (@ (@ tptp.member2057358096od_a_a Y4) Carrier2))) (@ (@ tptp.order_491428350od_a_a Carrier2) Relation2)))))
% 0.26/0.71 (assert (= tptp.prefer1292084992ence_a (lambda ((Carrier2 tptp.set_a) (Relation2 tptp.set_Product_prod_a_a)) (and (forall ((X4 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) Relation2) (@ (@ tptp.member_a X4) Carrier2))) (forall ((X4 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) Relation2) (@ (@ tptp.member_a Y4) Carrier2))) (@ (@ tptp.order_preorder_on_a Carrier2) Relation2)))))
% 0.26/0.71 (assert (= tptp.prefer1338892073od_a_a (lambda ((Carrier2 tptp.set_Product_prod_a_a) (Relation2 tptp.set_Pr1948701895od_a_a)) (and (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) Relation2) (@ (@ tptp.member449909584od_a_a X4) Carrier2))) (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) Relation2) (@ (@ tptp.member449909584od_a_a Y4) Carrier2))) (@ (@ tptp.order_359341630od_a_a Carrier2) Relation2)))))
% 0.26/0.71 (assert (forall ((Relation tptp.set_Pr1295299783od_a_a) (Carrier tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a) (Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) Relation) (@ (@ tptp.member2057358096od_a_a X3) Carrier))) (=> (forall ((X3 tptp.produc1572603623od_a_a) (Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) Relation) (@ (@ tptp.member2057358096od_a_a Y3) Carrier))) (=> (@ (@ tptp.order_491428350od_a_a Carrier) Relation) (@ (@ tptp.prefer1409946857od_a_a Carrier) Relation))))))
% 0.26/0.71 (assert (forall ((Relation tptp.set_Product_prod_a_a) (Carrier tptp.set_a)) (=> (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) Relation) (@ (@ tptp.member_a X3) Carrier))) (=> (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) Relation) (@ (@ tptp.member_a Y3) Carrier))) (=> (@ (@ tptp.order_preorder_on_a Carrier) Relation) (@ (@ tptp.prefer1292084992ence_a Carrier) Relation))))))
% 0.26/0.71 (assert (forall ((Relation tptp.set_Pr1948701895od_a_a) (Carrier tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) Relation) (@ (@ tptp.member449909584od_a_a X3) Carrier))) (=> (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) Relation) (@ (@ tptp.member449909584od_a_a Y3) Carrier))) (=> (@ (@ tptp.order_359341630od_a_a Carrier) Relation) (@ (@ tptp.prefer1338892073od_a_a Carrier) Relation))))))
% 0.26/0.71 (assert (forall ((Y tptp.a) (X tptp.a) (A4 tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y) X)) (@ (@ tptp.image_794773445od_a_a tptp.product_swap_a_a) A4)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) A4))))
% 0.26/0.71 (assert (forall ((Y tptp.product_prod_a_a) (X tptp.product_prod_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y) X)) (@ (@ tptp.image_236793797od_a_a tptp.produc1641853175od_a_a) A4)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) A4))))
% 0.26/0.71 (assert (forall ((B tptp.set_Pr1948701895od_a_a) (Y tptp.produc1572603623od_a_a) (Pr tptp.set_Pr1295299783od_a_a)) (= (@ tptp.collec1635618130od_a_a (lambda ((A5 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a A5) B) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A5) Y)) Pr) (not (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a Y) A5)) Pr))))) (@ (@ tptp.minus_1034916142od_a_a (@ (@ (@ tptp.prefer55414563od_a_a Y) B) Pr)) (@ (@ (@ tptp.prefer1867335523od_a_a Y) B) Pr)))))
% 0.26/0.71 (assert (forall ((B tptp.set_a) (Y tptp.a) (Pr tptp.set_Product_prod_a_a)) (= (@ tptp.collect_a (lambda ((A5 tptp.a)) (and (@ (@ tptp.member_a A5) B) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A5) Y)) Pr) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y) A5)) Pr))))) (@ (@ tptp.minus_minus_set_a (@ (@ (@ tptp.prefer161218362good_a Y) B) Pr)) (@ (@ (@ tptp.prefer436369274d_as_a Y) B) Pr)))))
% 0.26/0.71 (assert (forall ((B tptp.set_Product_prod_a_a) (Y tptp.product_prod_a_a) (Pr tptp.set_Pr1948701895od_a_a)) (= (@ tptp.collec645855634od_a_a (lambda ((A5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a A5) B) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A5) Y)) Pr) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y) A5)) Pr))))) (@ (@ tptp.minus_1507102574od_a_a (@ (@ (@ tptp.prefer477097315od_a_a Y) B) Pr)) (@ (@ (@ tptp.prefer74720675od_a_a Y) B) Pr)))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ (@ tptp.member449909584od_a_a A) (@ tptp.collec645855634od_a_a P2)) (@ P2 A))))
% 0.26/0.71 (assert (forall ((A tptp.a) (P2 (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P2)) (@ P2 A))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ (@ tptp.member2057358096od_a_a A) (@ tptp.collec1635618130od_a_a P2)) (@ P2 A))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a)) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A4))) A4)))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A4))) A4)))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a)) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A4))) A4)))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)))))))
% 0.26/0.71 (assert (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_794773445od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a)) (X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member_a B2) (@ (@ tptp.image_340790172_a_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1765377413od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (X tptp.a) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_1725938350od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (X tptp.a) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.produc1572603623od_a_a)) (X tptp.a) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1763923566od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_734753285od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member_a B2) (@ (@ tptp.image_1105229276_a_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_236793797od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (= (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (and (@ _let_1 A4) (not (@ _let_1 B)))))))
% 0.26/0.71 (assert (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (and (@ _let_1 A4) (not (@ _let_1 B)))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (= (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (and (@ _let_1 A4) (not (@ _let_1 B)))))))
% 0.26/0.71 (assert (= tptp.minus_1507102574od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (@ tptp.collec645855634od_a_a (@ (@ tptp.minus_1797478127_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A6))) (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) B5)))))))
% 0.26/0.71 (assert (= tptp.minus_minus_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (@ tptp.collect_a (@ (@ tptp.minus_minus_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A6))) (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) B5)))))))
% 0.26/0.71 (assert (= tptp.minus_1034916142od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec1635618130od_a_a (@ (@ tptp.minus_107310383_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A6))) (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) B5)))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_794773445od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member_a B2) (@ (@ tptp.image_340790172_a_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1765377413od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A4 tptp.set_a) (B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a))) (=> (@ (@ tptp.member_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_1725938350od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A4 tptp.set_a) (B2 tptp.a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A4 tptp.set_a) (B2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1763923566od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_734753285od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member_a B2) (@ (@ tptp.image_1105229276_a_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.produc1572603623od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_236793797od_a_a F) A4))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ F X)) (@ (@ tptp.image_794773445od_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member_a (@ F X)) (@ (@ tptp.image_340790172_a_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ F X)) (@ (@ tptp.image_1765377413od_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.product_prod_a_a))) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member449909584od_a_a (@ F X)) (@ (@ tptp.image_1725938350od_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member_a (@ F X)) (@ (@ tptp.image_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ F X)) (@ (@ tptp.image_1763923566od_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ F X)) (@ (@ tptp.image_734753285od_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member_a (@ F X)) (@ (@ tptp.image_1105229276_a_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ F X)) (@ (@ tptp.image_236793797od_a_a F) A4)))))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (not (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (not (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (not (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (@ _let_1 A4)))))
% 0.26/0.71 (assert (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (@ _let_1 A4)))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (@ _let_1 A4)))))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (not (=> (@ _let_1 A4) (@ _let_1 B)))))))
% 0.26/0.71 (assert (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (not (=> (@ _let_1 A4) (@ _let_1 B)))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (not (=> (@ _let_1 A4) (@ _let_1 B)))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_794773445od_a_a F) A4)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member449909584od_a_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (A4 tptp.set_a)) (=> (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_1725938350od_a_a F) A4)) (not (forall ((X3 tptp.a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_734753285od_a_a F) A4)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member2057358096od_a_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a)) (A4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member_a B2) (@ (@ tptp.image_340790172_a_a_a F) A4)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member449909584od_a_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (A4 tptp.set_a)) (=> (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A4)) (not (forall ((X3 tptp.a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member_a B2) (@ (@ tptp.image_1105229276_a_a_a F) A4)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member2057358096od_a_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1765377413od_a_a F) A4)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member449909584od_a_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.produc1572603623od_a_a)) (A4 tptp.set_a)) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1763923566od_a_a F) A4)) (not (forall ((X3 tptp.a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_236793797od_a_a F) A4)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member2057358096od_a_a X3) A4))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) (@ (@ tptp.image_794773445od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_794773445od_a_a F) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.a tptp.product_prod_a_a)) (A4 tptp.set_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) (@ (@ tptp.image_1725938350od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1725938350od_a_a F) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) (@ (@ tptp.image_734753285od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_734753285od_a_a F) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a tptp.a)) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.a Bool))) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) (@ (@ tptp.image_340790172_a_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_340790172_a_a_a F) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.a tptp.a)) (A4 tptp.set_a) (P2 (-> tptp.a Bool))) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) (@ (@ tptp.image_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_a_a F) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.produc1572603623od_a_a tptp.a)) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.a Bool))) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) (@ (@ tptp.image_1105229276_a_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1105229276_a_a_a F) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) (@ (@ tptp.image_1765377413od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1765377413od_a_a F) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.a tptp.produc1572603623od_a_a)) (A4 tptp.set_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) (@ (@ tptp.image_1763923566od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1763923566od_a_a F) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) (@ (@ tptp.image_236793797od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_236793797od_a_a F) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 (@ F X4)))))))))
% 0.26/0.71 (assert (= tptp.minus_1507102574od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X4))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 0.26/0.71 (assert (= tptp.minus_minus_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (@ tptp.collect_a (lambda ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 0.26/0.71 (assert (= tptp.minus_1034916142od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X4))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X) tptp.top_to398455383od_a_a)))
% 0.26/0.71 (assert (forall ((X tptp.a)) (@ (@ tptp.member_a X) tptp.top_top_set_a)))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X) tptp.top_to52711959od_a_a)))
% 0.26/0.71 (assert (exists ((X3 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X3) tptp.top_to398455383od_a_a)))
% 0.26/0.71 (assert (exists ((X3 tptp.a)) (@ (@ tptp.member_a X3) tptp.top_top_set_a)))
% 0.26/0.71 (assert (exists ((X3 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X3) tptp.top_to52711959od_a_a)))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X3) A4)) (= tptp.top_to398455383od_a_a A4))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a)) (=> (forall ((X3 tptp.a)) (@ (@ tptp.member_a X3) A4)) (= tptp.top_top_set_a A4))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X3) A4)) (= tptp.top_to52711959od_a_a A4))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X) tptp.top_to398455383od_a_a)))
% 0.26/0.71 (assert (forall ((X tptp.a)) (@ (@ tptp.member_a X) tptp.top_top_set_a)))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X) tptp.top_to52711959od_a_a)))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.a Bool)) (X tptp.a) (Y5 tptp.a) (Y tptp.a) (R2 (-> tptp.a tptp.set_Product_prod_a_a))) (let ((_let_1 (@ tptp.product_Pair_a_a X))) (=> (@ P2 X) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y5) Y)) (@ R2 X)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ _let_1 Y5)) (@ _let_1 Y))) (@ (@ tptp.same_fst_a_a P2) R2)))))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.product_prod_a_a Bool)) (X tptp.product_prod_a_a) (Y5 tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (R2 (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a))) (let ((_let_1 (@ tptp.produc1474507607od_a_a X))) (=> (@ P2 X) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y5) Y)) (@ R2 X)) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a (@ _let_1 Y5)) (@ _let_1 Y))) (@ (@ tptp.same_f1138477100od_a_a P2) R2)))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.a tptp.a)) (G (-> tptp.a tptp.a)) (A tptp.a) (B2 tptp.a)) (= (@ (@ (@ tptp.produc700022774_a_a_a F) G) (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.a tptp.product_prod_a_a)) (G (-> tptp.a tptp.product_prod_a_a)) (A tptp.a) (B2 tptp.a)) (= (@ (@ (@ tptp.produc2012818120od_a_a F) G) (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a tptp.a)) (G (-> tptp.product_prod_a_a tptp.a)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (= (@ (@ (@ tptp.produc363290532_a_a_a F) G) (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (= (@ (@ (@ tptp.produc1779756150od_a_a F) G) (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2)))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (R2 tptp.set_Product_prod_a_a) (F (-> tptp.a tptp.a)) (G (-> tptp.a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) R2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_794773445od_a_a (@ (@ tptp.produc700022774_a_a_a F) G)) R2)))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (R2 tptp.set_Product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (G (-> tptp.a tptp.product_prod_a_a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) R2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_1765377413od_a_a (@ (@ tptp.produc2012818120od_a_a F) G)) R2)))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (R2 tptp.set_Pr1948701895od_a_a) (F (-> tptp.product_prod_a_a tptp.a)) (G (-> tptp.product_prod_a_a tptp.a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) R2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_734753285od_a_a (@ (@ tptp.produc363290532_a_a_a F) G)) R2)))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (R2 tptp.set_Pr1948701895od_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) R2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_236793797od_a_a (@ (@ tptp.produc1779756150od_a_a F) G)) R2)))))
% 0.26/0.71 (assert (= tptp.top_to1483957574_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) tptp.top_to398455383od_a_a))))
% 0.26/0.71 (assert (= tptp.top_top_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) tptp.top_top_set_a))))
% 0.26/0.71 (assert (= tptp.top_to2011536774_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) tptp.top_to52711959od_a_a))))
% 0.26/0.71 (assert (forall ((X tptp.a) (Y tptp.a) (A tptp.a)) (=> (= (@ tptp.product_fst_a_a (@ (@ tptp.product_Pair_a_a X) Y)) A) (= X A))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (A tptp.product_prod_a_a)) (=> (= (@ tptp.produc2115494211od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) A) (= X A))))
% 0.26/0.71 (assert (forall ((X1 tptp.a) (X2 tptp.a)) (= (@ tptp.product_fst_a_a (@ (@ tptp.product_Pair_a_a X1) X2)) X1)))
% 0.26/0.71 (assert (forall ((X1 tptp.product_prod_a_a) (X2 tptp.product_prod_a_a)) (= (@ tptp.produc2115494211od_a_a (@ (@ tptp.produc1474507607od_a_a X1) X2)) X1)))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (F (-> tptp.a tptp.a)) (G (-> tptp.a tptp.a)) (R2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a C2) (@ (@ tptp.image_794773445od_a_a (@ (@ tptp.produc700022774_a_a_a F) G)) R2)) (not (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (= C2 (@ (@ tptp.product_Pair_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R2))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.a)) (G (-> tptp.product_prod_a_a tptp.a)) (R2 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member449909584od_a_a C2) (@ (@ tptp.image_734753285od_a_a (@ (@ tptp.produc363290532_a_a_a F) G)) R2)) (not (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (= C2 (@ (@ tptp.product_Pair_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R2))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (G (-> tptp.a tptp.product_prod_a_a)) (R2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a C2) (@ (@ tptp.image_1765377413od_a_a (@ (@ tptp.produc2012818120od_a_a F) G)) R2)) (not (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (= C2 (@ (@ tptp.produc1474507607od_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R2))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (R2 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a C2) (@ (@ tptp.image_236793797od_a_a (@ (@ tptp.produc1779756150od_a_a F) G)) R2)) (not (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (= C2 (@ (@ tptp.produc1474507607od_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R2))))))))
% 0.26/0.71 (assert (= tptp.top_top_a_a_o (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) tptp.top_to398455383od_a_a))))
% 0.26/0.71 (assert (= tptp.top_to993969022_a_a_o (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) tptp.top_to52711959od_a_a))))
% 0.26/0.71 (assert (forall ((A tptp.a) (P tptp.product_prod_a_a)) (= (= A (@ tptp.product_fst_a_a P)) (exists ((B6 tptp.a)) (= P (@ (@ tptp.product_Pair_a_a A) B6))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (P tptp.produc1572603623od_a_a)) (= (= A (@ tptp.produc2115494211od_a_a P)) (exists ((B6 tptp.product_prod_a_a)) (= P (@ (@ tptp.produc1474507607od_a_a A) B6))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Y tptp.a) (Z tptp.a)) (=> (= X (@ (@ tptp.product_Pair_a_a Y) Z)) (= (@ tptp.product_fst_a_a X) Y))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (Y tptp.product_prod_a_a) (Z tptp.product_prod_a_a)) (=> (= X (@ (@ tptp.produc1474507607od_a_a Y) Z)) (= (@ tptp.produc2115494211od_a_a X) Y))))
% 0.26/0.71 (assert (forall ((Prod tptp.product_prod_a_a)) (= (@ (@ tptp.product_Pair_a_a (@ tptp.product_fst_a_a Prod)) (@ tptp.product_snd_a_a Prod)) Prod)))
% 0.26/0.71 (assert (forall ((Prod tptp.produc1572603623od_a_a)) (= (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc2115494211od_a_a Prod)) (@ tptp.produc368344197od_a_a Prod)) Prod)))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (P tptp.product_prod_a_a)) (= (= B2 (@ tptp.product_snd_a_a P)) (exists ((A5 tptp.a)) (= P (@ (@ tptp.product_Pair_a_a A5) B2))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (P tptp.produc1572603623od_a_a)) (= (= B2 (@ tptp.produc368344197od_a_a P)) (exists ((A5 tptp.product_prod_a_a)) (= P (@ (@ tptp.produc1474507607od_a_a A5) B2))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Y tptp.a) (Z tptp.a)) (=> (= X (@ (@ tptp.product_Pair_a_a Y) Z)) (= (@ tptp.product_snd_a_a X) Z))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (Y tptp.product_prod_a_a) (Z tptp.product_prod_a_a)) (=> (= X (@ (@ tptp.produc1474507607od_a_a Y) Z)) (= (@ tptp.produc368344197od_a_a X) Z))))
% 0.26/0.71 (assert (forall ((X tptp.a) (Y tptp.a) (A tptp.a)) (=> (= (@ tptp.product_snd_a_a (@ (@ tptp.product_Pair_a_a X) Y)) A) (= Y A))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (A tptp.product_prod_a_a)) (=> (= (@ tptp.produc368344197od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) A) (= Y A))))
% 0.26/0.71 (assert (forall ((X1 tptp.a) (X2 tptp.a)) (= (@ tptp.product_snd_a_a (@ (@ tptp.product_Pair_a_a X1) X2)) X2)))
% 0.26/0.71 (assert (forall ((X1 tptp.product_prod_a_a) (X2 tptp.product_prod_a_a)) (= (@ tptp.produc368344197od_a_a (@ (@ tptp.produc1474507607od_a_a X1) X2)) X2)))
% 0.26/0.71 (assert (forall ((T tptp.product_prod_a_a)) (= T (@ (@ tptp.product_Pair_a_a (@ tptp.product_fst_a_a T)) (@ tptp.product_snd_a_a T)))))
% 0.26/0.71 (assert (forall ((T tptp.produc1572603623od_a_a)) (= T (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc2115494211od_a_a T)) (@ tptp.produc368344197od_a_a T)))))
% 0.26/0.71 (assert (forall ((Prod tptp.product_prod_a_a)) (= Prod (@ (@ tptp.product_Pair_a_a (@ tptp.product_fst_a_a Prod)) (@ tptp.product_snd_a_a Prod)))))
% 0.26/0.71 (assert (forall ((Prod tptp.produc1572603623od_a_a)) (= Prod (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc2115494211od_a_a Prod)) (@ tptp.produc368344197od_a_a Prod)))))
% 0.26/0.71 (assert (= tptp.product_swap_a_a (lambda ((P4 tptp.product_prod_a_a)) (@ (@ tptp.product_Pair_a_a (@ tptp.product_snd_a_a P4)) (@ tptp.product_fst_a_a P4)))))
% 0.26/0.71 (assert (= tptp.produc1641853175od_a_a (lambda ((P4 tptp.produc1572603623od_a_a)) (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc368344197od_a_a P4)) (@ tptp.produc2115494211od_a_a P4)))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (A tptp.product_prod_a_a)) (=> (@ (@ P2 X) Y) (=> (= A (@ (@ tptp.product_Pair_a_a X) Y)) (@ (@ P2 (@ tptp.product_fst_a_a A)) (@ tptp.product_snd_a_a A))))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (A tptp.produc1572603623od_a_a)) (=> (@ (@ P2 X) Y) (=> (= A (@ (@ tptp.produc1474507607od_a_a X) Y)) (@ (@ P2 (@ tptp.produc2115494211od_a_a A)) (@ tptp.produc368344197od_a_a A))))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.a Bool)) (P tptp.a) (Q (-> tptp.a Bool)) (Q2 tptp.a)) (let ((_let_1 (@ (@ tptp.product_Pair_a_a P) Q2))) (=> (@ P2 P) (=> (@ Q Q2) (and (@ P2 (@ tptp.product_fst_a_a _let_1)) (@ Q (@ tptp.product_snd_a_a _let_1))))))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.product_prod_a_a Bool)) (P tptp.product_prod_a_a) (Q (-> tptp.product_prod_a_a Bool)) (Q2 tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.produc1474507607od_a_a P) Q2))) (=> (@ P2 P) (=> (@ Q Q2) (and (@ P2 (@ tptp.produc2115494211od_a_a _let_1)) (@ Q (@ tptp.produc368344197od_a_a _let_1))))))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.a tptp.a Bool)) (Y tptp.a) (X tptp.a)) (let ((_let_1 (@ (@ tptp.product_Pair_a_a X) Y))) (=> (@ (@ P2 Y) X) (@ (@ P2 (@ tptp.product_snd_a_a _let_1)) (@ tptp.product_fst_a_a _let_1))))))
% 0.26/0.71 (assert (forall ((P2 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (Y tptp.product_prod_a_a) (X tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.produc1474507607od_a_a X) Y))) (=> (@ (@ P2 Y) X) (@ (@ P2 (@ tptp.produc368344197od_a_a _let_1)) (@ tptp.produc2115494211od_a_a _let_1))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a)) (X tptp.product_prod_a_a) (C2 tptp.a) (G (-> tptp.product_prod_a_a tptp.a)) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr1853143117_a_a_a A4) F) G)))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (X tptp.a) (C2 tptp.a) (G (-> tptp.a tptp.a)) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr423046308_a_a_a A4) F) G)))))))
% 0.26/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (X tptp.produc1572603623od_a_a) (C2 tptp.a) (G (-> tptp.produc1572603623od_a_a tptp.a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr356189709_a_a_a A4) F) G)))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (X tptp.product_prod_a_a) (C2 tptp.product_prod_a_a) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr200450189od_a_a A4) F) G)))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (X tptp.a) (C2 tptp.product_prod_a_a) (G (-> tptp.a tptp.product_prod_a_a)) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr1715025636od_a_a A4) F) G)))))))
% 0.26/0.71 (assert (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (X tptp.produc1572603623od_a_a) (C2 tptp.product_prod_a_a) (G (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr533818957od_a_a A4) F) G)))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.product_prod_a_a) (A2 tptp.a) (B3 tptp.product_prod_a_a) (R tptp.set_Product_prod_a_a) (S tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1361298640od_a_a (@ (@ tptp.produc563767703od_a_a (@ (@ tptp.produc1299253312od_a_a A) B2)) (@ (@ tptp.produc1299253312od_a_a A2) B3))) (@ (@ tptp.lex_pr1321960536od_a_a R) S)) (or (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) A2)) R) (and (= A A2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) B3)) S))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.a) (A2 tptp.product_prod_a_a) (B3 tptp.a) (R tptp.set_Pr1948701895od_a_a) (S tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member470802768_a_a_a (@ (@ tptp.produc2054708503_a_a_a (@ (@ tptp.produc2061588782_a_a_a A) B2)) (@ (@ tptp.produc2061588782_a_a_a A2) B3))) (@ (@ tptp.lex_pr2084296006_a_a_a R) S)) (or (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) A2)) R) (and (= A A2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) B3)) S))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (A2 tptp.product_prod_a_a) (B3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (S tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.produc1474507607od_a_a A))) (= (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a (@ _let_1 B2)) (@ (@ tptp.produc1474507607od_a_a A2) B3))) (@ (@ tptp.lex_pr942790511od_a_a R) S)) (or (@ (@ tptp.member2057358096od_a_a (@ _let_1 A2)) R) (and (= A A2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) B3)) S)))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (A2 tptp.a) (B3 tptp.a) (R tptp.set_Product_prod_a_a) (S tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.product_Pair_a_a A))) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ _let_1 B2)) (@ (@ tptp.product_Pair_a_a A2) B3))) (@ (@ tptp.lex_prod_a_a R) S)) (or (@ (@ tptp.member449909584od_a_a (@ _let_1 A2)) R) (and (= A A2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) B3)) S)))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_a))) (= (@ (@ tptp.member1403138919_a_a_a (@ (@ tptp.produc2061588782_a_a_a A) B2)) (@ (@ tptp.produc1282482655_a_a_a A4) B)) (and (@ (@ tptp.member449909584od_a_a A) A4) (@ (@ tptp.member_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a))) (= (@ (@ tptp.member122808528od_a_a (@ (@ tptp.produc1555606807od_a_a A) B2)) (@ (@ tptp.produc1227942600od_a_a A4) B)) (and (@ (@ tptp.member449909584od_a_a A) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.product_prod_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_Product_prod_a_a))) (= (@ (@ tptp.member160619001od_a_a (@ (@ tptp.produc1299253312od_a_a A) B2)) (@ (@ tptp.produc520147185od_a_a A4) B)) (and (@ (@ tptp.member_a A) A4) (@ (@ tptp.member449909584od_a_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.produc1572603623od_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_Pr1948701895od_a_a))) (= (@ (@ tptp.member448091577od_a_a (@ (@ tptp.produc1095491584od_a_a A) B2)) (@ (@ tptp.produc663418545od_a_a A4) B)) (and (@ (@ tptp.member_a A) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (B2 tptp.product_prod_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a))) (= (@ (@ tptp.member1545452880od_a_a (@ (@ tptp.produc524982679od_a_a A) B2)) (@ (@ tptp.produc197318472od_a_a A4) B)) (and (@ (@ tptp.member2057358096od_a_a A) A4) (@ (@ tptp.member449909584od_a_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (B2 tptp.a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_a))) (= (@ (@ tptp.member575366567_a_a_a (@ (@ tptp.produc436797294_a_a_a A) B2)) (@ (@ tptp.produc4724255_a_a_a A4) B)) (and (@ (@ tptp.member2057358096od_a_a A) A4) (@ (@ tptp.member_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (B2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a))) (= (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A) B2)) (@ (@ tptp.produc1460477704od_a_a A4) B)) (and (@ (@ tptp.member2057358096od_a_a A) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_a))) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.product_Sigma_a_a A4) B)) (and (@ (@ tptp.member_a A) A4) (@ (@ tptp.member_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.produc304751368od_a_a A4) B)) (and (@ (@ tptp.member449909584od_a_a A) A4) (@ (@ tptp.member449909584od_a_a B2) (@ B A))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.a) (B (-> tptp.product_prod_a_a tptp.set_a))) (=> (@ (@ tptp.member449909584od_a_a A) A4) (=> (@ (@ tptp.member_a B2) (@ B A)) (@ (@ tptp.member1403138919_a_a_a (@ (@ tptp.produc2061588782_a_a_a A) B2)) (@ (@ tptp.produc1282482655_a_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.produc1572603623od_a_a) (B (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member449909584od_a_a A) A4) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ B A)) (@ (@ tptp.member122808528od_a_a (@ (@ tptp.produc1555606807od_a_a A) B2)) (@ (@ tptp.produc1227942600od_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (A4 tptp.set_a) (B2 tptp.product_prod_a_a) (B (-> tptp.a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member_a A) A4) (=> (@ (@ tptp.member449909584od_a_a B2) (@ B A)) (@ (@ tptp.member160619001od_a_a (@ (@ tptp.produc1299253312od_a_a A) B2)) (@ (@ tptp.produc520147185od_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (A4 tptp.set_a) (B2 tptp.produc1572603623od_a_a) (B (-> tptp.a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member_a A) A4) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ B A)) (@ (@ tptp.member448091577od_a_a (@ (@ tptp.produc1095491584od_a_a A) B2)) (@ (@ tptp.produc663418545od_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.product_prod_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a A) A4) (=> (@ (@ tptp.member449909584od_a_a B2) (@ B A)) (@ (@ tptp.member1545452880od_a_a (@ (@ tptp.produc524982679od_a_a A) B2)) (@ (@ tptp.produc197318472od_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.a) (B (-> tptp.produc1572603623od_a_a tptp.set_a))) (=> (@ (@ tptp.member2057358096od_a_a A) A4) (=> (@ (@ tptp.member_a B2) (@ B A)) (@ (@ tptp.member575366567_a_a_a (@ (@ tptp.produc436797294_a_a_a A) B2)) (@ (@ tptp.produc4724255_a_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.produc1572603623od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member2057358096od_a_a A) A4) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ B A)) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A) B2)) (@ (@ tptp.produc1460477704od_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (A4 tptp.set_a) (B2 tptp.a) (B (-> tptp.a tptp.set_a))) (=> (@ (@ tptp.member_a A) A4) (=> (@ (@ tptp.member_a B2) (@ B A)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.product_Sigma_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member449909584od_a_a A) A4) (=> (@ (@ tptp.member449909584od_a_a B2) (@ B A)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.produc304751368od_a_a A4) B))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_a))) (=> (@ (@ tptp.member1403138919_a_a_a (@ (@ tptp.produc2061588782_a_a_a A) B2)) (@ (@ tptp.produc1282482655_a_a_a A4) B)) (not (=> (@ (@ tptp.member449909584od_a_a A) A4) (not (@ (@ tptp.member_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member122808528od_a_a (@ (@ tptp.produc1555606807od_a_a A) B2)) (@ (@ tptp.produc1227942600od_a_a A4) B)) (not (=> (@ (@ tptp.member449909584od_a_a A) A4) (not (@ (@ tptp.member2057358096od_a_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.product_prod_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member160619001od_a_a (@ (@ tptp.produc1299253312od_a_a A) B2)) (@ (@ tptp.produc520147185od_a_a A4) B)) (not (=> (@ (@ tptp.member_a A) A4) (not (@ (@ tptp.member449909584od_a_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.produc1572603623od_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member448091577od_a_a (@ (@ tptp.produc1095491584od_a_a A) B2)) (@ (@ tptp.produc663418545od_a_a A4) B)) (not (=> (@ (@ tptp.member_a A) A4) (not (@ (@ tptp.member2057358096od_a_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (B2 tptp.product_prod_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member1545452880od_a_a (@ (@ tptp.produc524982679od_a_a A) B2)) (@ (@ tptp.produc197318472od_a_a A4) B)) (not (=> (@ (@ tptp.member2057358096od_a_a A) A4) (not (@ (@ tptp.member449909584od_a_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (B2 tptp.a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_a))) (=> (@ (@ tptp.member575366567_a_a_a (@ (@ tptp.produc436797294_a_a_a A) B2)) (@ (@ tptp.produc4724255_a_a_a A4) B)) (not (=> (@ (@ tptp.member2057358096od_a_a A) A4) (not (@ (@ tptp.member_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.produc1572603623od_a_a) (B2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A) B2)) (@ (@ tptp.produc1460477704od_a_a A4) B)) (not (=> (@ (@ tptp.member2057358096od_a_a A) A4) (not (@ (@ tptp.member2057358096od_a_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.product_Sigma_a_a A4) B)) (not (=> (@ (@ tptp.member_a A) A4) (not (@ (@ tptp.member_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.produc304751368od_a_a A4) B)) (not (=> (@ (@ tptp.member449909584od_a_a A) A4) (not (@ (@ tptp.member449909584od_a_a B2) (@ B A))))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.product_Sigma_a_a A4) B)) (@ (@ tptp.member_a B2) (@ B A)))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.produc304751368od_a_a A4) B)) (@ (@ tptp.member449909584od_a_a B2) (@ B A)))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.product_Sigma_a_a A4) B)) (@ (@ tptp.member_a A) A4))))
% 0.26/0.71 (assert (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.produc304751368od_a_a A4) B)) (@ (@ tptp.member449909584od_a_a A) A4))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1016684094_a_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_a))) (=> (@ (@ tptp.member1403138919_a_a_a C2) (@ (@ tptp.produc1282482655_a_a_a A4) B)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc2061588782_a_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc772425383od_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member122808528od_a_a C2) (@ (@ tptp.produc1227942600od_a_a A4) B)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (forall ((Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc1555606807od_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1921647824od_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member160619001od_a_a C2) (@ (@ tptp.produc520147185od_a_a A4) B)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (forall ((Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc1299253312od_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1555800720od_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member448091577od_a_a C2) (@ (@ tptp.produc663418545od_a_a A4) B)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (forall ((Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc1095491584od_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc47586087od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member1545452880od_a_a C2) (@ (@ tptp.produc197318472od_a_a A4) B)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (forall ((Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc524982679od_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1683075710_a_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_a))) (=> (@ (@ tptp.member575366567_a_a_a C2) (@ (@ tptp.produc4724255_a_a_a A4) B)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc436797294_a_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1990712039od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B (-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a))) (=> (@ (@ tptp.member1899387664od_a_a C2) (@ (@ tptp.produc1460477704od_a_a A4) B)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (forall ((Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc1935643479od_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_a))) (=> (@ (@ tptp.member449909584od_a_a C2) (@ (@ tptp.product_Sigma_a_a A4) B)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.product_Pair_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a C2) (@ (@ tptp.produc304751368od_a_a A4) B)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (forall ((Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc1474507607od_a_a X3) Y3)))))))))))
% 0.26/0.71 (assert (forall ((X tptp.produc1016684094_a_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_a)) (= (@ (@ tptp.member1403138919_a_a_a X) (@ (@ tptp.produc1282482655_a_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B))) (and (@ (@ tptp.member449909584od_a_a (@ tptp.produc1805832986_a_a_a X)) A4) (@ (@ tptp.member_a (@ tptp.produc1954021468_a_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.produc772425383od_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member122808528od_a_a X) (@ (@ tptp.produc1227942600od_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B))) (and (@ (@ tptp.member449909584od_a_a (@ tptp.produc1775747843od_a_a X)) A4) (@ (@ tptp.member2057358096od_a_a (@ tptp.produc1055472197od_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1921647824od_a_a) (A4 tptp.set_a) (B tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member160619001od_a_a X) (@ (@ tptp.produc520147185od_a_a A4) (lambda ((Uu tptp.a)) B))) (and (@ (@ tptp.member_a (@ tptp.produc1043497516od_a_a X)) A4) (@ (@ tptp.member449909584od_a_a (@ tptp.produc1191685998od_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1555800720od_a_a) (A4 tptp.set_a) (B tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member448091577od_a_a X) (@ (@ tptp.produc663418545od_a_a A4) (lambda ((Uu tptp.a)) B))) (and (@ (@ tptp.member_a (@ tptp.produc530563564od_a_a X)) A4) (@ (@ tptp.member2057358096od_a_a (@ tptp.produc921029422od_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.produc47586087od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member1545452880od_a_a X) (@ (@ tptp.produc197318472od_a_a A4) (lambda ((Uu tptp.produc1572603623od_a_a)) B))) (and (@ (@ tptp.member2057358096od_a_a (@ tptp.produc745123715od_a_a X)) A4) (@ (@ tptp.member449909584od_a_a (@ tptp.produc24848069od_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1683075710_a_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_a)) (= (@ (@ tptp.member575366567_a_a_a X) (@ (@ tptp.produc4724255_a_a_a A4) (lambda ((Uu tptp.produc1572603623od_a_a)) B))) (and (@ (@ tptp.member2057358096od_a_a (@ tptp.produc2019352922_a_a_a X)) A4) (@ (@ tptp.member_a (@ tptp.produc262335132_a_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1990712039od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1899387664od_a_a X) (@ (@ tptp.produc1460477704od_a_a A4) (lambda ((Uu tptp.produc1572603623od_a_a)) B))) (and (@ (@ tptp.member2057358096od_a_a (@ tptp.produc303632707od_a_a X)) A4) (@ (@ tptp.member2057358096od_a_a (@ tptp.produc1441227909od_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.member449909584od_a_a X) (@ (@ tptp.product_Sigma_a_a A4) (lambda ((Uu tptp.a)) B))) (and (@ (@ tptp.member_a (@ tptp.product_fst_a_a X)) A4) (@ (@ tptp.member_a (@ tptp.product_snd_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member2057358096od_a_a X) (@ (@ tptp.produc304751368od_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B))) (and (@ (@ tptp.member449909584od_a_a (@ tptp.produc2115494211od_a_a X)) A4) (@ (@ tptp.member449909584od_a_a (@ tptp.produc368344197od_a_a X)) B)))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X))) (= (@ _let_1 (@ (@ tptp.product_product_a_a A4) B)) (@ _let_1 (@ (@ tptp.product_Sigma_a_a A4) (lambda ((Uu tptp.a)) B)))))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X))) (= (@ _let_1 (@ (@ tptp.produc905674258od_a_a A4) B)) (@ _let_1 (@ (@ tptp.produc304751368od_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B)))))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X3))) (=> (@ _let_1 A4) (@ _let_1 B)))) (@ (@ tptp.ord_le1824328871od_a_a A4) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a) (B tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A4) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a A4) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X3))) (=> (@ _let_1 A4) (@ _let_1 B)))) (@ (@ tptp.ord_le456379495od_a_a A4) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (@ (@ tptp.member449909584od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.image_794773445od_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.a)) (B tptp.set_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (@ (@ tptp.member_a (@ F X3)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_340790172_a_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (@ (@ tptp.member2057358096od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.image_1765377413od_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a) (F (-> tptp.a tptp.product_prod_a_a)) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (@ (@ tptp.member449909584od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.image_1725938350od_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a) (F (-> tptp.a tptp.a)) (B tptp.set_a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (@ (@ tptp.member_a (@ F X3)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a) (F (-> tptp.a tptp.produc1572603623od_a_a)) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (@ (@ tptp.member2057358096od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.image_1763923566od_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (@ (@ tptp.member449909584od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.image_734753285od_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (B tptp.set_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (@ (@ tptp.member_a (@ F X3)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_1105229276_a_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (@ (@ tptp.member2057358096od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.image_236793797od_a_a F) A4)) B))))
% 0.26/0.71 (assert (forall ((R tptp.set_Product_prod_a_a) (S tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.a) (Y3 tptp.a)) (let ((_let_1 (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le1824328871od_a_a R) S))))
% 0.26/0.71 (assert (forall ((R tptp.set_Pr1948701895od_a_a) (S tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le456379495od_a_a R) S))))
% 0.26/0.71 (assert (= tptp.ord_le1824328871od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (forall ((T2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 0.26/0.71 (assert (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 0.26/0.71 (assert (= tptp.ord_le456379495od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (forall ((T2 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 0.26/0.71 (assert (= tptp.ord_le1824328871od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (forall ((X4 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X4))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 0.26/0.71 (assert (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (forall ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 0.26/0.71 (assert (= tptp.ord_le456379495od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (forall ((X4 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X4))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a) (C2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ (@ tptp.ord_le1824328871od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a) (B tptp.set_a) (C2 tptp.a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a) (C2 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ (@ tptp.ord_le456379495od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a) (X tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X))) (=> (@ (@ tptp.ord_le1824328871od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a) (B tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a) (X tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X))) (=> (@ (@ tptp.ord_le456379495od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Z2 tptp.set_Product_prod_a_a) (X5 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (@ (@ tptp.member449909584od_a_a X) Z2) (=> (@ (@ tptp.ord_le1824328871od_a_a Z2) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) X5) (@ P2 X4))))) (@ P2 X)))))
% 0.26/0.71 (assert (forall ((X tptp.a) (Z2 tptp.set_a) (X5 tptp.set_a) (P2 (-> tptp.a Bool))) (=> (@ (@ tptp.member_a X) Z2) (=> (@ (@ tptp.ord_less_eq_set_a Z2) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) X5) (@ P2 X4))))) (@ P2 X)))))
% 0.26/0.71 (assert (forall ((X tptp.produc1572603623od_a_a) (Z2 tptp.set_Pr1948701895od_a_a) (X5 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (=> (@ (@ tptp.member2057358096od_a_a X) Z2) (=> (@ (@ tptp.ord_le456379495od_a_a Z2) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) X5) (@ P2 X4))))) (@ P2 X)))))
% 0.26/0.71 (assert (forall ((X5 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) X5) (@ P2 X4))))) X5)))
% 0.26/0.71 (assert (forall ((X5 tptp.set_a) (P2 (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) X5) (@ P2 X4))))) X5)))
% 0.26/0.71 (assert (forall ((X5 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (@ (@ tptp.ord_le456379495od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) X5) (@ P2 X4))))) X5)))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 X4))))) A4)))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a) (P2 (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 X4))))) A4)))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (@ (@ tptp.ord_le456379495od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 X4))))) A4)))
% 0.26/0.71 (assert (forall ((B tptp.set_Product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a B))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 X4))))) (forall ((X4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X4) B) (@ P2 X4))))))))
% 0.26/0.71 (assert (forall ((B tptp.set_a) (A4 tptp.set_a) (P2 (-> tptp.a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_a B))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 X4))))) (forall ((X4 tptp.a)) (=> (@ (@ tptp.member_a X4) B) (@ P2 X4))))))))
% 0.26/0.71 (assert (forall ((B tptp.set_Pr1948701895od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (let ((_let_1 (@ tptp.ord_le456379495od_a_a B))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 X4))))) (forall ((X4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X4) B) (@ P2 X4))))))))
% 0.26/0.71 (assert (forall ((B tptp.set_Product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (Q (-> tptp.product_prod_a_a Bool)) (P2 (-> tptp.product_prod_a_a Bool))) (=> (@ (@ tptp.ord_le1824328871od_a_a B) A4) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) B) (=> (@ Q X3) (@ P2 X3)))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) B) (@ Q X4))))) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 X4)))))))))
% 0.26/0.71 (assert (forall ((B tptp.set_a) (A4 tptp.set_a) (Q (-> tptp.a Bool)) (P2 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_set_a B) A4) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) B) (=> (@ Q X3) (@ P2 X3)))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) B) (@ Q X4))))) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 X4)))))))))
% 0.26/0.71 (assert (forall ((B tptp.set_Pr1948701895od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (Q (-> tptp.produc1572603623od_a_a Bool)) (P2 (-> tptp.produc1572603623od_a_a Bool))) (=> (@ (@ tptp.ord_le456379495od_a_a B) A4) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) B) (=> (@ Q X3) (@ P2 X3)))) (@ (@ tptp.ord_le456379495od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) B) (@ Q X4))))) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 X4)))))))))
% 0.26/0.71 (assert (forall ((R2 tptp.set_Product_prod_a_a) (S3 tptp.set_Product_prod_a_a)) (= (@ (@ tptp.ord_le1347718902_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) R2))) (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) S3))) (@ (@ tptp.ord_le1824328871od_a_a R2) S3))))
% 0.26/0.71 (assert (forall ((R2 tptp.set_a) (S3 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) R2))) (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) S3))) (@ (@ tptp.ord_less_eq_set_a R2) S3))))
% 0.26/0.71 (assert (forall ((R2 tptp.set_Pr1948701895od_a_a) (S3 tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.ord_le1525442358_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) R2))) (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) S3))) (@ (@ tptp.ord_le456379495od_a_a R2) S3))))
% 0.26/0.71 (assert (= tptp.ord_le1824328871od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1347718902_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A6))) (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) B5))))))
% 0.26/0.71 (assert (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (@ (@ tptp.ord_less_eq_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A6))) (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) B5))))))
% 0.26/0.71 (assert (= tptp.ord_le456379495od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (@ (@ tptp.ord_le1525442358_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A6))) (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) B5))))))
% 0.26/0.71 (assert (forall ((R2 tptp.set_Product_prod_a_a) (S3 tptp.set_Product_prod_a_a)) (= (@ (@ tptp.ord_less_eq_a_a_o (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R2))) (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) S3))) (@ (@ tptp.ord_le1824328871od_a_a R2) S3))))
% 0.26/0.71 (assert (forall ((R2 tptp.set_Pr1948701895od_a_a) (S3 tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.ord_le252190158_a_a_o (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R2))) (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) S3))) (@ (@ tptp.ord_le456379495od_a_a R2) S3))))
% 0.26/0.71 (assert (forall ((X tptp.a) (Fx tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Fx)) (@ (@ tptp.bNF_Gr_a_a A4) F)) (@ (@ tptp.member_a X) A4))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Fx tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Fx)) (@ (@ tptp.bNF_Gr1372473186od_a_a A4) F)) (@ (@ tptp.member449909584od_a_a X) A4))))
% 0.26/0.71 (assert (forall ((X tptp.a) (Fx tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Fx)) (@ (@ tptp.bNF_Gr_a_a A4) F)) (= (@ F X) Fx))))
% 0.26/0.71 (assert (forall ((X tptp.product_prod_a_a) (Fx tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Fx)) (@ (@ tptp.bNF_Gr1372473186od_a_a A4) F)) (= (@ F X) Fx))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a)) (= (forall ((X4 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a X4) A4))) (= A4 tptp.bot_bo2131659635od_a_a))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_a)) (= (forall ((X4 tptp.a)) (not (@ (@ tptp.member_a X4) A4))) (= A4 tptp.bot_bot_set_a))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a)) (= (forall ((X4 tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a X4) A4))) (= A4 tptp.bot_bo1116205875od_a_a))))
% 0.26/0.71 (assert (forall ((C2 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a C2) tptp.bot_bo2131659635od_a_a))))
% 0.26/0.71 (assert (forall ((C2 tptp.a)) (not (@ (@ tptp.member_a C2) tptp.bot_bot_set_a))))
% 0.26/0.71 (assert (forall ((C2 tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a C2) tptp.bot_bo1116205875od_a_a))))
% 0.26/0.71 (assert (forall ((A4 tptp.set_Product_prod_a_a)) (= (exists ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A4)) (not (= A4 tptp.bot_bo2131659635od_a_a)))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_a)) (= (exists ((X4 tptp.a)) (@ (@ tptp.member_a X4) A4)) (not (= A4 tptp.bot_bot_set_a)))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a)) (= (exists ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A4)) (not (= A4 tptp.bot_bo1116205875od_a_a)))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_Product_prod_a_a)) (=> (forall ((Y3 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a Y3) A4))) (= A4 tptp.bot_bo2131659635od_a_a))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_a)) (=> (forall ((Y3 tptp.a)) (not (@ (@ tptp.member_a Y3) A4))) (= A4 tptp.bot_bot_set_a))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a)) (=> (forall ((Y3 tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a Y3) A4))) (= A4 tptp.bot_bo1116205875od_a_a))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_Product_prod_a_a) (A tptp.product_prod_a_a)) (=> (= A4 tptp.bot_bo2131659635od_a_a) (not (@ (@ tptp.member449909584od_a_a A) A4)))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_a) (A tptp.a)) (=> (= A4 tptp.bot_bot_set_a) (not (@ (@ tptp.member_a A) A4)))))
% 0.55/1.22 (assert (forall ((A4 tptp.set_Pr1948701895od_a_a) (A tptp.produc1572603623od_a_a)) (=> (= A4 tptp.bot_bo1116205875od_a_a) (not (@ (@ tptp.member2057358096od_a_a A) A4)))))
% 0.55/1.22 (assert (forall ((A tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a A) tptp.bot_bo2131659635od_a_a))))
% 0.55/1.22 (assert (forall ((A tptp.a)) (not (@ (@ tptp.member_a A) tptp.bot_bot_set_a))))
% 0.55/1.22 (assert (forall ((A tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a A) tptp.bot_bo1116205875od_a_a))))
% 0.55/1.22 (assert (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a tptp.z) tptp.y)) tptp.pr)))
% 0.55/1.22 (set-info :filename cvc5---1.0.5_1472)
% 0.55/1.22 (check-sat-assuming ( true ))
% 0.55/1.22 ------- get file name : TPTP file name is ITP157^1
% 0.55/1.22 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1472.smt2...
% 0.55/1.22 --- Run --ho-elim --full-saturate-quant at 10...
% 0.55/1.22 % SZS status Theorem for ITP157^1
% 0.55/1.22 % SZS output start Proof for ITP157^1
% 0.55/1.22 (
% 0.55/1.22 (let ((_let_1 (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a tptp.z) tptp.y)) tptp.pr)))) (let ((_let_2 (= tptp.ord_le456379495od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (forall ((T2 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))) (let ((_let_3 (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))) (let ((_let_4 (= tptp.ord_le1824328871od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (forall ((T2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))) (let ((_let_5 (= tptp.produc1641853175od_a_a (lambda ((P4 tptp.produc1572603623od_a_a)) (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc368344197od_a_a P4)) (@ tptp.produc2115494211od_a_a P4)))))) (let ((_let_6 (= tptp.product_swap_a_a (lambda ((P4 tptp.product_prod_a_a)) (@ (@ tptp.product_Pair_a_a (@ tptp.product_snd_a_a P4)) (@ tptp.product_fst_a_a P4)))))) (let ((_let_7 (= tptp.top_to993969022_a_a_o (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) tptp.top_to52711959od_a_a))))) (let ((_let_8 (= tptp.top_top_a_a_o (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) tptp.top_to398455383od_a_a))))) (let ((_let_9 (= tptp.top_to2011536774_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) tptp.top_to52711959od_a_a))))) (let ((_let_10 (= tptp.top_top_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) tptp.top_top_set_a))))) (let ((_let_11 (= tptp.top_to1483957574_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) tptp.top_to398455383od_a_a))))) (let ((_let_12 (= tptp.minus_1034916142od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec1635618130od_a_a (@ (@ tptp.minus_107310383_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A6))) (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) B5)))))))) (let ((_let_13 (= tptp.minus_minus_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (@ tptp.collect_a (@ (@ tptp.minus_minus_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A6))) (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) B5)))))))) (let ((_let_14 (= tptp.minus_1507102574od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (@ tptp.collec645855634od_a_a (@ (@ tptp.minus_1797478127_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A6))) (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) B5)))))))) (let ((_let_15 (forall ((A tptp.a) (P2 (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P2)) (@ P2 A))))) (let ((_let_16 (= tptp.prefer1338892073od_a_a (lambda ((Carrier2 tptp.set_Product_prod_a_a) (Relation2 tptp.set_Pr1948701895od_a_a)) (and (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) Relation2) (@ (@ tptp.member449909584od_a_a X4) Carrier2))) (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) Relation2) (@ (@ tptp.member449909584od_a_a Y4) Carrier2))) (@ (@ tptp.order_359341630od_a_a Carrier2) Relation2)))))) (let ((_let_17 (= tptp.prefer1292084992ence_a (lambda ((Carrier2 tptp.set_a) (Relation2 tptp.set_Product_prod_a_a)) (and (forall ((X4 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) Relation2) (@ (@ tptp.member_a X4) Carrier2))) (forall ((X4 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) Relation2) (@ (@ tptp.member_a Y4) Carrier2))) (@ (@ tptp.order_preorder_on_a Carrier2) Relation2)))))) (let ((_let_18 (= tptp.prefer1409946857od_a_a (lambda ((Carrier2 tptp.set_Pr1948701895od_a_a) (Relation2 tptp.set_Pr1295299783od_a_a)) (and (forall ((X4 tptp.produc1572603623od_a_a) (Y4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) Relation2) (@ (@ tptp.member2057358096od_a_a X4) Carrier2))) (forall ((X4 tptp.produc1572603623od_a_a) (Y4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) Relation2) (@ (@ tptp.member2057358096od_a_a Y4) Carrier2))) (@ (@ tptp.order_491428350od_a_a Carrier2) Relation2)))))) (let ((_let_19 (= tptp.prefer74720675od_a_a (lambda ((X4 tptp.product_prod_a_a) (B5 tptp.set_Product_prod_a_a) (P3 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec645855634od_a_a (lambda ((Y4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Y4) B5) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) P3) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y4) X4)) P3)))))))) (let ((_let_20 (= tptp.prefer436369274d_as_a (lambda ((X4 tptp.a) (B5 tptp.set_a) (P3 tptp.set_Product_prod_a_a)) (@ tptp.collect_a (lambda ((Y4 tptp.a)) (and (@ (@ tptp.member_a Y4) B5) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) P3) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y4) X4)) P3)))))))) (let ((_let_21 (= tptp.prefer1867335523od_a_a (lambda ((X4 tptp.produc1572603623od_a_a) (B5 tptp.set_Pr1948701895od_a_a) (P3 tptp.set_Pr1295299783od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((Y4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a Y4) B5) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) P3) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a Y4) X4)) P3)))))))) (let ((_let_22 (= tptp.prefer1498087410od_a_a (lambda ((X4 tptp.product_prod_a_a) (B5 tptp.set_Product_prod_a_a) (P3 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec645855634od_a_a (lambda ((Y4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Y4) B5) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) P3)))))))) (let ((_let_23 (= tptp.prefer1676310729than_a (lambda ((X4 tptp.a) (B5 tptp.set_a) (P3 tptp.set_Product_prod_a_a)) (@ tptp.collect_a (lambda ((Y4 tptp.a)) (and (@ (@ tptp.member_a Y4) B5) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) P3)))))))) (let ((_let_24 (= tptp.prefer926864306od_a_a (lambda ((X4 tptp.produc1572603623od_a_a) (B5 tptp.set_Pr1948701895od_a_a) (P3 tptp.set_Pr1295299783od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((Y4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a Y4) B5) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) P3)))))))) (let ((_let_25 (= tptp.prefer477097315od_a_a (lambda ((X4 tptp.product_prod_a_a) (B5 tptp.set_Product_prod_a_a) (P3 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec645855634od_a_a (lambda ((Y4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Y4) B5) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y4) X4)) P3)))))))) (let ((_let_26 (= tptp.prefer161218362good_a (lambda ((X4 tptp.a) (B5 tptp.set_a) (P3 tptp.set_Product_prod_a_a)) (@ tptp.collect_a (lambda ((Y4 tptp.a)) (and (@ (@ tptp.member_a Y4) B5) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y4) X4)) P3)))))))) (let ((_let_27 (= tptp.prefer55414563od_a_a (lambda ((X4 tptp.produc1572603623od_a_a) (B5 tptp.set_Pr1948701895od_a_a) (P3 tptp.set_Pr1295299783od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((Y4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a Y4) B5) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a Y4) X4)) P3)))))))) (let ((_let_28 (@ tptp.member_a tptp.z))) (let ((_let_29 (@ _let_28 (@ (@ (@ tptp.prefer161218362good_a tptp.y) tptp.b) tptp.pr)))) (let ((_let_30 (ho_158 k_157 tptp.z))) (let ((_let_31 (ho_159 _let_30 (ho_306 k_305 k_465)))) (let ((_let_32 (ho_156 k_465 tptp.z))) (let ((_let_33 (= _let_31 _let_32))) (let ((_let_34 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_621 v ii) (ite (= i ii) e (ho_621 u ii)))))))))) (let ((_let_35 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_621 x z) (ho_621 y z)))) (= x y))))) (let ((_let_36 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_618 v ii) (ite (= i ii) e (ho_618 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_618 x z) (ho_618 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_609 v ii) (ite (= i ii) e (ho_609 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_609 x z) (ho_609 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_227 v ii) (ite (= i ii) e (ho_227 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_227 x z) (ho_227 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_607 v ii) (ite (= i ii) e (ho_607 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_607 x z) (ho_607 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|) (e tptp.set_Pr1295299783od_a_a) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_605 v ii) (ite (= i ii) e (ho_605 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_605 x z) (ho_605 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1295299783od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1295299783od_a_a)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1295299783od_a_a)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_601 v ii) (ite (= i ii) e (ho_601 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_601 x z) (ho_601 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|) (e tptp.set_Pr729215751_a_a_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_602 v ii) (ite (= i ii) e (ho_602 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr729215751_a_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_602 x z) (ho_602 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_598 v ii) (ite (= i ii) e (ho_598 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_598 x z) (ho_598 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_594 v ii) (ite (= i ii) e (ho_594 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_594 x z) (ho_594 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (e |u_(-> tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (i tptp.set_Pr1194146439od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|)) (not (forall ((ii tptp.set_Pr1194146439od_a_a)) (= (ho_487 v ii) (ite (= i ii) e (ho_487 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (y |u_(-> tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|)) (or (not (forall ((z tptp.set_Pr1194146439od_a_a)) (= (ho_487 x z) (ho_487 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_595 v ii) (ite (= i ii) e (ho_595 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_595 x z) (ho_595 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_596 v ii) (ite (= i ii) e (ho_596 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_596 x z) (ho_596 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_590 v ii) (ite (= i ii) e (ho_590 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_590 x z) (ho_590 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_586 v ii) (ite (= i ii) e (ho_586 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_586 x z) (ho_586 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_604 v ii) (ite (= i ii) e (ho_604 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_604 x z) (ho_604 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_584 v ii) (ite (= i ii) e (ho_584 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_584 x z) (ho_584 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_578 v ii) (ite (= i ii) e (ho_578 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_578 x z) (ho_578 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_571 v ii) (ite (= i ii) e (ho_571 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_571 x z) (ho_571 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_572 v ii) (ite (= i ii) e (ho_572 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_572 x z) (ho_572 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.produc1683075710_a_a_a tptp.a)|) (e tptp.a) (i tptp.produc1683075710_a_a_a)) (not (forall ((v |u_(-> tptp.produc1683075710_a_a_a tptp.a)|)) (not (forall ((ii tptp.produc1683075710_a_a_a)) (= (ho_668 v ii) (ite (= i ii) e (ho_668 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.produc1683075710_a_a_a tptp.a)|) (y |u_(-> tptp.produc1683075710_a_a_a tptp.a)|)) (or (not (forall ((z tptp.produc1683075710_a_a_a)) (= (ho_668 x z) (ho_668 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|) (e tptp.set_Pr231806599od_a_a) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_599 v ii) (ite (= i ii) e (ho_599 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr231806599od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_599 x z) (ho_599 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_290 v ii) (ite (= i ii) e (ho_290 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_290 x z) (ho_290 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_569 v ii) (ite (= i ii) e (ho_569 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_569 x z) (ho_569 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> tptp.produc47586087od_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.produc47586087od_a_a)) (not (forall ((v |u_(-> tptp.produc47586087od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.produc47586087od_a_a)) (= (ho_666 v ii) (ite (= i ii) e (ho_666 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.produc47586087od_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.produc47586087od_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.produc47586087od_a_a)) (= (ho_666 x z) (ho_666 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (i |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_565 v ii) (ite (= i ii) e (ho_565 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_565 x z) (ho_565 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (i |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_566 v ii) (ite (= i ii) e (ho_566 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_566 x z) (ho_566 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.a tptp.set_a)|) (e tptp.set_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_a)|)) (not (forall ((ii tptp.a)) (= (ho_271 v ii) (ite (= i ii) e (ho_271 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.a tptp.set_a)|) (y |u_(-> tptp.a tptp.set_a)|)) (or (not (forall ((z tptp.a)) (= (ho_271 x z) (ho_271 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_562 v ii) (ite (= i ii) e (ho_562 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_562 x z) (ho_562 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_379 v ii) (ite (= i ii) e (ho_379 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_379 x z) (ho_379 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_552 v ii) (ite (= i ii) e (ho_552 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_552 x z) (ho_552 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_245 v ii) (ite (= i ii) e (ho_245 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_245 x z) (ho_245 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> tptp.set_a tptp.set_Product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_550 v ii) (ite (= i ii) e (ho_550 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.set_a tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.set_a tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_550 x z) (ho_550 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_408 v ii) (ite (= i ii) e (ho_408 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_408 x z) (ho_408 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_548 v ii) (ite (= i ii) e (ho_548 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_548 x z) (ho_548 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.a tptp.a Bool)|) (e |u_(-> tptp.a tptp.a Bool)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.a tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_546 v ii) (ite (= i ii) e (ho_546 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.a tptp.a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.a tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_546 x z) (ho_546 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.produc1921647824od_a_a Bool)|) (e Bool) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a Bool)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_544 v ii) (ite (= i ii) e (ho_544 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.produc1921647824od_a_a Bool)|) (y |u_(-> tptp.produc1921647824od_a_a Bool)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_544 x z) (ho_544 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> tptp.produc1016684094_a_a_a Bool)|) (e Bool) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a Bool)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_542 v ii) (ite (= i ii) e (ho_542 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.produc1016684094_a_a_a Bool)|) (y |u_(-> tptp.produc1016684094_a_a_a Bool)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_542 x z) (ho_542 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.produc1555800720od_a_a Bool)|) (e Bool) (i tptp.produc1555800720od_a_a)) (not (forall ((v |u_(-> tptp.produc1555800720od_a_a Bool)|)) (not (forall ((ii tptp.produc1555800720od_a_a)) (= (ho_543 v ii) (ite (= i ii) e (ho_543 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.produc1555800720od_a_a Bool)|) (y |u_(-> tptp.produc1555800720od_a_a Bool)|)) (or (not (forall ((z tptp.produc1555800720od_a_a)) (= (ho_543 x z) (ho_543 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (e tptp.produc1921647824od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_539 v ii) (ite (= i ii) e (ho_539 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_539 x z) (ho_539 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_246 v ii) (ite (= i ii) e (ho_246 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.a tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_535 v ii) (ite (= i ii) e (ho_535 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.a tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|) (y |u_(-> tptp.a tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_535 x z) (ho_535 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_383 v ii) (ite (= i ii) e (ho_383 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_383 x z) (ho_383 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_529 v ii) (ite (= i ii) e (ho_529 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_529 x z) (ho_529 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_386 v ii) (ite (= i ii) e (ho_386 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_386 x z) (ho_386 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|) (e tptp.set_Pr1689873822_a_a_a) (i |u_(-> tptp.product_prod_a_a tptp.set_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.set_a)|)) (= (ho_610 v ii) (ite (= i ii) e (ho_610 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_a)_ tptp.set_Pr1689873822_a_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.set_a)|)) (= (ho_610 x z) (ho_610 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|) (e tptp.produc772425383od_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_530 v ii) (ite (= i ii) e (ho_530 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.produc772425383od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_530 x z) (ho_530 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_372 v ii) (ite (= i ii) e (ho_372 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_372 x z) (ho_372 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (e |u_(-> tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_522 v ii) (ite (= i ii) e (ho_522 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (y |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_522 x z) (ho_522 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> tptp.produc1921647824od_a_a tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|) (e |u_(-> tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_519 v ii) (ite (= i ii) e (ho_519 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> tptp.produc1921647824od_a_a tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|) (y |u_(-> tptp.produc1921647824od_a_a tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_519 x z) (ho_519 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_382 v ii) (ite (= i ii) e (ho_382 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_382 x z) (ho_382 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a tptp.produc47586087od_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.produc47586087od_a_a)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a tptp.produc47586087od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_624 v ii) (ite (= i ii) e (ho_624 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a tptp.produc47586087od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a tptp.produc47586087od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_624 x z) (ho_624 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|) (e tptp.produc2010915495od_a_a) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_520 v ii) (ite (= i ii) e (ho_520 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|) (y |u_(-> tptp.produc1921647824od_a_a tptp.produc2010915495od_a_a)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_520 x z) (ho_520 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a Bool)|) (e |u_(-> tptp.set_Pr195866352od_a_a Bool)|) (i tptp.produc1555800720od_a_a)) (not (forall ((v |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a Bool)|)) (not (forall ((ii tptp.produc1555800720od_a_a)) (= (ho_516 v ii) (ite (= i ii) e (ho_516 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a Bool)|) (y |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a Bool)|)) (or (not (forall ((z tptp.produc1555800720od_a_a)) (= (ho_516 x z) (ho_516 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.set_Pr195866352od_a_a Bool)|) (e Bool) (i tptp.set_Pr195866352od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr195866352od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr195866352od_a_a)) (= (ho_517 v ii) (ite (= i ii) e (ho_517 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.set_Pr195866352od_a_a Bool)|) (y |u_(-> tptp.set_Pr195866352od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr195866352od_a_a)) (= (ho_517 x z) (ho_517 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.product_prod_a_a tptp.produc47586087od_a_a)|) (e tptp.produc47586087od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.produc47586087od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_625 v ii) (ite (= i ii) e (ho_625 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.product_prod_a_a tptp.produc47586087od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.produc47586087od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_625 x z) (ho_625 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (e |u_(-> tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (i tptp.set_Pr195866352od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|)) (not (forall ((ii tptp.set_Pr195866352od_a_a)) (= (ho_513 v ii) (ite (= i ii) e (ho_513 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (y |u_(-> tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|)) (or (not (forall ((z tptp.set_Pr195866352od_a_a)) (= (ho_513 x z) (ho_513 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_681 v ii) (ite (= i ii) e (ho_681 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_681 x z) (ho_681 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> tptp.produc1546279079od_a_a tptp.set_Pr660101255od_a_a Bool)|) (e |u_(-> tptp.set_Pr660101255od_a_a Bool)|) (i tptp.produc1546279079od_a_a)) (not (forall ((v |u_(-> tptp.produc1546279079od_a_a tptp.set_Pr660101255od_a_a Bool)|)) (not (forall ((ii tptp.produc1546279079od_a_a)) (= (ho_509 v ii) (ite (= i ii) e (ho_509 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> tptp.produc1546279079od_a_a tptp.set_Pr660101255od_a_a Bool)|) (y |u_(-> tptp.produc1546279079od_a_a tptp.set_Pr660101255od_a_a Bool)|)) (or (not (forall ((z tptp.produc1546279079od_a_a)) (= (ho_509 x z) (ho_509 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> tptp.produc1555800720od_a_a tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|) (e |u_(-> tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|) (i tptp.produc1555800720od_a_a)) (not (forall ((v |u_(-> tptp.produc1555800720od_a_a tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|)) (not (forall ((ii tptp.produc1555800720od_a_a)) (= (ho_506 v ii) (ite (= i ii) e (ho_506 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> tptp.produc1555800720od_a_a tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|) (y |u_(-> tptp.produc1555800720od_a_a tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|)) (or (not (forall ((z tptp.produc1555800720od_a_a)) (= (ho_506 x z) (ho_506 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> tptp.set_Product_prod_a_a Bool)|) (e Bool) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|) (e tptp.produc1546279079od_a_a) (i tptp.produc1555800720od_a_a)) (not (forall ((v |u_(-> tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|)) (not (forall ((ii tptp.produc1555800720od_a_a)) (= (ho_507 v ii) (ite (= i ii) e (ho_507 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|) (y |u_(-> tptp.produc1555800720od_a_a tptp.produc1546279079od_a_a)|)) (or (not (forall ((z tptp.produc1555800720od_a_a)) (= (ho_507 x z) (ho_507 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (e |u_(-> tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (i tptp.produc1555800720od_a_a)) (not (forall ((v |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|)) (not (forall ((ii tptp.produc1555800720od_a_a)) (= (ho_512 v ii) (ite (= i ii) e (ho_512 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (y |u_(-> tptp.produc1555800720od_a_a tptp.set_Pr195866352od_a_a tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|)) (or (not (forall ((z tptp.produc1555800720od_a_a)) (= (ho_512 x z) (ho_512 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> tptp.set_Pr660101255od_a_a Bool)|) (e Bool) (i tptp.set_Pr660101255od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr660101255od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr660101255od_a_a)) (= (ho_510 v ii) (ite (= i ii) e (ho_510 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> tptp.set_Pr660101255od_a_a Bool)|) (y |u_(-> tptp.set_Pr660101255od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr660101255od_a_a)) (= (ho_510 x z) (ho_510 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_219 v ii) (ite (= i ii) e (ho_219 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_219 x z) (ho_219 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a Bool)|) (e |u_(-> tptp.set_Pr1689873822_a_a_a Bool)|) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a Bool)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_503 v ii) (ite (= i ii) e (ho_503 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a Bool)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a Bool)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_503 x z) (ho_503 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (e |u_(-> tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_499 v ii) (ite (= i ii) e (ho_499 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_499 x z) (ho_499 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (e |u_(-> tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (i tptp.set_Pr1689873822_a_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|)) (not (forall ((ii tptp.set_Pr1689873822_a_a_a)) (= (ho_500 v ii) (ite (= i ii) e (ho_500 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (y |u_(-> tptp.set_Pr1689873822_a_a_a tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|)) (or (not (forall ((z tptp.set_Pr1689873822_a_a_a)) (= (ho_500 x z) (ho_500 y z)))) (= x y))))) (let ((_let_172 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_173 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_174 (forall ((u |u_(-> tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (e tptp.set_Pr1689873822_a_a_a) (i tptp.set_Pr729215751_a_a_a)) (not (forall ((v |u_(-> tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|)) (not (forall ((ii tptp.set_Pr729215751_a_a_a)) (= (ho_501 v ii) (ite (= i ii) e (ho_501 u ii)))))))))) (let ((_let_175 (forall ((x |u_(-> tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|) (y |u_(-> tptp.set_Pr729215751_a_a_a tptp.set_Pr1689873822_a_a_a)|)) (or (not (forall ((z tptp.set_Pr729215751_a_a_a)) (= (ho_501 x z) (ho_501 y z)))) (= x y))))) (let ((_let_176 (forall ((u |u_(-> _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|) (e tptp.set_Pr195866352od_a_a) (i |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|)) (= (ho_619 v ii) (ite (= i ii) e (ho_619 u ii)))))))))) (let ((_let_177 (forall ((x |u_(-> _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr195866352od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|)) (= (ho_619 x z) (ho_619 y z)))) (= x y))))) (let ((_let_178 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|) (e tptp.produc1120419623_a_a_a) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_494 v ii) (ite (= i ii) e (ho_494 u ii)))))))))) (let ((_let_179 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_494 x z) (ho_494 y z)))) (= x y))))) (let ((_let_180 (forall ((u |u_(-> tptp.set_Pr729215751_a_a_a Bool)|) (e Bool) (i tptp.set_Pr729215751_a_a_a)) (not (forall ((v |u_(-> tptp.set_Pr729215751_a_a_a Bool)|)) (not (forall ((ii tptp.set_Pr729215751_a_a_a)) (= (ho_497 v ii) (ite (= i ii) e (ho_497 u ii)))))))))) (let ((_let_181 (forall ((x |u_(-> tptp.set_Pr729215751_a_a_a Bool)|) (y |u_(-> tptp.set_Pr729215751_a_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr729215751_a_a_a)) (= (ho_497 x z) (ho_497 y z)))) (= x y))))) (let ((_let_182 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a Bool)|) (e |u_(-> tptp.set_Pr1295299783od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_554 v ii) (ite (= i ii) e (ho_554 u ii)))))))))) (let ((_let_183 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1295299783od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_554 x z) (ho_554 y z)))) (= x y))))) (let ((_let_184 (forall ((u |u_(-> tptp.set_Pr1194146439od_a_a Bool)|) (e Bool) (i tptp.set_Pr1194146439od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1194146439od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1194146439od_a_a)) (= (ho_491 v ii) (ite (= i ii) e (ho_491 u ii)))))))))) (let ((_let_185 (forall ((x |u_(-> tptp.set_Pr1194146439od_a_a Bool)|) (y |u_(-> tptp.set_Pr1194146439od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1194146439od_a_a)) (= (ho_491 x z) (ho_491 y z)))) (= x y))))) (let ((_let_186 (forall ((u |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (e |u_(-> tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (i tptp.produc772425383od_a_a)) (not (forall ((v |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|)) (not (forall ((ii tptp.produc772425383od_a_a)) (= (ho_486 v ii) (ite (= i ii) e (ho_486 u ii)))))))))) (let ((_let_187 (forall ((x |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (y |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|)) (or (not (forall ((z tptp.produc772425383od_a_a)) (= (ho_486 x z) (ho_486 y z)))) (= x y))))) (let ((_let_188 (forall ((u |u_(-> tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (e tptp.set_Pr1194146439od_a_a) (i tptp.set_Pr2081559751od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|)) (not (forall ((ii tptp.set_Pr2081559751od_a_a)) (= (ho_488 v ii) (ite (= i ii) e (ho_488 u ii)))))))))) (let ((_let_189 (forall ((x |u_(-> tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|) (y |u_(-> tptp.set_Pr2081559751od_a_a tptp.set_Pr1194146439od_a_a)|)) (or (not (forall ((z tptp.set_Pr2081559751od_a_a)) (= (ho_488 x z) (ho_488 y z)))) (= x y))))) (let ((_let_190 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.a)|) (e tptp.a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_349 v ii) (ite (= i ii) e (ho_349 u ii)))))))))) (let ((_let_191 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_349 x z) (ho_349 y z)))) (= x y))))) (let ((_let_192 (forall ((u |u_(-> tptp.produc1423126247od_a_a tptp.set_Pr2081559751od_a_a Bool)|) (e |u_(-> tptp.set_Pr2081559751od_a_a Bool)|) (i tptp.produc1423126247od_a_a)) (not (forall ((v |u_(-> tptp.produc1423126247od_a_a tptp.set_Pr2081559751od_a_a Bool)|)) (not (forall ((ii tptp.produc1423126247od_a_a)) (= (ho_483 v ii) (ite (= i ii) e (ho_483 u ii)))))))))) (let ((_let_193 (forall ((x |u_(-> tptp.produc1423126247od_a_a tptp.set_Pr2081559751od_a_a Bool)|) (y |u_(-> tptp.produc1423126247od_a_a tptp.set_Pr2081559751od_a_a Bool)|)) (or (not (forall ((z tptp.produc1423126247od_a_a)) (= (ho_483 x z) (ho_483 y z)))) (= x y))))) (let ((_let_194 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_358 v ii) (ite (= i ii) e (ho_358 u ii)))))))))) (let ((_let_195 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_358 x z) (ho_358 y z)))) (= x y))))) (let ((_let_196 (forall ((u |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (e tptp.set_Pr681306928od_a_a) (i tptp.set_Pr231806599od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|)) (not (forall ((ii tptp.set_Pr231806599od_a_a)) (= (ho_524 v ii) (ite (= i ii) e (ho_524 u ii)))))))))) (let ((_let_197 (forall ((x |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (y |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|)) (or (not (forall ((z tptp.set_Pr231806599od_a_a)) (= (ho_524 x z) (ho_524 y z)))) (= x y))))) (let ((_let_198 (forall ((u |u_(-> tptp.set_Pr6137822_a_a_a Bool)|) (e Bool) (i tptp.set_Pr6137822_a_a_a)) (not (forall ((v |u_(-> tptp.set_Pr6137822_a_a_a Bool)|)) (not (forall ((ii tptp.set_Pr6137822_a_a_a)) (= (ho_637 v ii) (ite (= i ii) e (ho_637 u ii)))))))))) (let ((_let_199 (forall ((x |u_(-> tptp.set_Pr6137822_a_a_a Bool)|) (y |u_(-> tptp.set_Pr6137822_a_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr6137822_a_a_a)) (= (ho_637 x z) (ho_637 y z)))) (= x y))))) (let ((_let_200 (forall ((u |u_(-> tptp.produc772425383od_a_a tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|) (e |u_(-> tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|) (i tptp.produc772425383od_a_a)) (not (forall ((v |u_(-> tptp.produc772425383od_a_a tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|)) (not (forall ((ii tptp.produc772425383od_a_a)) (= (ho_480 v ii) (ite (= i ii) e (ho_480 u ii)))))))))) (let ((_let_201 (forall ((x |u_(-> tptp.produc772425383od_a_a tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|) (y |u_(-> tptp.produc772425383od_a_a tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|)) (or (not (forall ((z tptp.produc772425383od_a_a)) (= (ho_480 x z) (ho_480 y z)))) (= x y))))) (let ((_let_202 (forall ((u |u_(-> tptp.set_Pr1295299783od_a_a Bool)|) (e Bool) (i tptp.set_Pr1295299783od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1295299783od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1295299783od_a_a)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_203 (forall ((x |u_(-> tptp.set_Pr1295299783od_a_a Bool)|) (y |u_(-> tptp.set_Pr1295299783od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1295299783od_a_a)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_204 (forall ((u |u_(-> tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|) (e tptp.produc1423126247od_a_a) (i tptp.produc772425383od_a_a)) (not (forall ((v |u_(-> tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|)) (not (forall ((ii tptp.produc772425383od_a_a)) (= (ho_481 v ii) (ite (= i ii) e (ho_481 u ii)))))))))) (let ((_let_205 (forall ((x |u_(-> tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|) (y |u_(-> tptp.produc772425383od_a_a tptp.produc1423126247od_a_a)|)) (or (not (forall ((z tptp.produc772425383od_a_a)) (= (ho_481 x z) (ho_481 y z)))) (= x y))))) (let ((_let_206 (forall ((u |u_(-> tptp.set_Pr2081559751od_a_a Bool)|) (e Bool) (i tptp.set_Pr2081559751od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr2081559751od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr2081559751od_a_a)) (= (ho_484 v ii) (ite (= i ii) e (ho_484 u ii)))))))))) (let ((_let_207 (forall ((x |u_(-> tptp.set_Pr2081559751od_a_a Bool)|) (y |u_(-> tptp.set_Pr2081559751od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr2081559751od_a_a)) (= (ho_484 x z) (ho_484 y z)))) (= x y))))) (let ((_let_208 (forall ((u |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a Bool)|) (e |u_(-> tptp.set_Pr231806599od_a_a Bool)|) (i tptp.produc2010915495od_a_a)) (not (forall ((v |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a Bool)|)) (not (forall ((ii tptp.produc2010915495od_a_a)) (= (ho_477 v ii) (ite (= i ii) e (ho_477 u ii)))))))))) (let ((_let_209 (forall ((x |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a Bool)|) (y |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a Bool)|)) (or (not (forall ((z tptp.produc2010915495od_a_a)) (= (ho_477 x z) (ho_477 y z)))) (= x y))))) (let ((_let_210 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|) (e tptp.set_Pr173461255od_a_a) (i |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|)) (= (ho_622 v ii) (ite (= i ii) e (ho_622 u ii)))))))))) (let ((_let_211 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr173461255od_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|)) (= (ho_622 x z) (ho_622 y z)))) (= x y))))) (let ((_let_212 (forall ((u |u_(-> tptp.set_Pr231806599od_a_a Bool)|) (e Bool) (i tptp.set_Pr231806599od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr231806599od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr231806599od_a_a)) (= (ho_478 v ii) (ite (= i ii) e (ho_478 u ii)))))))))) (let ((_let_213 (forall ((x |u_(-> tptp.set_Pr231806599od_a_a Bool)|) (y |u_(-> tptp.set_Pr231806599od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr231806599od_a_a)) (= (ho_478 x z) (ho_478 y z)))) (= x y))))) (let ((_let_214 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_574 v ii) (ite (= i ii) e (ho_574 u ii)))))))))) (let ((_let_215 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_574 x z) (ho_574 y z)))) (= x y))))) (let ((_let_216 (forall ((u |u_(-> tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (e tptp.set_Pr231806599od_a_a) (i tptp.set_Pr532616391od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|)) (not (forall ((ii tptp.set_Pr532616391od_a_a)) (= (ho_475 v ii) (ite (= i ii) e (ho_475 u ii)))))))))) (let ((_let_217 (forall ((x |u_(-> tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (y |u_(-> tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|)) (or (not (forall ((z tptp.set_Pr532616391od_a_a)) (= (ho_475 x z) (ho_475 y z)))) (= x y))))) (let ((_let_218 (forall ((u |u_(-> tptp.produc1056976615od_a_a tptp.set_Pr532616391od_a_a Bool)|) (e |u_(-> tptp.set_Pr532616391od_a_a Bool)|) (i tptp.produc1056976615od_a_a)) (not (forall ((v |u_(-> tptp.produc1056976615od_a_a tptp.set_Pr532616391od_a_a Bool)|)) (not (forall ((ii tptp.produc1056976615od_a_a)) (= (ho_470 v ii) (ite (= i ii) e (ho_470 u ii)))))))))) (let ((_let_219 (forall ((x |u_(-> tptp.produc1056976615od_a_a tptp.set_Pr532616391od_a_a Bool)|) (y |u_(-> tptp.produc1056976615od_a_a tptp.set_Pr532616391od_a_a Bool)|)) (or (not (forall ((z tptp.produc1056976615od_a_a)) (= (ho_470 x z) (ho_470 y z)))) (= x y))))) (let ((_let_220 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_352 v ii) (ite (= i ii) e (ho_352 u ii)))))))))) (let ((_let_221 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_352 x z) (ho_352 y z)))) (= x y))))) (let ((_let_222 (forall ((u |u_(-> tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (e |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (i tptp.set_Pr681306928od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|)) (not (forall ((ii tptp.set_Pr681306928od_a_a)) (= (ho_523 v ii) (ite (= i ii) e (ho_523 u ii)))))))))) (let ((_let_223 (forall ((x |u_(-> tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|) (y |u_(-> tptp.set_Pr681306928od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr681306928od_a_a)|)) (or (not (forall ((z tptp.set_Pr681306928od_a_a)) (= (ho_523 x z) (ho_523 y z)))) (= x y))))) (let ((_let_224 (forall ((u |u_(-> tptp.produc2010915495od_a_a tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|) (e |u_(-> tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|) (i tptp.produc2010915495od_a_a)) (not (forall ((v |u_(-> tptp.produc2010915495od_a_a tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|)) (not (forall ((ii tptp.produc2010915495od_a_a)) (= (ho_467 v ii) (ite (= i ii) e (ho_467 u ii)))))))))) (let ((_let_225 (forall ((x |u_(-> tptp.produc2010915495od_a_a tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|) (y |u_(-> tptp.produc2010915495od_a_a tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|)) (or (not (forall ((z tptp.produc2010915495od_a_a)) (= (ho_467 x z) (ho_467 y z)))) (= x y))))) (let ((_let_226 (forall ((u |u_(-> tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|) (e tptp.produc1056976615od_a_a) (i tptp.produc2010915495od_a_a)) (not (forall ((v |u_(-> tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|)) (not (forall ((ii tptp.produc2010915495od_a_a)) (= (ho_468 v ii) (ite (= i ii) e (ho_468 u ii)))))))))) (let ((_let_227 (forall ((x |u_(-> tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|) (y |u_(-> tptp.produc2010915495od_a_a tptp.produc1056976615od_a_a)|)) (or (not (forall ((z tptp.produc2010915495od_a_a)) (= (ho_468 x z) (ho_468 y z)))) (= x y))))) (let ((_let_228 (forall ((u |u_(-> tptp.set_Pr681306928od_a_a Bool)|) (e Bool) (i tptp.set_Pr681306928od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr681306928od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr681306928od_a_a)) (= (ho_527 v ii) (ite (= i ii) e (ho_527 u ii)))))))))) (let ((_let_229 (forall ((x |u_(-> tptp.set_Pr681306928od_a_a Bool)|) (y |u_(-> tptp.set_Pr681306928od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr681306928od_a_a)) (= (ho_527 x z) (ho_527 y z)))) (= x y))))) (let ((_let_230 (forall ((u |u_(-> tptp.set_a tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_396 v ii) (ite (= i ii) e (ho_396 u ii)))))))))) (let ((_let_231 (forall ((x |u_(-> tptp.set_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_396 x z) (ho_396 y z)))) (= x y))))) (let ((_let_232 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_409 v ii) (ite (= i ii) e (ho_409 u ii)))))))))) (let ((_let_233 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_409 x z) (ho_409 y z)))) (= x y))))) (let ((_let_234 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_405 v ii) (ite (= i ii) e (ho_405 u ii)))))))))) (let ((_let_235 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_405 x z) (ho_405 y z)))) (= x y))))) (let ((_let_236 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_403 v ii) (ite (= i ii) e (ho_403 u ii)))))))))) (let ((_let_237 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_403 x z) (ho_403 y z)))) (= x y))))) (let ((_let_238 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_300 v ii) (ite (= i ii) e (ho_300 u ii)))))))))) (let ((_let_239 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_300 x z) (ho_300 y z)))) (= x y))))) (let ((_let_240 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_612 v ii) (ite (= i ii) e (ho_612 u ii)))))))))) (let ((_let_241 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_612 x z) (ho_612 y z)))) (= x y))))) (let ((_let_242 (forall ((u |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_400 v ii) (ite (= i ii) e (ho_400 u ii)))))))))) (let ((_let_243 (forall ((x |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_400 x z) (ho_400 y z)))) (= x y))))) (let ((_let_244 (forall ((u |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.set_a tptp.set_Product_prod_a_a)|) (i |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_395 v ii) (ite (= i ii) e (ho_395 u ii)))))))))) (let ((_let_245 (forall ((x |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_395 x z) (ho_395 y z)))) (= x y))))) (let ((_let_246 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_576 v ii) (ite (= i ii) e (ho_576 u ii)))))))))) (let ((_let_247 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_576 x z) (ho_576 y z)))) (= x y))))) (let ((_let_248 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_249 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_250 (forall ((u |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_392 v ii) (ite (= i ii) e (ho_392 u ii)))))))))) (let ((_let_251 (forall ((x |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_392 x z) (ho_392 y z)))) (= x y))))) (let ((_let_252 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_393 v ii) (ite (= i ii) e (ho_393 u ii)))))))))) (let ((_let_253 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_393 x z) (ho_393 y z)))) (= x y))))) (let ((_let_254 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_390 v ii) (ite (= i ii) e (ho_390 u ii)))))))))) (let ((_let_255 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_390 x z) (ho_390 y z)))) (= x y))))) (let ((_let_256 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_385 v ii) (ite (= i ii) e (ho_385 u ii)))))))))) (let ((_let_257 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (= (ho_385 x z) (ho_385 y z)))) (= x y))))) (let ((_let_258 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_276 v ii) (ite (= i ii) e (ho_276 u ii)))))))))) (let ((_let_259 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_276 x z) (ho_276 y z)))) (= x y))))) (let ((_let_260 (forall ((u |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|) (e |u_(-> tptp.a tptp.produc1016684094_a_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_532 v ii) (ite (= i ii) e (ho_532 u ii)))))))))) (let ((_let_261 (forall ((x |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_532 x z) (ho_532 y z)))) (= x y))))) (let ((_let_262 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_337 v ii) (ite (= i ii) e (ho_337 u ii)))))))))) (let ((_let_263 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_337 x z) (ho_337 y z)))) (= x y))))) (let ((_let_264 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_268 v ii) (ite (= i ii) e (ho_268 u ii)))))))))) (let ((_let_265 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_268 x z) (ho_268 y z)))) (= x y))))) (let ((_let_266 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_238 v ii) (ite (= i ii) e (ho_238 u ii)))))))))) (let ((_let_267 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_238 x z) (ho_238 y z)))) (= x y))))) (let ((_let_268 (forall ((u |u_(-> tptp.produc47586087od_a_a tptp.set_Pr173461255od_a_a Bool)|) (e |u_(-> tptp.set_Pr173461255od_a_a Bool)|) (i tptp.produc47586087od_a_a)) (not (forall ((v |u_(-> tptp.produc47586087od_a_a tptp.set_Pr173461255od_a_a Bool)|)) (not (forall ((ii tptp.produc47586087od_a_a)) (= (ho_627 v ii) (ite (= i ii) e (ho_627 u ii)))))))))) (let ((_let_269 (forall ((x |u_(-> tptp.produc47586087od_a_a tptp.set_Pr173461255od_a_a Bool)|) (y |u_(-> tptp.produc47586087od_a_a tptp.set_Pr173461255od_a_a Bool)|)) (or (not (forall ((z tptp.produc47586087od_a_a)) (= (ho_627 x z) (ho_627 y z)))) (= x y))))) (let ((_let_270 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_271 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_272 (forall ((u |u_(-> tptp.set_a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_273 (forall ((x |u_(-> tptp.set_a tptp.set_a Bool)|) (y |u_(-> tptp.set_a tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_274 (forall ((u |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (e |u_(-> tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (i tptp.set_Pr231806599od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|)) (not (forall ((ii tptp.set_Pr231806599od_a_a)) (= (ho_474 v ii) (ite (= i ii) e (ho_474 u ii)))))))))) (let ((_let_275 (forall ((x |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (y |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|)) (or (not (forall ((z tptp.set_Pr231806599od_a_a)) (= (ho_474 x z) (ho_474 y z)))) (= x y))))) (let ((_let_276 (forall ((u |u_(-> tptp.set_a tptp.a tptp.set_a)|) (e |u_(-> tptp.a tptp.set_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_270 v ii) (ite (= i ii) e (ho_270 u ii)))))))))) (let ((_let_277 (forall ((x |u_(-> tptp.set_a tptp.a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_270 x z) (ho_270 y z)))) (= x y))))) (let ((_let_278 (forall ((u |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_591 v ii) (ite (= i ii) e (ho_591 u ii)))))))))) (let ((_let_279 (forall ((x |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_591 x z) (ho_591 y z)))) (= x y))))) (let ((_let_280 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|) (e tptp.set_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_375 v ii) (ite (= i ii) e (ho_375 u ii)))))))))) (let ((_let_281 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_375 x z) (ho_375 y z)))) (= x y))))) (let ((_let_282 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_222 v ii) (ite (= i ii) e (ho_222 u ii)))))))))) (let ((_let_283 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_284 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_378 v ii) (ite (= i ii) e (ho_378 u ii)))))))))) (let ((_let_285 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_378 x z) (ho_378 y z)))) (= x y))))) (let ((_let_286 (forall ((u |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_285 v ii) (ite (= i ii) e (ho_285 u ii)))))))))) (let ((_let_287 (forall ((x |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_285 x z) (ho_285 y z)))) (= x y))))) (let ((_let_288 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_216 v ii) (ite (= i ii) e (ho_216 u ii)))))))))) (let ((_let_289 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_216 x z) (ho_216 y z)))) (= x y))))) (let ((_let_290 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_359 v ii) (ite (= i ii) e (ho_359 u ii)))))))))) (let ((_let_291 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_359 x z) (ho_359 y z)))) (= x y))))) (let ((_let_292 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_575 v ii) (ite (= i ii) e (ho_575 u ii)))))))))) (let ((_let_293 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_575 x z) (ho_575 y z)))) (= x y))))) (let ((_let_294 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_295 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_296 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ Bool)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_297 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_298 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_344 v ii) (ite (= i ii) e (ho_344 u ii)))))))))) (let ((_let_299 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_344 x z) (ho_344 y z)))) (= x y))))) (let ((_let_300 (forall ((u |u_(-> tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (e tptp.set_Pr195866352od_a_a) (i tptp.set_Pr660101255od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|)) (not (forall ((ii tptp.set_Pr660101255od_a_a)) (= (ho_514 v ii) (ite (= i ii) e (ho_514 u ii)))))))))) (let ((_let_301 (forall ((x |u_(-> tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|) (y |u_(-> tptp.set_Pr660101255od_a_a tptp.set_Pr195866352od_a_a)|)) (or (not (forall ((z tptp.set_Pr660101255od_a_a)) (= (ho_514 x z) (ho_514 y z)))) (= x y))))) (let ((_let_302 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_587 v ii) (ite (= i ii) e (ho_587 u ii)))))))))) (let ((_let_303 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_587 x z) (ho_587 y z)))) (= x y))))) (let ((_let_304 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_241 v ii) (ite (= i ii) e (ho_241 u ii)))))))))) (let ((_let_305 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_241 x z) (ho_241 y z)))) (= x y))))) (let ((_let_306 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.a Bool)|) (e |u_(-> tptp.a tptp.a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_212 v ii) (ite (= i ii) e (ho_212 u ii)))))))))) (let ((_let_307 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_212 x z) (ho_212 y z)))) (= x y))))) (let ((_let_308 (forall ((u |u_(-> tptp.produc1120419623_a_a_a tptp.set_Pr729215751_a_a_a Bool)|) (e |u_(-> tptp.set_Pr729215751_a_a_a Bool)|) (i tptp.produc1120419623_a_a_a)) (not (forall ((v |u_(-> tptp.produc1120419623_a_a_a tptp.set_Pr729215751_a_a_a Bool)|)) (not (forall ((ii tptp.produc1120419623_a_a_a)) (= (ho_496 v ii) (ite (= i ii) e (ho_496 u ii)))))))))) (let ((_let_309 (forall ((x |u_(-> tptp.produc1120419623_a_a_a tptp.set_Pr729215751_a_a_a Bool)|) (y |u_(-> tptp.produc1120419623_a_a_a tptp.set_Pr729215751_a_a_a Bool)|)) (or (not (forall ((z tptp.produc1120419623_a_a_a)) (= (ho_496 x z) (ho_496 y z)))) (= x y))))) (let ((_let_310 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_311 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_312 (forall ((u |u_(-> tptp.set_Pr1689873822_a_a_a Bool)|) (e Bool) (i tptp.set_Pr1689873822_a_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1689873822_a_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1689873822_a_a_a)) (= (ho_504 v ii) (ite (= i ii) e (ho_504 u ii)))))))))) (let ((_let_313 (forall ((x |u_(-> tptp.set_Pr1689873822_a_a_a Bool)|) (y |u_(-> tptp.set_Pr1689873822_a_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1689873822_a_a_a)) (= (ho_504 x z) (ho_504 y z)))) (= x y))))) (let ((_let_314 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_312 v ii) (ite (= i ii) e (ho_312 u ii)))))))))) (let ((_let_315 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a Bool)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_312 x z) (ho_312 y z)))) (= x y))))) (let ((_let_316 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_213 v ii) (ite (= i ii) e (ho_213 u ii)))))))))) (let ((_let_317 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_213 x z) (ho_213 y z)))) (= x y))))) (let ((_let_318 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|) (e tptp.set_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_279 v ii) (ite (= i ii) e (ho_279 u ii)))))))))) (let ((_let_319 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_279 x z) (ho_279 y z)))) (= x y))))) (let ((_let_320 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_556 v ii) (ite (= i ii) e (ho_556 u ii)))))))))) (let ((_let_321 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_556 x z) (ho_556 y z)))) (= x y))))) (let ((_let_322 (forall ((u |u_(-> tptp.set_a tptp.set_a)|) (e tptp.set_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_309 v ii) (ite (= i ii) e (ho_309 u ii)))))))))) (let ((_let_323 (forall ((x |u_(-> tptp.set_a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_309 x z) (ho_309 y z)))) (= x y))))) (let ((_let_324 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_325 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_326 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|) (e tptp.set_Pr1194146439od_a_a) (i |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (= (ho_613 v ii) (ite (= i ii) e (ho_613 u ii)))))))))) (let ((_let_327 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1194146439od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (= (ho_613 x z) (ho_613 y z)))) (= x y))))) (let ((_let_328 (forall ((u |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_209 v ii) (ite (= i ii) e (ho_209 u ii)))))))))) (let ((_let_329 (forall ((x |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_209 x z) (ho_209 y z)))) (= x y))))) (let ((_let_330 (forall ((u |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|) (e |u_(-> tptp.set_Pr1295299783od_a_a Bool)|) (i tptp.produc1990712039od_a_a)) (not (forall ((v |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|)) (not (forall ((ii tptp.produc1990712039od_a_a)) (= (ho_204 v ii) (ite (= i ii) e (ho_204 u ii)))))))))) (let ((_let_331 (forall ((x |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|) (y |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|)) (or (not (forall ((z tptp.produc1990712039od_a_a)) (= (ho_204 x z) (ho_204 y z)))) (= x y))))) (let ((_let_332 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_201 v ii) (ite (= i ii) e (ho_201 u ii)))))))))) (let ((_let_333 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_334 (forall ((u |u_(-> tptp.set_a tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_334 v ii) (ite (= i ii) e (ho_334 u ii)))))))))) (let ((_let_335 (forall ((x |u_(-> tptp.set_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_334 x z) (ho_334 y z)))) (= x y))))) (let ((_let_336 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_337 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_338 (forall ((u |u_(-> tptp.set_a tptp.product_prod_a_a tptp.set_a)|) (e |u_(-> tptp.product_prod_a_a tptp.set_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.product_prod_a_a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_293 v ii) (ite (= i ii) e (ho_293 u ii)))))))))) (let ((_let_339 (forall ((x |u_(-> tptp.set_a tptp.product_prod_a_a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.product_prod_a_a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_293 x z) (ho_293 y z)))) (= x y))))) (let ((_let_340 (forall ((u |u_(-> tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_341 (forall ((x |u_(-> tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|) (y |u_(-> tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_342 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (e tptp.set_Pr1295299783od_a_a) (i |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (= (ho_560 v ii) (ite (= i ii) e (ho_560 u ii)))))))))) (let ((_let_343 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (= (ho_560 x z) (ho_560 y z)))) (= x y))))) (let ((_let_344 (forall ((u |u_(-> tptp.product_prod_a_a Bool)|) (e Bool) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_163 v ii) (ite (= i ii) e (ho_163 u ii)))))))))) (let ((_let_345 (forall ((x |u_(-> tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_163 x z) (ho_163 y z)))) (= x y))))) (let ((_let_346 (forall ((u |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (e |u_(-> tptp.a tptp.product_prod_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_347 (forall ((x |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_348 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (e tptp.produc1990712039od_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_202 v ii) (ite (= i ii) e (ho_202 u ii)))))))))) (let ((_let_349 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_202 x z) (ho_202 y z)))) (= x y))))) (let ((_let_350 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_197 v ii) (ite (= i ii) e (ho_197 u ii)))))))))) (let ((_let_351 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_197 x z) (ho_197 y z)))) (= x y))))) (let ((_let_352 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_346 v ii) (ite (= i ii) e (ho_346 u ii)))))))))) (let ((_let_353 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_346 x z) (ho_346 y z)))) (= x y))))) (let ((_let_354 (forall ((u |u_(-> tptp.set_Pr532616391od_a_a Bool)|) (e Bool) (i tptp.set_Pr532616391od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr532616391od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr532616391od_a_a)) (= (ho_471 v ii) (ite (= i ii) e (ho_471 u ii)))))))))) (let ((_let_355 (forall ((x |u_(-> tptp.set_Pr532616391od_a_a Bool)|) (y |u_(-> tptp.set_Pr532616391od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr532616391od_a_a)) (= (ho_471 x z) (ho_471 y z)))) (= x y))))) (let ((_let_356 (forall ((u |u_(-> tptp.produc1572603623od_a_a Bool)|) (e Bool) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_357 (forall ((x |u_(-> tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_358 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_a)|) (e tptp.set_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_294 v ii) (ite (= i ii) e (ho_294 u ii)))))))))) (let ((_let_359 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_a)|) (y |u_(-> tptp.product_prod_a_a tptp.set_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_294 x z) (ho_294 y z)))) (= x y))))) (let ((_let_360 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_361 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1295299783od_a_a tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_362 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_389 v ii) (ite (= i ii) e (ho_389 u ii)))))))))) (let ((_let_363 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_389 x z) (ho_389 y z)))) (= x y))))) (let ((_let_364 (forall ((u |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_538 v ii) (ite (= i ii) e (ho_538 u ii)))))))))) (let ((_let_365 (forall ((x |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (y |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_538 x z) (ho_538 y z)))) (= x y))))) (let ((_let_366 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_301 v ii) (ite (= i ii) e (ho_301 u ii)))))))))) (let ((_let_367 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_301 x z) (ho_301 y z)))) (= x y))))) (let ((_let_368 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_319 v ii) (ite (= i ii) e (ho_319 u ii)))))))))) (let ((_let_369 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_319 x z) (ho_319 y z)))) (= x y))))) (let ((_let_370 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_559 v ii) (ite (= i ii) e (ho_559 u ii)))))))))) (let ((_let_371 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_559 x z) (ho_559 y z)))) (= x y))))) (let ((_let_372 (forall ((u |u_(-> tptp.set_a tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|) (e |u_(-> tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_373 (forall ((x |u_(-> tptp.set_a tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|) (y |u_(-> tptp.set_a tptp.a tptp.set_Product_prod_a_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_374 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_375 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_376 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_399 v ii) (ite (= i ii) e (ho_399 u ii)))))))))) (let ((_let_377 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_399 x z) (ho_399 y z)))) (= x y))))) (let ((_let_378 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_291 v ii) (ite (= i ii) e (ho_291 u ii)))))))))) (let ((_let_379 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_291 x z) (ho_291 y z)))) (= x y))))) (let ((_let_380 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_a)|) (e tptp.set_a) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_355 v ii) (ite (= i ii) e (ho_355 u ii)))))))))) (let ((_let_381 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_355 x z) (ho_355 y z)))) (= x y))))) (let ((_let_382 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_377 v ii) (ite (= i ii) e (ho_377 u ii)))))))))) (let ((_let_383 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_377 x z) (ho_377 y z)))) (= x y))))) (let ((_let_384 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|)) (= (ho_646 v ii) (ite (= i ii) e (ho_646 u ii)))))))))) (let ((_let_385 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|)) (= (ho_646 x z) (ho_646 y z)))) (= x y))))) (let ((_let_386 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_360 v ii) (ite (= i ii) e (ho_360 u ii)))))))))) (let ((_let_387 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_360 x z) (ho_360 y z)))) (= x y))))) (let ((_let_388 (forall ((u |u_(-> tptp.set_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_155 v ii) (ite (= i ii) e (ho_155 u ii)))))))))) (let ((_let_389 (forall ((x |u_(-> tptp.set_a tptp.a Bool)|) (y |u_(-> tptp.set_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_390 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_588 v ii) (ite (= i ii) e (ho_588 u ii)))))))))) (let ((_let_391 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_588 x z) (ho_588 y z)))) (= x y))))) (let ((_let_392 (forall ((u |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (= (ho_338 v ii) (ite (= i ii) e (ho_338 u ii)))))))))) (let ((_let_393 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (= (ho_338 x z) (ho_338 y z)))) (= x y))))) (let ((_let_394 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_367 v ii) (ite (= i ii) e (ho_367 u ii)))))))))) (let ((_let_395 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_367 x z) (ho_367 y z)))) (= x y))))) (let ((_let_396 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_397 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_398 (forall ((u |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (= (ho_557 v ii) (ite (= i ii) e (ho_557 u ii)))))))))) (let ((_let_399 (forall ((x |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (= (ho_557 x z) (ho_557 y z)))) (= x y))))) (let ((_let_400 (forall ((u |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_401 v ii) (ite (= i ii) e (ho_401 u ii)))))))))) (let ((_let_401 (forall ((x |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_401 x z) (ho_401 y z)))) (= x y))))) (let ((_let_402 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_403 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_404 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_275 v ii) (ite (= i ii) e (ho_275 u ii)))))))))) (let ((_let_405 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_275 x z) (ho_275 y z)))) (= x y))))) (let ((_let_406 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_325 v ii) (ite (= i ii) e (ho_325 u ii)))))))))) (let ((_let_407 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_325 x z) (ho_325 y z)))) (= x y))))) (let ((_let_408 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_615 v ii) (ite (= i ii) e (ho_615 u ii)))))))))) (let ((_let_409 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_615 x z) (ho_615 y z)))) (= x y))))) (let ((_let_410 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_388 v ii) (ite (= i ii) e (ho_388 u ii)))))))))) (let ((_let_411 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_388 x z) (ho_388 y z)))) (= x y))))) (let ((_let_412 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (e tptp.set_Pr1295299783od_a_a) (i |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|)) (= (ho_640 v ii) (ite (= i ii) e (ho_640 u ii)))))))))) (let ((_let_413 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)|)) (= (ho_640 x z) (ho_640 y z)))) (= x y))))) (let ((_let_414 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (= (ho_321 v ii) (ite (= i ii) e (ho_321 u ii)))))))))) (let ((_let_415 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (= (ho_321 x z) (ho_321 y z)))) (= x y))))) (let ((_let_416 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_221 v ii) (ite (= i ii) e (ho_221 u ii)))))))))) (let ((_let_417 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_221 x z) (ho_221 y z)))) (= x y))))) (let ((_let_418 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_331 v ii) (ite (= i ii) e (ho_331 u ii)))))))))) (let ((_let_419 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_331 x z) (ho_331 y z)))) (= x y))))) (let ((_let_420 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (e Bool) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_421 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_422 (forall ((u |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_185 v ii) (ite (= i ii) e (ho_185 u ii)))))))))) (let ((_let_423 (forall ((x |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_424 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_191 v ii) (ite (= i ii) e (ho_191 u ii)))))))))) (let ((_let_425 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_426 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|) (e |u_(-> tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_493 v ii) (ite (= i ii) e (ho_493 u ii)))))))))) (let ((_let_427 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.produc1016684094_a_a_a tptp.produc1120419623_a_a_a)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_493 x z) (ho_493 y z)))) (= x y))))) (let ((_let_428 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_398 v ii) (ite (= i ii) e (ho_398 u ii)))))))))) (let ((_let_429 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|) (y |u_(-> tptp.set_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_398 x z) (ho_398 y z)))) (= x y))))) (let ((_let_430 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_678 v ii) (ite (= i ii) e (ho_678 u ii)))))))))) (let ((_let_431 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_678 x z) (ho_678 y z)))) (= x y))))) (let ((_let_432 (forall ((u |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (= (ho_330 v ii) (ite (= i ii) e (ho_330 u ii)))))))))) (let ((_let_433 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_434 (forall ((u |u_(-> tptp.set_a tptp.set_a tptp.a Bool)|) (e |u_(-> tptp.set_a tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_435 (forall ((x |u_(-> tptp.set_a tptp.set_a tptp.a Bool)|) (y |u_(-> tptp.set_a tptp.set_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_436 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_437 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_438 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a tptp.set_a)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|) (i |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_374 v ii) (ite (= i ii) e (ho_374 u ii)))))))))) (let ((_let_439 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a tptp.set_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_374 x z) (ho_374 y z)))) (= x y))))) (let ((_let_440 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_441 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_442 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|) (e |u_(-> tptp.set_a tptp.set_a)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_364 v ii) (ite (= i ii) e (ho_364 u ii)))))))))) (let ((_let_443 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_364 x z) (ho_364 y z)))) (= x y))))) (let ((_let_444 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_347 v ii) (ite (= i ii) e (ho_347 u ii)))))))))) (let ((_let_445 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_347 x z) (ho_347 y z)))) (= x y))))) (let ((_let_446 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_682 v ii) (ite (= i ii) e (ho_682 u ii)))))))))) (let ((_let_447 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_682 x z) (ho_682 y z)))) (= x y))))) (let ((_let_448 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (= (ho_323 v ii) (ite (= i ii) e (ho_323 u ii)))))))))) (let ((_let_449 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (= (ho_323 x z) (ho_323 y z)))) (= x y))))) (let ((_let_450 (forall ((u |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_451 (forall ((x |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_452 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_357 v ii) (ite (= i ii) e (ho_357 u ii)))))))))) (let ((_let_453 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_357 x z) (ho_357 y z)))) (= x y))))) (let ((_let_454 (forall ((u |u_(-> tptp.set_a Bool)|) (e Bool) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_455 (forall ((x |u_(-> tptp.set_a Bool)|) (y |u_(-> tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_456 (forall ((u |u_(-> tptp.a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_194 v ii) (ite (= i ii) e (ho_194 u ii)))))))))) (let ((_let_457 (forall ((x |u_(-> tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_194 x z) (ho_194 y z)))) (= x y))))) (let ((_let_458 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_579 v ii) (ite (= i ii) e (ho_579 u ii)))))))))) (let ((_let_459 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_579 x z) (ho_579 y z)))) (= x y))))) (let ((_let_460 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_282 v ii) (ite (= i ii) e (ho_282 u ii)))))))))) (let ((_let_461 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_282 x z) (ho_282 y z)))) (= x y))))) (let ((_let_462 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_281 v ii) (ite (= i ii) e (ho_281 u ii)))))))))) (let ((_let_463 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.produc1572603623od_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_281 x z) (ho_281 y z)))) (= x y))))) (let ((_let_464 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|) (e tptp.produc1555800720od_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_536 v ii) (ite (= i ii) e (ho_536 u ii)))))))))) (let ((_let_465 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.produc1555800720od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_536 x z) (ho_536 y z)))) (= x y))))) (let ((_let_466 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_362 v ii) (ite (= i ii) e (ho_362 u ii)))))))))) (let ((_let_467 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_362 x z) (ho_362 y z)))) (= x y))))) (let ((_let_468 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.a tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_284 v ii) (ite (= i ii) e (ho_284 u ii)))))))))) (let ((_let_469 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_284 x z) (ho_284 y z)))) (= x y))))) (let ((_let_470 (forall ((u |u_(-> tptp.produc2010915495od_a_a Bool)|) (e Bool) (i tptp.produc2010915495od_a_a)) (not (forall ((v |u_(-> tptp.produc2010915495od_a_a Bool)|)) (not (forall ((ii tptp.produc2010915495od_a_a)) (= (ho_540 v ii) (ite (= i ii) e (ho_540 u ii)))))))))) (let ((_let_471 (forall ((x |u_(-> tptp.produc2010915495od_a_a Bool)|) (y |u_(-> tptp.produc2010915495od_a_a Bool)|)) (or (not (forall ((z tptp.produc2010915495od_a_a)) (= (ho_540 x z) (ho_540 y z)))) (= x y))))) (let ((_let_472 (forall ((u |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|) (e tptp.set_Pr681306928od_a_a) (i |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (= (ho_616 v ii) (ite (= i ii) e (ho_616 u ii)))))))))) (let ((_let_473 (forall ((x |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.set_Product_prod_a_a)_ tptp.set_Pr681306928od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (= (ho_616 x z) (ho_616 y z)))) (= x y))))) (let ((_let_474 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_582 v ii) (ite (= i ii) e (ho_582 u ii)))))))))) (let ((_let_475 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_582 x z) (ho_582 y z)))) (= x y))))) (let ((_let_476 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_583 v ii) (ite (= i ii) e (ho_583 u ii)))))))))) (let ((_let_477 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_583 x z) (ho_583 y z)))) (= x y))))) (let ((_let_478 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_336 v ii) (ite (= i ii) e (ho_336 u ii)))))))))) (let ((_let_479 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|) (y |u_(-> tptp.set_a _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_336 x z) (ho_336 y z)))) (= x y))))) (let ((_let_480 (forall ((u |u_(-> tptp.a tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_288 v ii) (ite (= i ii) e (ho_288 u ii)))))))))) (let ((_let_481 (forall ((x |u_(-> tptp.a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_288 x z) (ho_288 y z)))) (= x y))))) (let ((_let_482 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.a tptp.set_Product_prod_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_287 v ii) (ite (= i ii) e (ho_287 u ii)))))))))) (let ((_let_483 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_287 x z) (ho_287 y z)))) (= x y))))) (let ((_let_484 (forall ((u |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (e |u_(-> tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (i tptp.produc2010915495od_a_a)) (not (forall ((v |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|)) (not (forall ((ii tptp.produc2010915495od_a_a)) (= (ho_473 v ii) (ite (= i ii) e (ho_473 u ii)))))))))) (let ((_let_485 (forall ((x |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|) (y |u_(-> tptp.produc2010915495od_a_a tptp.set_Pr231806599od_a_a tptp.set_Pr532616391od_a_a tptp.set_Pr231806599od_a_a)|)) (or (not (forall ((z tptp.produc2010915495od_a_a)) (= (ho_473 x z) (ho_473 y z)))) (= x y))))) (let ((_let_486 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (= (ho_348 v ii) (ite (= i ii) e (ho_348 u ii)))))))))) (let ((_let_487 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (= (ho_348 x z) (ho_348 y z)))) (= x y))))) (let ((_let_488 (forall ((u |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_592 v ii) (ite (= i ii) e (ho_592 u ii)))))))))) (let ((_let_489 (forall ((x |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.product_prod_a_a)|)) (= (ho_592 x z) (ho_592 y z)))) (= x y))))) (let ((_let_490 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_296 v ii) (ite (= i ii) e (ho_296 u ii)))))))))) (let ((_let_491 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_296 x z) (ho_296 y z)))) (= x y))))) (let ((_let_492 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_580 v ii) (ite (= i ii) e (ho_580 u ii)))))))))) (let ((_let_493 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_580 x z) (ho_580 y z)))) (= x y))))) (let ((_let_494 (forall ((u |u_(-> tptp.a tptp.produc1016684094_a_a_a)|) (e tptp.produc1016684094_a_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.produc1016684094_a_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_533 v ii) (ite (= i ii) e (ho_533 u ii)))))))))) (let ((_let_495 (forall ((x |u_(-> tptp.a tptp.produc1016684094_a_a_a)|) (y |u_(-> tptp.a tptp.produc1016684094_a_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_533 x z) (ho_533 y z)))) (= x y))))) (let ((_let_496 (forall ((u |u_(-> tptp.produc1555800720od_a_a tptp.a)|) (e tptp.a) (i tptp.produc1555800720od_a_a)) (not (forall ((v |u_(-> tptp.produc1555800720od_a_a tptp.a)|)) (not (forall ((ii tptp.produc1555800720od_a_a)) (= (ho_662 v ii) (ite (= i ii) e (ho_662 u ii)))))))))) (let ((_let_497 (forall ((x |u_(-> tptp.produc1555800720od_a_a tptp.a)|) (y |u_(-> tptp.produc1555800720od_a_a tptp.a)|)) (or (not (forall ((z tptp.produc1555800720od_a_a)) (= (ho_662 x z) (ho_662 y z)))) (= x y))))) (let ((_let_498 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.set_Pr1948701895od_a_a)|) (e tptp.set_Pr1948701895od_a_a) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_298 v ii) (ite (= i ii) e (ho_298 u ii)))))))))) (let ((_let_499 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_298 x z) (ho_298 y z)))) (= x y))))) (let ((_let_500 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_368 v ii) (ite (= i ii) e (ho_368 u ii)))))))))) (let ((_let_501 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_368 x z) (ho_368 y z)))) (= x y))))) (let ((_let_502 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (e |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_407 v ii) (ite (= i ii) e (ho_407 u ii)))))))))) (let ((_let_503 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a Bool)_ _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_407 x z) (ho_407 y z)))) (= x y))))) (let ((_let_504 (forall ((u |u_(-> tptp.product_prod_a_a tptp.a)|) (e tptp.a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_369 v ii) (ite (= i ii) e (ho_369 u ii)))))))))) (let ((_let_505 (forall ((x |u_(-> tptp.product_prod_a_a tptp.a)|) (y |u_(-> tptp.product_prod_a_a tptp.a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_369 x z) (ho_369 y z)))) (= x y))))) (let ((_let_506 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (= (ho_340 v ii) (ite (= i ii) e (ho_340 u ii)))))))))) (let ((_let_507 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (= (ho_340 x z) (ho_340 y z)))) (= x y))))) (let ((_let_508 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_304 v ii) (ite (= i ii) e (ho_304 u ii)))))))))) (let ((_let_509 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_510 (forall ((u |u_(-> tptp.produc772425383od_a_a Bool)|) (e Bool) (i tptp.produc772425383od_a_a)) (not (forall ((v |u_(-> tptp.produc772425383od_a_a Bool)|)) (not (forall ((ii tptp.produc772425383od_a_a)) (= (ho_541 v ii) (ite (= i ii) e (ho_541 u ii)))))))))) (let ((_let_511 (forall ((x |u_(-> tptp.produc772425383od_a_a Bool)|) (y |u_(-> tptp.produc772425383od_a_a Bool)|)) (or (not (forall ((z tptp.produc772425383od_a_a)) (= (ho_541 x z) (ho_541 y z)))) (= x y))))) (let ((_let_512 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (e tptp.set_a) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_306 v ii) (ite (= i ii) e (ho_306 u ii)))))))))) (let ((_let_513 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_306 x z) (ho_306 y z)))) (= x y))))) (let ((_let_514 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_351 v ii) (ite (= i ii) e (ho_351 u ii)))))))))) (let ((_let_515 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_351 x z) (ho_351 y z)))) (= x y))))) (let ((_let_516 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_267 v ii) (ite (= i ii) e (ho_267 u ii)))))))))) (let ((_let_517 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_267 x z) (ho_267 y z)))) (= x y))))) (let ((_let_518 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_316 v ii) (ite (= i ii) e (ho_316 u ii)))))))))) (let ((_let_519 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_316 x z) (ho_316 y z)))) (= x y))))) (let ((_let_520 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_568 v ii) (ite (= i ii) e (ho_568 u ii)))))))))) (let ((_let_521 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_568 x z) (ho_568 y z)))) (= x y))))) (let ((_let_522 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (= (ho_327 v ii) (ite (= i ii) e (ho_327 u ii)))))))))) (let ((_let_523 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|)) (= (ho_327 x z) (ho_327 y z)))) (= x y))))) (let ((_let_524 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_317 v ii) (ite (= i ii) e (ho_317 u ii)))))))))) (let ((_let_525 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_317 x z) (ho_317 y z)))) (= x y))))) (let ((_let_526 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_326 v ii) (ite (= i ii) e (ho_326 u ii)))))))))) (let ((_let_527 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ _u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_326 x z) (ho_326 y z)))) (= x y))))) (let ((_let_528 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_529 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a Bool)|)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_530 (forall ((u |u_(-> tptp.produc47586087od_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.produc47586087od_a_a)) (not (forall ((v |u_(-> tptp.produc47586087od_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.produc47586087od_a_a)) (= (ho_664 v ii) (ite (= i ii) e (ho_664 u ii)))))))))) (let ((_let_531 (forall ((x |u_(-> tptp.produc47586087od_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.produc47586087od_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.produc47586087od_a_a)) (= (ho_664 x z) (ho_664 y z)))) (= x y))))) (let ((_let_532 (forall ((u |u_(-> tptp.a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_328 v ii) (ite (= i ii) e (ho_328 u ii)))))))))) (let ((_let_533 (forall ((x |u_(-> tptp.a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_328 x z) (ho_328 y z)))) (= x y))))) (let ((_let_534 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_182 v ii) (ite (= i ii) e (ho_182 u ii)))))))))) (let ((_let_535 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_536 (forall ((u |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.set_a tptp.set_Pr1948701895od_a_a)|) (i |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (= (ho_333 v ii) (ite (= i ii) e (ho_333 u ii)))))))))) (let ((_let_537 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.produc1572603623od_a_a)_ tptp.set_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc1572603623od_a_a)|)) (= (ho_333 x z) (ho_333 y z)))) (= x y))))) (let ((_let_538 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_341 v ii) (ite (= i ii) e (ho_341 u ii)))))))))) (let ((_let_539 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.produc1572603623od_a_a Bool)_ tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_341 x z) (ho_341 y z)))) (= x y))))) (let ((_let_540 (forall ((u |u_(-> tptp.set_a tptp.set_a tptp.set_a)|) (e |u_(-> tptp.set_a tptp.set_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_308 v ii) (ite (= i ii) e (ho_308 u ii)))))))))) (let ((_let_541 (forall ((x |u_(-> tptp.set_a tptp.set_a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.set_a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_308 x z) (ho_308 y z)))) (= x y))))) (let ((_let_542 (forall ((u |u_(-> tptp.set_Pr173461255od_a_a Bool)|) (e Bool) (i tptp.set_Pr173461255od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr173461255od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr173461255od_a_a)) (= (ho_628 v ii) (ite (= i ii) e (ho_628 u ii)))))))))) (let ((_let_543 (forall ((x |u_(-> tptp.set_Pr173461255od_a_a Bool)|) (y |u_(-> tptp.set_Pr173461255od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr173461255od_a_a)) (= (ho_628 x z) (ho_628 y z)))) (= x y))))) (let ((_let_544 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_563 v ii) (ite (= i ii) e (ho_563 u ii)))))))))) (let ((_let_545 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.product_prod_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_563 x z) (ho_563 y z)))) (= x y))))) (let ((_let_546 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_630 v ii) (ite (= i ii) e (ho_630 u ii)))))))))) (let ((_let_547 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_630 x z) (ho_630 y z)))) (= x y))))) (let ((_let_548 (forall ((u |u_(-> tptp.a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_549 (forall ((x |u_(-> tptp.a tptp.set_a Bool)|) (y |u_(-> tptp.a tptp.set_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_550 (forall ((u |u_(-> tptp.set_a tptp.produc1572603623od_a_a tptp.set_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.produc1572603623od_a_a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_278 v ii) (ite (= i ii) e (ho_278 u ii)))))))))) (let ((_let_551 (forall ((x |u_(-> tptp.set_a tptp.produc1572603623od_a_a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.produc1572603623od_a_a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_278 x z) (ho_278 y z)))) (= x y))))) (let ((_let_552 (forall ((u |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a Bool)|) (e |u_(-> tptp.set_Pr1194146439od_a_a Bool)|) (i tptp.produc772425383od_a_a)) (not (forall ((v |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a Bool)|)) (not (forall ((ii tptp.produc772425383od_a_a)) (= (ho_490 v ii) (ite (= i ii) e (ho_490 u ii)))))))))) (let ((_let_553 (forall ((x |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a Bool)|) (y |u_(-> tptp.produc772425383od_a_a tptp.set_Pr1194146439od_a_a Bool)|)) (or (not (forall ((z tptp.produc772425383od_a_a)) (= (ho_490 x z) (ho_490 y z)))) (= x y))))) (let ((_let_554 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_679 v ii) (ite (= i ii) e (ho_679 u ii)))))))))) (let ((_let_555 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_679 x z) (ho_679 y z)))) (= x y))))) (let ((_let_556 (forall ((u |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a Bool)|) (e |u_(-> tptp.set_Pr681306928od_a_a Bool)|) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a Bool)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_526 v ii) (ite (= i ii) e (ho_526 u ii)))))))))) (let ((_let_557 (forall ((x |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a Bool)|) (y |u_(-> tptp.produc1921647824od_a_a tptp.set_Pr681306928od_a_a Bool)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_526 x z) (ho_526 y z)))) (= x y))))) (let ((_let_558 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_380 v ii) (ite (= i ii) e (ho_380 u ii)))))))))) (let ((_let_559 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_380 x z) (ho_380 y z)))) (= x y))))) (let ((_let_560 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_366 v ii) (ite (= i ii) e (ho_366 u ii)))))))))) (let ((_let_561 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|) (y |u_(-> tptp.set_a _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.a)_ tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_366 x z) (ho_366 y z)))) (= x y))))) (let ((_let_562 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a tptp.set_a)|) (e |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_a)|) (i |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_354 v ii) (ite (= i ii) e (ho_354 u ii)))))))))) (let ((_let_563 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a tptp.set_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.a)_ tptp.set_Pr1948701895od_a_a tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.a)|)) (= (ho_354 x z) (ho_354 y z)))) (= x y))))) (let ((_let_564 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_181 v ii) (ite (= i ii) e (ho_181 u ii)))))))))) (let ((_let_565 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_566 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_314 v ii) (ite (= i ii) e (ho_314 u ii)))))))))) (let ((_let_567 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_314 x z) (ho_314 y z)))) (= x y))))) (let ((_let_568 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_371 v ii) (ite (= i ii) e (ho_371 u ii)))))))))) (let ((_let_569 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.a)_ tptp.set_Product_prod_a_a _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.a)|)) (= (ho_371 x z) (ho_371 y z)))) (= x y))))) (let ((_let_570 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (e |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (= (ho_343 v ii) (ite (= i ii) e (ho_343 u ii)))))))))) (let ((_let_571 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)_ tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (= (ho_343 x z) (ho_343 y z)))) (= x y))))) (let ((_let_572 (forall ((u |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|) (e tptp.set_Pr6137822_a_a_a) (i |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|)) (not (forall ((ii |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|)) (= (ho_631 v ii) (ite (= i ii) e (ho_631 u ii)))))))))) (let ((_let_573 (forall ((x |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|) (y |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_a)_ tptp.set_Pr6137822_a_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc1572603623od_a_a tptp.set_a)|)) (= (ho_631 x z) (ho_631 y z)))) (= x y))))) (let ((_let_574 (forall ((u |u_(-> tptp.a tptp.produc1683075710_a_a_a)|) (e tptp.produc1683075710_a_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.produc1683075710_a_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_634 v ii) (ite (= i ii) e (ho_634 u ii)))))))))) (let ((_let_575 (forall ((x |u_(-> tptp.a tptp.produc1683075710_a_a_a)|) (y |u_(-> tptp.a tptp.produc1683075710_a_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_634 x z) (ho_634 y z)))) (= x y))))) (let ((_let_576 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.a tptp.produc1683075710_a_a_a)|) (e |u_(-> tptp.a tptp.produc1683075710_a_a_a)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.a tptp.produc1683075710_a_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_633 v ii) (ite (= i ii) e (ho_633 u ii)))))))))) (let ((_let_577 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.a tptp.produc1683075710_a_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.a tptp.produc1683075710_a_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_633 x z) (ho_633 y z)))) (= x y))))) (let ((_let_578 (forall ((u |u_(-> tptp.produc1683075710_a_a_a tptp.set_Pr6137822_a_a_a Bool)|) (e |u_(-> tptp.set_Pr6137822_a_a_a Bool)|) (i tptp.produc1683075710_a_a_a)) (not (forall ((v |u_(-> tptp.produc1683075710_a_a_a tptp.set_Pr6137822_a_a_a Bool)|)) (not (forall ((ii tptp.produc1683075710_a_a_a)) (= (ho_636 v ii) (ite (= i ii) e (ho_636 u ii)))))))))) (let ((_let_579 (forall ((x |u_(-> tptp.produc1683075710_a_a_a tptp.set_Pr6137822_a_a_a Bool)|) (y |u_(-> tptp.produc1683075710_a_a_a tptp.set_Pr6137822_a_a_a Bool)|)) (or (not (forall ((z tptp.produc1683075710_a_a_a)) (= (ho_636 x z) (ho_636 y z)))) (= x y))))) (let ((_let_580 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (e |u_(-> _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_639 v ii) (ite (= i ii) e (ho_639 u ii)))))))))) (let ((_let_581 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a _u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a)_ tptp.set_Pr1295299783od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_639 x z) (ho_639 y z)))) (= x y))))) (let ((_let_582 (forall ((u |u_(-> _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i |u_(-> tptp.a tptp.set_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.set_a)|)) (= (ho_643 v ii) (ite (= i ii) e (ho_643 u ii)))))))))) (let ((_let_583 (forall ((x |u_(-> _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.set_a)|)) (= (ho_643 x z) (ho_643 y z)))) (= x y))))) (let ((_let_584 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_642 v ii) (ite (= i ii) e (ho_642 u ii)))))))))) (let ((_let_585 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.set_a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_642 x z) (ho_642 y z)))) (= x y))))) (let ((_let_586 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_645 v ii) (ite (= i ii) e (ho_645 u ii)))))))))) (let ((_let_587 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_645 x z) (ho_645 y z)))) (= x y))))) (let ((_let_588 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.a)|) (e tptp.a) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.a)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_648 v ii) (ite (= i ii) e (ho_648 u ii)))))))))) (let ((_let_589 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.a)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.a)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_648 x z) (ho_648 y z)))) (= x y))))) (let ((_let_590 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_650 v ii) (ite (= i ii) e (ho_650 u ii)))))))))) (let ((_let_591 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_650 x z) (ho_650 y z)))) (= x y))))) (let ((_let_592 (forall ((u |u_(-> tptp.produc772425383od_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.produc772425383od_a_a)) (not (forall ((v |u_(-> tptp.produc772425383od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.produc772425383od_a_a)) (= (ho_652 v ii) (ite (= i ii) e (ho_652 u ii)))))))))) (let ((_let_593 (forall ((x |u_(-> tptp.produc772425383od_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.produc772425383od_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.produc772425383od_a_a)) (= (ho_652 x z) (ho_652 y z)))) (= x y))))) (let ((_let_594 (forall ((u |u_(-> tptp.produc772425383od_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.produc772425383od_a_a)) (not (forall ((v |u_(-> tptp.produc772425383od_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.produc772425383od_a_a)) (= (ho_654 v ii) (ite (= i ii) e (ho_654 u ii)))))))))) (let ((_let_595 (forall ((x |u_(-> tptp.produc772425383od_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.produc772425383od_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.produc772425383od_a_a)) (= (ho_654 x z) (ho_654 y z)))) (= x y))))) (let ((_let_596 (forall ((u |u_(-> tptp.produc1921647824od_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_656 v ii) (ite (= i ii) e (ho_656 u ii)))))))))) (let ((_let_597 (forall ((x |u_(-> tptp.produc1921647824od_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.produc1921647824od_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_656 x z) (ho_656 y z)))) (= x y))))) (let ((_let_598 (forall ((u |u_(-> tptp.produc1921647824od_a_a tptp.a)|) (e tptp.a) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a tptp.a)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_658 v ii) (ite (= i ii) e (ho_658 u ii)))))))))) (let ((_let_599 (forall ((x |u_(-> tptp.produc1921647824od_a_a tptp.a)|) (y |u_(-> tptp.produc1921647824od_a_a tptp.a)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_658 x z) (ho_658 y z)))) (= x y))))) (let ((_let_600 (forall ((u |u_(-> tptp.produc1555800720od_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.produc1555800720od_a_a)) (not (forall ((v |u_(-> tptp.produc1555800720od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.produc1555800720od_a_a)) (= (ho_660 v ii) (ite (= i ii) e (ho_660 u ii)))))))))) (let ((_let_601 (forall ((x |u_(-> tptp.produc1555800720od_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.produc1555800720od_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.produc1555800720od_a_a)) (= (ho_660 x z) (ho_660 y z)))) (= x y))))) (let ((_let_602 (forall ((u |u_(-> tptp.produc1683075710_a_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.produc1683075710_a_a_a)) (not (forall ((v |u_(-> tptp.produc1683075710_a_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.produc1683075710_a_a_a)) (= (ho_670 v ii) (ite (= i ii) e (ho_670 u ii)))))))))) (let ((_let_603 (forall ((x |u_(-> tptp.produc1683075710_a_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.produc1683075710_a_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.produc1683075710_a_a_a)) (= (ho_670 x z) (ho_670 y z)))) (= x y))))) (let ((_let_604 (forall ((u |u_(-> tptp.produc1990712039od_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.produc1990712039od_a_a)) (not (forall ((v |u_(-> tptp.produc1990712039od_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.produc1990712039od_a_a)) (= (ho_672 v ii) (ite (= i ii) e (ho_672 u ii)))))))))) (let ((_let_605 (forall ((x |u_(-> tptp.produc1990712039od_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.produc1990712039od_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.produc1990712039od_a_a)) (= (ho_672 x z) (ho_672 y z)))) (= x y))))) (let ((_let_606 (forall ((u |u_(-> tptp.set_a tptp.set_a tptp.set_Product_prod_a_a)|) (e |u_(-> tptp.set_a tptp.set_Product_prod_a_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_675 v ii) (ite (= i ii) e (ho_675 u ii)))))))))) (let ((_let_607 (forall ((x |u_(-> tptp.set_a tptp.set_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_a tptp.set_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_675 x z) (ho_675 y z)))) (= x y))))) (let ((_let_608 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_684 v ii) (ite (= i ii) e (ho_684 u ii)))))))))) (let ((_let_609 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_684 x z) (ho_684 y z)))) (= x y))))) (let ((_let_610 (forall ((u |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_686 v ii) (ite (= i ii) e (ho_686 u ii)))))))))) (let ((_let_611 (forall ((x |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.set_Pr1948701895od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_686 x z) (ho_686 y z)))) (= x y))))) (let ((_let_612 (forall ((BOUND_VARIABLE_14474 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14475 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_147 BOUND_VARIABLE_14474) BOUND_VARIABLE_14475) (ho_152 (ho_151 k_150 BOUND_VARIABLE_14475) BOUND_VARIABLE_14474))))) (let ((_let_613 (forall ((BOUND_VARIABLE_14466 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14467 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_153 BOUND_VARIABLE_14466) BOUND_VARIABLE_14467) (ho_152 (ho_151 k_150 BOUND_VARIABLE_14467) BOUND_VARIABLE_14466))))) (let ((_let_614 (forall ((BOUND_VARIABLE_14458 tptp.set_a) (BOUND_VARIABLE_14459 tptp.a)) (= (ho_156 (ho_155 k_154 BOUND_VARIABLE_14458) BOUND_VARIABLE_14459) (ho_159 (ho_158 k_157 BOUND_VARIABLE_14459) BOUND_VARIABLE_14458))))) (let ((_let_615 (forall ((BOUND_VARIABLE_14450 tptp.set_a) (BOUND_VARIABLE_14451 tptp.a)) (= (ho_156 (ho_155 k_160 BOUND_VARIABLE_14450) BOUND_VARIABLE_14451) (ho_159 (ho_158 k_157 BOUND_VARIABLE_14451) BOUND_VARIABLE_14450))))) (let ((_let_616 (forall ((BOUND_VARIABLE_14442 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14443 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_161 BOUND_VARIABLE_14442) BOUND_VARIABLE_14443) (ho_166 (ho_165 k_164 BOUND_VARIABLE_14443) BOUND_VARIABLE_14442))))) (let ((_let_617 (forall ((BOUND_VARIABLE_14434 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14435 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_167 BOUND_VARIABLE_14434) BOUND_VARIABLE_14435) (ho_166 (ho_165 k_164 BOUND_VARIABLE_14435) BOUND_VARIABLE_14434))))) (let ((_let_618 (forall ((BOUND_VARIABLE_14426 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14427 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_168 BOUND_VARIABLE_14426) BOUND_VARIABLE_14427) (ho_152 (ho_151 k_150 BOUND_VARIABLE_14427) BOUND_VARIABLE_14426))))) (let ((_let_619 (forall ((BOUND_VARIABLE_14418 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14419 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_169 BOUND_VARIABLE_14418) BOUND_VARIABLE_14419) (ho_152 (ho_151 k_150 BOUND_VARIABLE_14419) BOUND_VARIABLE_14418))))) (let ((_let_620 (forall ((BOUND_VARIABLE_14406 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14407 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14408 tptp.produc1572603623od_a_a)) (let ((_let_1 (ho_151 k_150 BOUND_VARIABLE_14408))) (= (ho_149 (ho_148 (ho_171 k_170 BOUND_VARIABLE_14406) BOUND_VARIABLE_14407) BOUND_VARIABLE_14408) (and (ho_152 _let_1 BOUND_VARIABLE_14406) (not (ho_152 _let_1 BOUND_VARIABLE_14407)))))))) (let ((_let_621 (forall ((BOUND_VARIABLE_14398 tptp.set_a) (BOUND_VARIABLE_14399 tptp.a)) (= (ho_156 (ho_155 k_172 BOUND_VARIABLE_14398) BOUND_VARIABLE_14399) (ho_159 (ho_158 k_157 BOUND_VARIABLE_14399) BOUND_VARIABLE_14398))))) (let ((_let_622 (forall ((BOUND_VARIABLE_14390 tptp.set_a) (BOUND_VARIABLE_14391 tptp.a)) (= (ho_156 (ho_155 k_173 BOUND_VARIABLE_14390) BOUND_VARIABLE_14391) (ho_159 (ho_158 k_157 BOUND_VARIABLE_14391) BOUND_VARIABLE_14390))))) (let ((_let_623 (forall ((BOUND_VARIABLE_14378 tptp.set_a) (BOUND_VARIABLE_14379 tptp.set_a) (BOUND_VARIABLE_14380 tptp.a)) (let ((_let_1 (ho_158 k_157 BOUND_VARIABLE_14380))) (= (ho_156 (ho_155 (ho_175 k_174 BOUND_VARIABLE_14378) BOUND_VARIABLE_14379) BOUND_VARIABLE_14380) (and (ho_159 _let_1 BOUND_VARIABLE_14378) (not (ho_159 _let_1 BOUND_VARIABLE_14379)))))))) (let ((_let_624 (forall ((BOUND_VARIABLE_14370 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14371 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_176 BOUND_VARIABLE_14370) BOUND_VARIABLE_14371) (ho_166 (ho_165 k_164 BOUND_VARIABLE_14371) BOUND_VARIABLE_14370))))) (let ((_let_625 (forall ((BOUND_VARIABLE_14362 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14363 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_177 BOUND_VARIABLE_14362) BOUND_VARIABLE_14363) (ho_166 (ho_165 k_164 BOUND_VARIABLE_14363) BOUND_VARIABLE_14362))))) (let ((_let_626 (forall ((BOUND_VARIABLE_14350 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14351 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14352 tptp.product_prod_a_a)) (let ((_let_1 (ho_165 k_164 BOUND_VARIABLE_14352))) (= (ho_163 (ho_162 (ho_179 k_178 BOUND_VARIABLE_14350) BOUND_VARIABLE_14351) BOUND_VARIABLE_14352) (and (ho_166 _let_1 BOUND_VARIABLE_14350) (not (ho_166 _let_1 BOUND_VARIABLE_14351)))))))) (let ((_let_627 (forall ((BOUND_VARIABLE_14335 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14336 tptp.product_prod_a_a) (BOUND_VARIABLE_14337 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14338 tptp.product_prod_a_a)) (= (ho_163 (ho_183 (ho_182 (ho_181 k_180 BOUND_VARIABLE_14335) BOUND_VARIABLE_14336) BOUND_VARIABLE_14337) BOUND_VARIABLE_14338) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_14338) BOUND_VARIABLE_14335) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_14338) BOUND_VARIABLE_14336)) BOUND_VARIABLE_14337)))))) (let ((_let_628 (forall ((BOUND_VARIABLE_14316 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14317 tptp.product_prod_a_a) (BOUND_VARIABLE_14318 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14319 tptp.product_prod_a_a)) (= (ho_163 (ho_183 (ho_182 (ho_181 k_187 BOUND_VARIABLE_14316) BOUND_VARIABLE_14317) BOUND_VARIABLE_14318) BOUND_VARIABLE_14319) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_14319) BOUND_VARIABLE_14316) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_14317) BOUND_VARIABLE_14319)) BOUND_VARIABLE_14318) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_14319) BOUND_VARIABLE_14317)) BOUND_VARIABLE_14318)))))) (let ((_let_629 (forall ((BOUND_VARIABLE_14301 tptp.set_a) (BOUND_VARIABLE_14302 tptp.a) (BOUND_VARIABLE_14303 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14304 tptp.a)) (= (ho_156 (ho_191 (ho_190 (ho_189 k_188 BOUND_VARIABLE_14301) BOUND_VARIABLE_14302) BOUND_VARIABLE_14303) BOUND_VARIABLE_14304) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_14304) BOUND_VARIABLE_14301) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_14304) BOUND_VARIABLE_14302)) BOUND_VARIABLE_14303)))))) (let ((_let_630 (forall ((BOUND_VARIABLE_14282 tptp.set_a) (BOUND_VARIABLE_14283 tptp.a) (BOUND_VARIABLE_14284 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14285 tptp.a)) (= (ho_156 (ho_191 (ho_190 (ho_189 k_195 BOUND_VARIABLE_14282) BOUND_VARIABLE_14283) BOUND_VARIABLE_14284) BOUND_VARIABLE_14285) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_14285) BOUND_VARIABLE_14282) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_14283) BOUND_VARIABLE_14285)) BOUND_VARIABLE_14284) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_14285) BOUND_VARIABLE_14283)) BOUND_VARIABLE_14284)))))) (let ((_let_631 (forall ((BOUND_VARIABLE_14267 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14268 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_14269 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_14270 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_199 (ho_198 (ho_197 k_196 BOUND_VARIABLE_14267) BOUND_VARIABLE_14268) BOUND_VARIABLE_14269) BOUND_VARIABLE_14270) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_14270) BOUND_VARIABLE_14267) (ho_205 (ho_204 k_203 (ho_202 (ho_201 k_200 BOUND_VARIABLE_14270) BOUND_VARIABLE_14268)) BOUND_VARIABLE_14269)))))) (let ((_let_632 (forall ((BOUND_VARIABLE_14248 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14249 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_14250 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_14251 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_199 (ho_198 (ho_197 k_206 BOUND_VARIABLE_14248) BOUND_VARIABLE_14249) BOUND_VARIABLE_14250) BOUND_VARIABLE_14251) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_14251) BOUND_VARIABLE_14248) (ho_205 (ho_204 k_203 (ho_202 (ho_201 k_200 BOUND_VARIABLE_14249) BOUND_VARIABLE_14251)) BOUND_VARIABLE_14250) (ho_205 (ho_204 k_203 (ho_202 (ho_201 k_200 BOUND_VARIABLE_14251) BOUND_VARIABLE_14249)) BOUND_VARIABLE_14250)))))) (let ((_let_633 (forall ((BOUND_VARIABLE_14237 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14238 tptp.product_prod_a_a) (BOUND_VARIABLE_14239 tptp.product_prod_a_a)) (= (ho_163 (ho_209 (ho_208 k_207 BOUND_VARIABLE_14237) BOUND_VARIABLE_14238) BOUND_VARIABLE_14239) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_14238) BOUND_VARIABLE_14239)) BOUND_VARIABLE_14237))))) (let ((_let_634 (forall ((BOUND_VARIABLE_14226 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14227 tptp.product_prod_a_a) (BOUND_VARIABLE_14228 tptp.product_prod_a_a)) (= (ho_163 (ho_209 (ho_208 k_210 BOUND_VARIABLE_14226) BOUND_VARIABLE_14227) BOUND_VARIABLE_14228) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_14227) BOUND_VARIABLE_14228)) BOUND_VARIABLE_14226))))) (let ((_let_635 (forall ((BOUND_VARIABLE_14215 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14216 tptp.a) (BOUND_VARIABLE_14217 tptp.a)) (= (ho_156 (ho_213 (ho_212 k_211 BOUND_VARIABLE_14215) BOUND_VARIABLE_14216) BOUND_VARIABLE_14217) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_14216) BOUND_VARIABLE_14217)) BOUND_VARIABLE_14215))))) (let ((_let_636 (forall ((BOUND_VARIABLE_14204 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14205 tptp.a) (BOUND_VARIABLE_14206 tptp.a)) (= (ho_156 (ho_213 (ho_212 k_214 BOUND_VARIABLE_14204) BOUND_VARIABLE_14205) BOUND_VARIABLE_14206) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_14205) BOUND_VARIABLE_14206)) BOUND_VARIABLE_14204))))) (let ((_let_637 (forall ((BOUND_VARIABLE_14176 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14177 tptp.set_Pr1948701895od_a_a)) (= (ho_217 (ho_216 k_215 (ho_148 k_147 BOUND_VARIABLE_14176)) (ho_148 k_153 BOUND_VARIABLE_14177)) (ho_152 (ho_219 k_218 BOUND_VARIABLE_14176) BOUND_VARIABLE_14177))))) (let ((_let_638 (forall ((BOUND_VARIABLE_14148 tptp.set_a) (BOUND_VARIABLE_14149 tptp.set_a)) (= (ho_222 (ho_221 k_220 (ho_155 k_154 BOUND_VARIABLE_14148)) (ho_155 k_160 BOUND_VARIABLE_14149)) (ho_159 (ho_224 k_223 BOUND_VARIABLE_14148) BOUND_VARIABLE_14149))))) (let ((_let_639 (forall ((BOUND_VARIABLE_14120 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14121 tptp.set_Product_prod_a_a)) (= (ho_227 (ho_226 k_225 (ho_162 k_161 BOUND_VARIABLE_14120)) (ho_162 k_167 BOUND_VARIABLE_14121)) (ho_166 (ho_229 k_228 BOUND_VARIABLE_14120) BOUND_VARIABLE_14121))))) (let ((_let_640 (forall ((BOUND_VARIABLE_14112 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14113 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_230 BOUND_VARIABLE_14112) BOUND_VARIABLE_14113) (ho_152 (ho_151 k_150 BOUND_VARIABLE_14113) BOUND_VARIABLE_14112))))) (let ((_let_641 (forall ((BOUND_VARIABLE_14104 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14105 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_231 BOUND_VARIABLE_14104) BOUND_VARIABLE_14105) (ho_152 (ho_151 k_150 BOUND_VARIABLE_14105) BOUND_VARIABLE_14104))))) (let ((_let_642 (forall ((BOUND_VARIABLE_14096 tptp.set_a) (BOUND_VARIABLE_14097 tptp.a)) (= (ho_156 (ho_155 k_232 BOUND_VARIABLE_14096) BOUND_VARIABLE_14097) (ho_159 (ho_158 k_157 BOUND_VARIABLE_14097) BOUND_VARIABLE_14096))))) (let ((_let_643 (forall ((BOUND_VARIABLE_14088 tptp.set_a) (BOUND_VARIABLE_14089 tptp.a)) (= (ho_156 (ho_155 k_233 BOUND_VARIABLE_14088) BOUND_VARIABLE_14089) (ho_159 (ho_158 k_157 BOUND_VARIABLE_14089) BOUND_VARIABLE_14088))))) (let ((_let_644 (forall ((BOUND_VARIABLE_14080 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14081 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_234 BOUND_VARIABLE_14080) BOUND_VARIABLE_14081) (ho_166 (ho_165 k_164 BOUND_VARIABLE_14081) BOUND_VARIABLE_14080))))) (let ((_let_645 (forall ((BOUND_VARIABLE_14072 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14073 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_235 BOUND_VARIABLE_14072) BOUND_VARIABLE_14073) (ho_166 (ho_165 k_164 BOUND_VARIABLE_14073) BOUND_VARIABLE_14072))))) (let ((_let_646 (forall ((BOUND_VARIABLE_14061 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15309 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_14063 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_237 k_236 BOUND_VARIABLE_14061) BOUND_VARIABLE_15309) BOUND_VARIABLE_14063) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_14063) BOUND_VARIABLE_14061) (ho_149 BOUND_VARIABLE_15309 BOUND_VARIABLE_14063)))))) (let ((_let_647 (forall ((BOUND_VARIABLE_14050 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15331 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_14052 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_237 k_239 BOUND_VARIABLE_14050) BOUND_VARIABLE_15331) BOUND_VARIABLE_14052) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_14052) BOUND_VARIABLE_14050) (ho_149 BOUND_VARIABLE_15331 BOUND_VARIABLE_14052)))))) (let ((_let_648 (forall ((BOUND_VARIABLE_14039 tptp.set_a) (BOUND_VARIABLE_15346 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_14041 tptp.a)) (= (ho_156 (ho_242 (ho_241 k_240 BOUND_VARIABLE_14039) BOUND_VARIABLE_15346) BOUND_VARIABLE_14041) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_14041) BOUND_VARIABLE_14039) (ho_156 BOUND_VARIABLE_15346 BOUND_VARIABLE_14041)))))) (let ((_let_649 (forall ((BOUND_VARIABLE_14028 tptp.set_a) (BOUND_VARIABLE_15368 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_14030 tptp.a)) (= (ho_156 (ho_242 (ho_241 k_243 BOUND_VARIABLE_14028) BOUND_VARIABLE_15368) BOUND_VARIABLE_14030) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_14030) BOUND_VARIABLE_14028) (ho_156 BOUND_VARIABLE_15368 BOUND_VARIABLE_14030)))))) (let ((_let_650 (forall ((BOUND_VARIABLE_14017 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_15383 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_14019 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_245 k_244 BOUND_VARIABLE_14017) BOUND_VARIABLE_15383) BOUND_VARIABLE_14019) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_14019) BOUND_VARIABLE_14017) (ho_163 BOUND_VARIABLE_15383 BOUND_VARIABLE_14019)))))) (let ((_let_651 (forall ((BOUND_VARIABLE_14006 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_15405 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_14008 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_245 k_247 BOUND_VARIABLE_14006) BOUND_VARIABLE_15405) BOUND_VARIABLE_14008) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_14008) BOUND_VARIABLE_14006) (ho_163 BOUND_VARIABLE_15405 BOUND_VARIABLE_14008)))))) (let ((_let_652 (forall ((BOUND_VARIABLE_13995 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15420 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_13997 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_237 k_248 BOUND_VARIABLE_13995) BOUND_VARIABLE_15420) BOUND_VARIABLE_13997) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13997) BOUND_VARIABLE_13995) (ho_149 BOUND_VARIABLE_15420 BOUND_VARIABLE_13997)))))) (let ((_let_653 (forall ((BOUND_VARIABLE_13984 tptp.set_a) (BOUND_VARIABLE_15435 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_13986 tptp.a)) (= (ho_156 (ho_242 (ho_241 k_249 BOUND_VARIABLE_13984) BOUND_VARIABLE_15435) BOUND_VARIABLE_13986) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13986) BOUND_VARIABLE_13984) (ho_156 BOUND_VARIABLE_15435 BOUND_VARIABLE_13986)))))) (let ((_let_654 (forall ((BOUND_VARIABLE_13973 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_15450 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_13975 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_245 k_250 BOUND_VARIABLE_13973) BOUND_VARIABLE_15450) BOUND_VARIABLE_13975) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13975) BOUND_VARIABLE_13973) (ho_163 BOUND_VARIABLE_15450 BOUND_VARIABLE_13975)))))) (let ((_let_655 (forall ((BOUND_VARIABLE_13962 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15465 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_13964 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_237 k_251 BOUND_VARIABLE_13962) BOUND_VARIABLE_15465) BOUND_VARIABLE_13964) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13964) BOUND_VARIABLE_13962) (ho_149 BOUND_VARIABLE_15465 BOUND_VARIABLE_13964)))))) (let ((_let_656 (forall ((BOUND_VARIABLE_13951 tptp.set_a) (BOUND_VARIABLE_15480 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_13953 tptp.a)) (= (ho_156 (ho_242 (ho_241 k_252 BOUND_VARIABLE_13951) BOUND_VARIABLE_15480) BOUND_VARIABLE_13953) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13953) BOUND_VARIABLE_13951) (ho_156 BOUND_VARIABLE_15480 BOUND_VARIABLE_13953)))))) (let ((_let_657 (forall ((BOUND_VARIABLE_13940 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_15495 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_13942 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_245 k_253 BOUND_VARIABLE_13940) BOUND_VARIABLE_15495) BOUND_VARIABLE_13942) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13942) BOUND_VARIABLE_13940) (ho_163 BOUND_VARIABLE_15495 BOUND_VARIABLE_13942)))))) (let ((_let_658 (forall ((BOUND_VARIABLE_13929 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15510 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_13931 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_237 k_254 BOUND_VARIABLE_13929) BOUND_VARIABLE_15510) BOUND_VARIABLE_13931) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13931) BOUND_VARIABLE_13929) (ho_149 BOUND_VARIABLE_15510 BOUND_VARIABLE_13931)))))) (let ((_let_659 (forall ((BOUND_VARIABLE_13918 tptp.set_a) (BOUND_VARIABLE_15525 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_13920 tptp.a)) (= (ho_156 (ho_242 (ho_241 k_255 BOUND_VARIABLE_13918) BOUND_VARIABLE_15525) BOUND_VARIABLE_13920) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13920) BOUND_VARIABLE_13918) (ho_156 BOUND_VARIABLE_15525 BOUND_VARIABLE_13920)))))) (let ((_let_660 (forall ((BOUND_VARIABLE_13907 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_15540 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_13909 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_245 k_256 BOUND_VARIABLE_13907) BOUND_VARIABLE_15540) BOUND_VARIABLE_13909) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13909) BOUND_VARIABLE_13907) (ho_163 BOUND_VARIABLE_15540 BOUND_VARIABLE_13909)))))) (let ((_let_661 (forall ((BOUND_VARIABLE_13896 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15555 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_13898 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_237 k_257 BOUND_VARIABLE_13896) BOUND_VARIABLE_15555) BOUND_VARIABLE_13898) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13898) BOUND_VARIABLE_13896) (ho_149 BOUND_VARIABLE_15555 BOUND_VARIABLE_13898)))))) (let ((_let_662 (forall ((BOUND_VARIABLE_13885 tptp.set_a) (BOUND_VARIABLE_15570 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_13887 tptp.a)) (= (ho_156 (ho_242 (ho_241 k_258 BOUND_VARIABLE_13885) BOUND_VARIABLE_15570) BOUND_VARIABLE_13887) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13887) BOUND_VARIABLE_13885) (ho_156 BOUND_VARIABLE_15570 BOUND_VARIABLE_13887)))))) (let ((_let_663 (forall ((BOUND_VARIABLE_13874 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_15585 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_13876 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_245 k_259 BOUND_VARIABLE_13874) BOUND_VARIABLE_15585) BOUND_VARIABLE_13876) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13876) BOUND_VARIABLE_13874) (ho_163 BOUND_VARIABLE_15585 BOUND_VARIABLE_13876)))))) (let ((_let_664 (forall ((BOUND_VARIABLE_13863 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13864 tptp.set_Pr1948701895od_a_a)) (= (ho_152 (ho_219 k_260 BOUND_VARIABLE_13863) BOUND_VARIABLE_13864) (forall ((T2 tptp.produc1572603623od_a_a)) (let ((_let_1 (ho_151 k_150 T2))) (or (not (ho_152 _let_1 BOUND_VARIABLE_13863)) (ho_152 _let_1 BOUND_VARIABLE_13864)))))))) (let ((_let_665 (forall ((BOUND_VARIABLE_13852 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13853 tptp.set_Pr1948701895od_a_a)) (= (ho_152 (ho_219 k_261 BOUND_VARIABLE_13852) BOUND_VARIABLE_13853) (forall ((X4 tptp.produc1572603623od_a_a)) (let ((_let_1 (ho_151 k_150 X4))) (or (not (ho_152 _let_1 BOUND_VARIABLE_13852)) (ho_152 _let_1 BOUND_VARIABLE_13853)))))))) (let ((_let_666 (forall ((BOUND_VARIABLE_13841 tptp.set_a) (BOUND_VARIABLE_13842 tptp.set_a)) (= (ho_159 (ho_224 k_262 BOUND_VARIABLE_13841) BOUND_VARIABLE_13842) (forall ((T2 tptp.a)) (let ((_let_1 (ho_158 k_157 T2))) (or (not (ho_159 _let_1 BOUND_VARIABLE_13841)) (ho_159 _let_1 BOUND_VARIABLE_13842)))))))) (let ((_let_667 (forall ((BOUND_VARIABLE_13830 tptp.set_a) (BOUND_VARIABLE_13831 tptp.set_a)) (= (ho_159 (ho_224 k_263 BOUND_VARIABLE_13830) BOUND_VARIABLE_13831) (forall ((X4 tptp.a)) (let ((_let_1 (ho_158 k_157 X4))) (or (not (ho_159 _let_1 BOUND_VARIABLE_13830)) (ho_159 _let_1 BOUND_VARIABLE_13831)))))))) (let ((_let_668 (forall ((BOUND_VARIABLE_13819 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13820 tptp.set_Product_prod_a_a)) (= (ho_166 (ho_229 k_264 BOUND_VARIABLE_13819) BOUND_VARIABLE_13820) (forall ((T2 tptp.product_prod_a_a)) (let ((_let_1 (ho_165 k_164 T2))) (or (not (ho_166 _let_1 BOUND_VARIABLE_13819)) (ho_166 _let_1 BOUND_VARIABLE_13820)))))))) (let ((_let_669 (forall ((BOUND_VARIABLE_13808 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13809 tptp.set_Product_prod_a_a)) (= (ho_166 (ho_229 k_265 BOUND_VARIABLE_13808) BOUND_VARIABLE_13809) (forall ((X4 tptp.product_prod_a_a)) (let ((_let_1 (ho_165 k_164 X4))) (or (not (ho_166 _let_1 BOUND_VARIABLE_13808)) (ho_166 _let_1 BOUND_VARIABLE_13809)))))))) (let ((_let_670 (forall ((BOUND_VARIABLE_13802 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13803 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13802 (ho_268 (ho_267 k_266 BOUND_VARIABLE_13802) BOUND_VARIABLE_13803))))) (let ((_let_671 (forall ((BOUND_VARIABLE_13796 tptp.set_a) (BOUND_VARIABLE_13797 tptp.a)) (= BOUND_VARIABLE_13796 (ho_271 (ho_270 k_269 BOUND_VARIABLE_13796) BOUND_VARIABLE_13797))))) (let ((_let_672 (forall ((BOUND_VARIABLE_13790 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13791 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13790 (ho_268 (ho_267 k_272 BOUND_VARIABLE_13790) BOUND_VARIABLE_13791))))) (let ((_let_673 (forall ((BOUND_VARIABLE_13784 tptp.set_a) (BOUND_VARIABLE_13785 tptp.a)) (= BOUND_VARIABLE_13784 (ho_271 (ho_270 k_273 BOUND_VARIABLE_13784) BOUND_VARIABLE_13785))))) (let ((_let_674 (forall ((BOUND_VARIABLE_13778 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13779 tptp.produc1572603623od_a_a)) (= BOUND_VARIABLE_13778 (ho_276 (ho_275 k_274 BOUND_VARIABLE_13778) BOUND_VARIABLE_13779))))) (let ((_let_675 (forall ((BOUND_VARIABLE_13772 tptp.set_a) (BOUND_VARIABLE_13773 tptp.produc1572603623od_a_a)) (= BOUND_VARIABLE_13772 (ho_279 (ho_278 k_277 BOUND_VARIABLE_13772) BOUND_VARIABLE_13773))))) (let ((_let_676 (forall ((BOUND_VARIABLE_13766 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13767 tptp.produc1572603623od_a_a)) (= BOUND_VARIABLE_13766 (ho_282 (ho_281 k_280 BOUND_VARIABLE_13766) BOUND_VARIABLE_13767))))) (let ((_let_677 (forall ((BOUND_VARIABLE_13760 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13761 tptp.a)) (= BOUND_VARIABLE_13760 (ho_285 (ho_284 k_283 BOUND_VARIABLE_13760) BOUND_VARIABLE_13761))))) (let ((_let_678 (forall ((BOUND_VARIABLE_13754 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13755 tptp.a)) (= BOUND_VARIABLE_13754 (ho_288 (ho_287 k_286 BOUND_VARIABLE_13754) BOUND_VARIABLE_13755))))) (let ((_let_679 (forall ((BOUND_VARIABLE_13748 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13749 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13748 (ho_291 (ho_290 k_289 BOUND_VARIABLE_13748) BOUND_VARIABLE_13749))))) (let ((_let_680 (forall ((BOUND_VARIABLE_13742 tptp.set_a) (BOUND_VARIABLE_13743 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13742 (ho_294 (ho_293 k_292 BOUND_VARIABLE_13742) BOUND_VARIABLE_13743))))) (let ((_let_681 (forall ((BOUND_VARIABLE_13712 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13713 tptp.set_Pr1948701895od_a_a)) (= (ho_298 k_297 (ho_238 (ho_296 k_295 (ho_148 k_168 BOUND_VARIABLE_13712)) (ho_148 k_169 BOUND_VARIABLE_13713))) (ho_301 (ho_300 k_299 BOUND_VARIABLE_13712) BOUND_VARIABLE_13713))))) (let ((_let_682 (forall ((BOUND_VARIABLE_13685 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13686 tptp.set_Pr1948701895od_a_a)) (= (ho_298 k_297 (ho_148 (ho_171 k_170 BOUND_VARIABLE_13685) BOUND_VARIABLE_13686)) (ho_301 (ho_300 k_302 BOUND_VARIABLE_13685) BOUND_VARIABLE_13686))))) (let ((_let_683 (forall ((BOUND_VARIABLE_13655 tptp.set_a) (BOUND_VARIABLE_13656 tptp.set_a)) (= (ho_306 k_305 (ho_242 (ho_304 k_303 (ho_155 k_172 BOUND_VARIABLE_13655)) (ho_155 k_173 BOUND_VARIABLE_13656))) (ho_309 (ho_308 k_307 BOUND_VARIABLE_13655) BOUND_VARIABLE_13656))))) (let ((_let_684 (forall ((BOUND_VARIABLE_13628 tptp.set_a) (BOUND_VARIABLE_13629 tptp.set_a)) (= (ho_306 k_305 (ho_155 (ho_175 k_174 BOUND_VARIABLE_13628) BOUND_VARIABLE_13629)) (ho_309 (ho_308 k_310 BOUND_VARIABLE_13628) BOUND_VARIABLE_13629))))) (let ((_let_685 (forall ((BOUND_VARIABLE_13598 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13599 tptp.set_Product_prod_a_a)) (= (ho_314 k_313 (ho_246 (ho_312 k_311 (ho_162 k_176 BOUND_VARIABLE_13598)) (ho_162 k_177 BOUND_VARIABLE_13599))) (ho_317 (ho_316 k_315 BOUND_VARIABLE_13598) BOUND_VARIABLE_13599))))) (let ((_let_686 (forall ((BOUND_VARIABLE_13571 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13572 tptp.set_Product_prod_a_a)) (= (ho_314 k_313 (ho_162 (ho_179 k_178 BOUND_VARIABLE_13571) BOUND_VARIABLE_13572)) (ho_317 (ho_316 k_318 BOUND_VARIABLE_13571) BOUND_VARIABLE_13572))))) (let ((_let_687 (forall ((BOUND_VARIABLE_15926 |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (BOUND_VARIABLE_13558 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15924 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_13560 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_237 (ho_321 k_320 BOUND_VARIABLE_15926) BOUND_VARIABLE_13558) BOUND_VARIABLE_15924) BOUND_VARIABLE_13560) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13560) (ho_301 (ho_323 k_322 BOUND_VARIABLE_15926) BOUND_VARIABLE_13558)) (ho_149 BOUND_VARIABLE_15924 BOUND_VARIABLE_13560)))))) (let ((_let_688 (forall ((BOUND_VARIABLE_13544 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_15957 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_15956 |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)|) (BOUND_VARIABLE_13547 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_327 (ho_326 (ho_325 k_324 BOUND_VARIABLE_13544) BOUND_VARIABLE_15957) BOUND_VARIABLE_15956) BOUND_VARIABLE_13547) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13547) BOUND_VARIABLE_13544) (ho_149 BOUND_VARIABLE_15957 (ho_319 BOUND_VARIABLE_15956 BOUND_VARIABLE_13547))))))) (let ((_let_689 (forall ((BOUND_VARIABLE_15989 |u_(-> tptp.a tptp.produc1572603623od_a_a)|) (BOUND_VARIABLE_13531 tptp.set_a) (BOUND_VARIABLE_15987 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_13533 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_331 (ho_330 k_329 BOUND_VARIABLE_15989) BOUND_VARIABLE_13531) BOUND_VARIABLE_15987) BOUND_VARIABLE_13533) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13533) (ho_334 (ho_333 k_332 BOUND_VARIABLE_15989) BOUND_VARIABLE_13531)) (ho_149 BOUND_VARIABLE_15987 BOUND_VARIABLE_13533)))))) (let ((_let_690 (forall ((BOUND_VARIABLE_13517 tptp.set_a) (BOUND_VARIABLE_16027 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_16026 |u_(-> tptp.a tptp.produc1572603623od_a_a)|) (BOUND_VARIABLE_13520 tptp.a)) (= (ho_156 (ho_338 (ho_337 (ho_336 k_335 BOUND_VARIABLE_13517) BOUND_VARIABLE_16027) BOUND_VARIABLE_16026) BOUND_VARIABLE_13520) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13520) BOUND_VARIABLE_13517) (ho_149 BOUND_VARIABLE_16027 (ho_328 BOUND_VARIABLE_16026 BOUND_VARIABLE_13520))))))) (let ((_let_691 (forall ((BOUND_VARIABLE_16058 |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (BOUND_VARIABLE_13504 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_16057 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_13506 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_238 (ho_341 (ho_340 k_339 BOUND_VARIABLE_16058) BOUND_VARIABLE_13504) BOUND_VARIABLE_16057) BOUND_VARIABLE_13506) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13506) (ho_344 (ho_343 k_342 BOUND_VARIABLE_16058) BOUND_VARIABLE_13504)) (ho_149 BOUND_VARIABLE_16057 BOUND_VARIABLE_13506)))))) (let ((_let_692 (forall ((BOUND_VARIABLE_13490 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_16094 |u_(-> tptp.produc1572603623od_a_a Bool)|) (BOUND_VARIABLE_16093 |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (BOUND_VARIABLE_13493 tptp.product_prod_a_a)) (= (ho_163 (ho_348 (ho_347 (ho_346 k_345 BOUND_VARIABLE_13490) BOUND_VARIABLE_16094) BOUND_VARIABLE_16093) BOUND_VARIABLE_13493) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13493) BOUND_VARIABLE_13490) (ho_149 BOUND_VARIABLE_16094 (ho_186 BOUND_VARIABLE_16093 BOUND_VARIABLE_13493))))))) (let ((_let_693 (forall ((BOUND_VARIABLE_16126 |u_(-> tptp.produc1572603623od_a_a tptp.a)|) (BOUND_VARIABLE_13477 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_16124 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_13479 tptp.a)) (= (ho_156 (ho_242 (ho_352 (ho_351 k_350 BOUND_VARIABLE_16126) BOUND_VARIABLE_13477) BOUND_VARIABLE_16124) BOUND_VARIABLE_13479) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13479) (ho_355 (ho_354 k_353 BOUND_VARIABLE_16126) BOUND_VARIABLE_13477)) (ho_156 BOUND_VARIABLE_16124 BOUND_VARIABLE_13479)))))) (let ((_let_694 (forall ((BOUND_VARIABLE_13463 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_16164 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_16163 |u_(-> tptp.produc1572603623od_a_a tptp.a)|) (BOUND_VARIABLE_13466 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_359 (ho_358 (ho_357 k_356 BOUND_VARIABLE_13463) BOUND_VARIABLE_16164) BOUND_VARIABLE_16163) BOUND_VARIABLE_13466) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13466) BOUND_VARIABLE_13463) (ho_156 BOUND_VARIABLE_16164 (ho_349 BOUND_VARIABLE_16163 BOUND_VARIABLE_13466))))))) (let ((_let_695 (forall ((BOUND_VARIABLE_16196 |u_(-> tptp.a tptp.a)|) (BOUND_VARIABLE_13450 tptp.set_a) (BOUND_VARIABLE_16194 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_13452 tptp.a)) (= (ho_156 (ho_242 (ho_241 (ho_362 k_361 BOUND_VARIABLE_16196) BOUND_VARIABLE_13450) BOUND_VARIABLE_16194) BOUND_VARIABLE_13452) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13452) (ho_309 (ho_364 k_363 BOUND_VARIABLE_16196) BOUND_VARIABLE_13450)) (ho_156 BOUND_VARIABLE_16194 BOUND_VARIABLE_13452)))))) (let ((_let_696 (forall ((BOUND_VARIABLE_13436 tptp.set_a) (BOUND_VARIABLE_16227 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_16226 |u_(-> tptp.a tptp.a)|) (BOUND_VARIABLE_13439 tptp.a)) (= (ho_156 (ho_368 (ho_367 (ho_366 k_365 BOUND_VARIABLE_13436) BOUND_VARIABLE_16227) BOUND_VARIABLE_16226) BOUND_VARIABLE_13439) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13439) BOUND_VARIABLE_13436) (ho_156 BOUND_VARIABLE_16227 (ho_360 BOUND_VARIABLE_16226 BOUND_VARIABLE_13439))))))) (let ((_let_697 (forall ((BOUND_VARIABLE_16259 |u_(-> tptp.product_prod_a_a tptp.a)|) (BOUND_VARIABLE_13423 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_16257 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_13425 tptp.a)) (= (ho_156 (ho_242 (ho_372 (ho_371 k_370 BOUND_VARIABLE_16259) BOUND_VARIABLE_13423) BOUND_VARIABLE_16257) BOUND_VARIABLE_13425) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13425) (ho_375 (ho_374 k_373 BOUND_VARIABLE_16259) BOUND_VARIABLE_13423)) (ho_156 BOUND_VARIABLE_16257 BOUND_VARIABLE_13425)))))) (let ((_let_698 (forall ((BOUND_VARIABLE_13409 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_16297 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_16296 |u_(-> tptp.product_prod_a_a tptp.a)|) (BOUND_VARIABLE_13412 tptp.product_prod_a_a)) (= (ho_163 (ho_379 (ho_378 (ho_377 k_376 BOUND_VARIABLE_13409) BOUND_VARIABLE_16297) BOUND_VARIABLE_16296) BOUND_VARIABLE_13412) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13412) BOUND_VARIABLE_13409) (ho_156 BOUND_VARIABLE_16297 (ho_369 BOUND_VARIABLE_16296 BOUND_VARIABLE_13412))))))) (let ((_let_699 (forall ((BOUND_VARIABLE_16329 |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (BOUND_VARIABLE_13396 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_16327 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_13398 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_383 (ho_382 k_381 BOUND_VARIABLE_16329) BOUND_VARIABLE_13396) BOUND_VARIABLE_16327) BOUND_VARIABLE_13398) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13398) (ho_386 (ho_385 k_384 BOUND_VARIABLE_16329) BOUND_VARIABLE_13396)) (ho_163 BOUND_VARIABLE_16327 BOUND_VARIABLE_13398)))))) (let ((_let_700 (forall ((BOUND_VARIABLE_13382 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_16367 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_16366 |u_(-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)|) (BOUND_VARIABLE_13385 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_390 (ho_389 (ho_388 k_387 BOUND_VARIABLE_13382) BOUND_VARIABLE_16367) BOUND_VARIABLE_16366) BOUND_VARIABLE_13385) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_13385) BOUND_VARIABLE_13382) (ho_163 BOUND_VARIABLE_16367 (ho_380 BOUND_VARIABLE_16366 BOUND_VARIABLE_13385))))))) (let ((_let_701 (forall ((BOUND_VARIABLE_16398 |u_(-> tptp.a tptp.product_prod_a_a)|) (BOUND_VARIABLE_13369 tptp.set_a) (BOUND_VARIABLE_16397 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_13371 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_393 (ho_392 k_391 BOUND_VARIABLE_16398) BOUND_VARIABLE_13369) BOUND_VARIABLE_16397) BOUND_VARIABLE_13371) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13371) (ho_396 (ho_395 k_394 BOUND_VARIABLE_16398) BOUND_VARIABLE_13369)) (ho_163 BOUND_VARIABLE_16397 BOUND_VARIABLE_13371)))))) (let ((_let_702 (forall ((BOUND_VARIABLE_13355 tptp.set_a) (BOUND_VARIABLE_16434 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_16433 |u_(-> tptp.a tptp.product_prod_a_a)|) (BOUND_VARIABLE_13358 tptp.a)) (= (ho_156 (ho_400 (ho_399 (ho_398 k_397 BOUND_VARIABLE_13355) BOUND_VARIABLE_16434) BOUND_VARIABLE_16433) BOUND_VARIABLE_13358) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_13358) BOUND_VARIABLE_13355) (ho_163 BOUND_VARIABLE_16434 (ho_194 BOUND_VARIABLE_16433 BOUND_VARIABLE_13358))))))) (let ((_let_703 (forall ((BOUND_VARIABLE_16466 |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|) (BOUND_VARIABLE_13342 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_16464 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_13344 tptp.product_prod_a_a)) (= (ho_163 (ho_246 (ho_245 (ho_403 k_402 BOUND_VARIABLE_16466) BOUND_VARIABLE_13342) BOUND_VARIABLE_16464) BOUND_VARIABLE_13344) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13344) (ho_317 (ho_405 k_404 BOUND_VARIABLE_16466) BOUND_VARIABLE_13342)) (ho_163 BOUND_VARIABLE_16464 BOUND_VARIABLE_13344)))))) (let ((_let_704 (forall ((BOUND_VARIABLE_13328 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_16497 |u_(-> tptp.product_prod_a_a Bool)|) (BOUND_VARIABLE_16496 |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|) (BOUND_VARIABLE_13331 tptp.product_prod_a_a)) (= (ho_163 (ho_409 (ho_408 (ho_407 k_406 BOUND_VARIABLE_13328) BOUND_VARIABLE_16497) BOUND_VARIABLE_16496) BOUND_VARIABLE_13331) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13331) BOUND_VARIABLE_13328) (ho_163 BOUND_VARIABLE_16497 (ho_401 BOUND_VARIABLE_16496 BOUND_VARIABLE_13331))))))) (let ((_let_705 (forall ((BOUND_VARIABLE_13320 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13321 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_410 BOUND_VARIABLE_13320) BOUND_VARIABLE_13321) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13321) BOUND_VARIABLE_13320))))) (let ((_let_706 (forall ((BOUND_VARIABLE_13312 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13313 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_411 BOUND_VARIABLE_13312) BOUND_VARIABLE_13313) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13313) BOUND_VARIABLE_13312))))) (let ((_let_707 (forall ((BOUND_VARIABLE_13304 tptp.set_a) (BOUND_VARIABLE_13305 tptp.a)) (= (ho_156 (ho_155 k_412 BOUND_VARIABLE_13304) BOUND_VARIABLE_13305) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13305) BOUND_VARIABLE_13304))))) (let ((_let_708 (forall ((BOUND_VARIABLE_13296 tptp.set_a) (BOUND_VARIABLE_13297 tptp.a)) (= (ho_156 (ho_155 k_413 BOUND_VARIABLE_13296) BOUND_VARIABLE_13297) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13297) BOUND_VARIABLE_13296))))) (let ((_let_709 (forall ((BOUND_VARIABLE_13288 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13289 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_414 BOUND_VARIABLE_13288) BOUND_VARIABLE_13289) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13289) BOUND_VARIABLE_13288))))) (let ((_let_710 (forall ((BOUND_VARIABLE_13280 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13281 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_415 BOUND_VARIABLE_13280) BOUND_VARIABLE_13281) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13281) BOUND_VARIABLE_13280))))) (let ((_let_711 (forall ((BOUND_VARIABLE_13272 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13273 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_416 BOUND_VARIABLE_13272) BOUND_VARIABLE_13273) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13273) BOUND_VARIABLE_13272))))) (let ((_let_712 (forall ((BOUND_VARIABLE_13264 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13265 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_417 BOUND_VARIABLE_13264) BOUND_VARIABLE_13265) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13265) BOUND_VARIABLE_13264))))) (let ((_let_713 (forall ((BOUND_VARIABLE_13256 tptp.set_a) (BOUND_VARIABLE_13257 tptp.a)) (= (ho_156 (ho_155 k_418 BOUND_VARIABLE_13256) BOUND_VARIABLE_13257) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13257) BOUND_VARIABLE_13256))))) (let ((_let_714 (forall ((BOUND_VARIABLE_13248 tptp.set_a) (BOUND_VARIABLE_13249 tptp.a)) (= (ho_156 (ho_155 k_419 BOUND_VARIABLE_13248) BOUND_VARIABLE_13249) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13249) BOUND_VARIABLE_13248))))) (let ((_let_715 (forall ((BOUND_VARIABLE_13240 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13241 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_420 BOUND_VARIABLE_13240) BOUND_VARIABLE_13241) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13241) BOUND_VARIABLE_13240))))) (let ((_let_716 (forall ((BOUND_VARIABLE_13232 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13233 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_421 BOUND_VARIABLE_13232) BOUND_VARIABLE_13233) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13233) BOUND_VARIABLE_13232))))) (let ((_let_717 (forall ((BOUND_VARIABLE_13224 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13225 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_422 BOUND_VARIABLE_13224) BOUND_VARIABLE_13225) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13225) BOUND_VARIABLE_13224))))) (let ((_let_718 (forall ((BOUND_VARIABLE_13216 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13217 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_423 BOUND_VARIABLE_13216) BOUND_VARIABLE_13217) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13217) BOUND_VARIABLE_13216))))) (let ((_let_719 (forall ((BOUND_VARIABLE_13208 tptp.set_a) (BOUND_VARIABLE_13209 tptp.a)) (= (ho_156 (ho_155 k_424 BOUND_VARIABLE_13208) BOUND_VARIABLE_13209) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13209) BOUND_VARIABLE_13208))))) (let ((_let_720 (forall ((BOUND_VARIABLE_13200 tptp.set_a) (BOUND_VARIABLE_13201 tptp.a)) (= (ho_156 (ho_155 k_425 BOUND_VARIABLE_13200) BOUND_VARIABLE_13201) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13201) BOUND_VARIABLE_13200))))) (let ((_let_721 (forall ((BOUND_VARIABLE_13192 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13193 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_426 BOUND_VARIABLE_13192) BOUND_VARIABLE_13193) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13193) BOUND_VARIABLE_13192))))) (let ((_let_722 (forall ((BOUND_VARIABLE_13184 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13185 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_427 BOUND_VARIABLE_13184) BOUND_VARIABLE_13185) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13185) BOUND_VARIABLE_13184))))) (let ((_let_723 (forall ((BOUND_VARIABLE_13176 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13177 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_428 BOUND_VARIABLE_13176) BOUND_VARIABLE_13177) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13177) BOUND_VARIABLE_13176))))) (let ((_let_724 (forall ((BOUND_VARIABLE_13168 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13169 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_429 BOUND_VARIABLE_13168) BOUND_VARIABLE_13169) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13169) BOUND_VARIABLE_13168))))) (let ((_let_725 (forall ((BOUND_VARIABLE_13160 tptp.set_a) (BOUND_VARIABLE_13161 tptp.a)) (= (ho_156 (ho_155 k_430 BOUND_VARIABLE_13160) BOUND_VARIABLE_13161) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13161) BOUND_VARIABLE_13160))))) (let ((_let_726 (forall ((BOUND_VARIABLE_13152 tptp.set_a) (BOUND_VARIABLE_13153 tptp.a)) (= (ho_156 (ho_155 k_431 BOUND_VARIABLE_13152) BOUND_VARIABLE_13153) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13153) BOUND_VARIABLE_13152))))) (let ((_let_727 (forall ((BOUND_VARIABLE_13144 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13145 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_432 BOUND_VARIABLE_13144) BOUND_VARIABLE_13145) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13145) BOUND_VARIABLE_13144))))) (let ((_let_728 (forall ((BOUND_VARIABLE_13136 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13137 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_433 BOUND_VARIABLE_13136) BOUND_VARIABLE_13137) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13137) BOUND_VARIABLE_13136))))) (let ((_let_729 (forall ((BOUND_VARIABLE_13128 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13129 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_434 BOUND_VARIABLE_13128) BOUND_VARIABLE_13129) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13129) BOUND_VARIABLE_13128))))) (let ((_let_730 (forall ((BOUND_VARIABLE_13120 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13121 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_435 BOUND_VARIABLE_13120) BOUND_VARIABLE_13121) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13121) BOUND_VARIABLE_13120))))) (let ((_let_731 (forall ((BOUND_VARIABLE_13112 tptp.set_a) (BOUND_VARIABLE_13113 tptp.a)) (= (ho_156 (ho_155 k_436 BOUND_VARIABLE_13112) BOUND_VARIABLE_13113) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13113) BOUND_VARIABLE_13112))))) (let ((_let_732 (forall ((BOUND_VARIABLE_13104 tptp.set_a) (BOUND_VARIABLE_13105 tptp.a)) (= (ho_156 (ho_155 k_437 BOUND_VARIABLE_13104) BOUND_VARIABLE_13105) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13105) BOUND_VARIABLE_13104))))) (let ((_let_733 (forall ((BOUND_VARIABLE_13096 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13097 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_438 BOUND_VARIABLE_13096) BOUND_VARIABLE_13097) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13097) BOUND_VARIABLE_13096))))) (let ((_let_734 (forall ((BOUND_VARIABLE_13088 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13089 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_439 BOUND_VARIABLE_13088) BOUND_VARIABLE_13089) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13089) BOUND_VARIABLE_13088))))) (let ((_let_735 (forall ((BOUND_VARIABLE_13080 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13081 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_148 k_440 BOUND_VARIABLE_13080) BOUND_VARIABLE_13081) (ho_152 (ho_151 k_150 BOUND_VARIABLE_13081) BOUND_VARIABLE_13080))))) (let ((_let_736 (forall ((BOUND_VARIABLE_13072 tptp.set_a) (BOUND_VARIABLE_13073 tptp.a)) (= (ho_156 (ho_155 k_441 BOUND_VARIABLE_13072) BOUND_VARIABLE_13073) (ho_159 (ho_158 k_157 BOUND_VARIABLE_13073) BOUND_VARIABLE_13072))))) (let ((_let_737 (forall ((BOUND_VARIABLE_13064 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13065 tptp.product_prod_a_a)) (= (ho_163 (ho_162 k_442 BOUND_VARIABLE_13064) BOUND_VARIABLE_13065) (ho_166 (ho_165 k_164 BOUND_VARIABLE_13065) BOUND_VARIABLE_13064))))) (let ((_let_738 (forall ((BOUND_VARIABLE_13044 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13045 tptp.product_prod_a_a) (BOUND_VARIABLE_13046 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13047 tptp.product_prod_a_a)) (= (ho_163 (ho_183 (ho_182 (ho_181 k_443 BOUND_VARIABLE_13044) BOUND_VARIABLE_13045) BOUND_VARIABLE_13046) BOUND_VARIABLE_13047) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_13047) BOUND_VARIABLE_13044) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_13047) BOUND_VARIABLE_13045)) BOUND_VARIABLE_13046) (not (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_13045) BOUND_VARIABLE_13047)) BOUND_VARIABLE_13046))))))) (let ((_let_739 (forall ((BOUND_VARIABLE_13009 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13010 tptp.product_prod_a_a) (BOUND_VARIABLE_13011 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13012 tptp.product_prod_a_a)) (= (ho_166 (ho_165 k_164 BOUND_VARIABLE_13012) (ho_314 k_313 (ho_183 (ho_182 (ho_181 k_180 BOUND_VARIABLE_13009) BOUND_VARIABLE_13010) BOUND_VARIABLE_13011))) (ho_163 (ho_183 (ho_182 (ho_181 k_444 BOUND_VARIABLE_13009) BOUND_VARIABLE_13010) BOUND_VARIABLE_13011) BOUND_VARIABLE_13012))))) (let ((_let_740 (forall ((BOUND_VARIABLE_12966 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12967 tptp.product_prod_a_a) (BOUND_VARIABLE_12968 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12969 tptp.product_prod_a_a)) (= (ho_166 (ho_165 k_164 BOUND_VARIABLE_12969) (ho_314 k_313 (ho_183 (ho_182 (ho_181 k_187 BOUND_VARIABLE_12966) BOUND_VARIABLE_12967) BOUND_VARIABLE_12968))) (ho_163 (ho_183 (ho_182 (ho_181 k_445 BOUND_VARIABLE_12966) BOUND_VARIABLE_12967) BOUND_VARIABLE_12968) BOUND_VARIABLE_12969))))) (let ((_let_741 (forall ((BOUND_VARIABLE_12946 tptp.set_a) (BOUND_VARIABLE_12947 tptp.a) (BOUND_VARIABLE_12948 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12949 tptp.a)) (= (ho_156 (ho_191 (ho_190 (ho_189 k_446 BOUND_VARIABLE_12946) BOUND_VARIABLE_12947) BOUND_VARIABLE_12948) BOUND_VARIABLE_12949) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_12949) BOUND_VARIABLE_12946) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_12949) BOUND_VARIABLE_12947)) BOUND_VARIABLE_12948) (not (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_12947) BOUND_VARIABLE_12949)) BOUND_VARIABLE_12948))))))) (let ((_let_742 (forall ((BOUND_VARIABLE_12911 tptp.set_a) (BOUND_VARIABLE_12912 tptp.a) (BOUND_VARIABLE_12913 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12914 tptp.a)) (= (ho_159 (ho_158 k_157 BOUND_VARIABLE_12914) (ho_306 k_305 (ho_191 (ho_190 (ho_189 k_188 BOUND_VARIABLE_12911) BOUND_VARIABLE_12912) BOUND_VARIABLE_12913))) (ho_156 (ho_191 (ho_190 (ho_189 k_447 BOUND_VARIABLE_12911) BOUND_VARIABLE_12912) BOUND_VARIABLE_12913) BOUND_VARIABLE_12914))))) (let ((_let_743 (forall ((BOUND_VARIABLE_12868 tptp.set_a) (BOUND_VARIABLE_12869 tptp.a) (BOUND_VARIABLE_12870 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12871 tptp.a)) (= (ho_159 (ho_158 k_157 BOUND_VARIABLE_12871) (ho_306 k_305 (ho_191 (ho_190 (ho_189 k_195 BOUND_VARIABLE_12868) BOUND_VARIABLE_12869) BOUND_VARIABLE_12870))) (ho_156 (ho_191 (ho_190 (ho_189 k_448 BOUND_VARIABLE_12868) BOUND_VARIABLE_12869) BOUND_VARIABLE_12870) BOUND_VARIABLE_12871))))) (let ((_let_744 (forall ((BOUND_VARIABLE_12848 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12849 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12850 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12851 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_199 (ho_198 (ho_197 k_449 BOUND_VARIABLE_12848) BOUND_VARIABLE_12849) BOUND_VARIABLE_12850) BOUND_VARIABLE_12851) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_12851) BOUND_VARIABLE_12848) (ho_205 (ho_204 k_203 (ho_202 (ho_201 k_200 BOUND_VARIABLE_12851) BOUND_VARIABLE_12849)) BOUND_VARIABLE_12850) (not (ho_205 (ho_204 k_203 (ho_202 (ho_201 k_200 BOUND_VARIABLE_12849) BOUND_VARIABLE_12851)) BOUND_VARIABLE_12850))))))) (let ((_let_745 (forall ((BOUND_VARIABLE_12813 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12814 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12815 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12816 tptp.produc1572603623od_a_a)) (= (ho_152 (ho_151 k_150 BOUND_VARIABLE_12816) (ho_298 k_297 (ho_199 (ho_198 (ho_197 k_196 BOUND_VARIABLE_12813) BOUND_VARIABLE_12814) BOUND_VARIABLE_12815))) (ho_149 (ho_199 (ho_198 (ho_197 k_450 BOUND_VARIABLE_12813) BOUND_VARIABLE_12814) BOUND_VARIABLE_12815) BOUND_VARIABLE_12816))))) (let ((_let_746 (forall ((BOUND_VARIABLE_12770 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12771 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12772 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12773 tptp.produc1572603623od_a_a)) (= (ho_152 (ho_151 k_150 BOUND_VARIABLE_12773) (ho_298 k_297 (ho_199 (ho_198 (ho_197 k_206 BOUND_VARIABLE_12770) BOUND_VARIABLE_12771) BOUND_VARIABLE_12772))) (ho_149 (ho_199 (ho_198 (ho_197 k_451 BOUND_VARIABLE_12770) BOUND_VARIABLE_12771) BOUND_VARIABLE_12772) BOUND_VARIABLE_12773))))) (let ((_let_747 (forall ((BOUND_VARIABLE_12761 tptp.produc1572603623od_a_a)) (= (ho_319 k_452 BOUND_VARIABLE_12761) (ho_186 (ho_185 k_184 (ho_380 k_454 BOUND_VARIABLE_12761)) (ho_380 k_453 BOUND_VARIABLE_12761)))))) (let ((_let_748 (forall ((BOUND_VARIABLE_12752 tptp.product_prod_a_a)) (= (ho_401 k_455 BOUND_VARIABLE_12752) (ho_194 (ho_193 k_192 (ho_369 k_457 BOUND_VARIABLE_12752)) (ho_369 k_456 BOUND_VARIABLE_12752)))))) (let ((_let_749 (forall ((BOUND_VARIABLE_12741 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12742 tptp.product_prod_a_a) (BOUND_VARIABLE_12743 tptp.product_prod_a_a)) (= (ho_163 (ho_209 (ho_208 k_458 BOUND_VARIABLE_12741) BOUND_VARIABLE_12742) BOUND_VARIABLE_12743) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_12742) BOUND_VARIABLE_12743)) BOUND_VARIABLE_12741))))) (let ((_let_750 (forall ((BOUND_VARIABLE_12730 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12731 tptp.product_prod_a_a) (BOUND_VARIABLE_12732 tptp.product_prod_a_a)) (= (ho_163 (ho_209 (ho_208 k_459 BOUND_VARIABLE_12730) BOUND_VARIABLE_12731) BOUND_VARIABLE_12732) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_12731) BOUND_VARIABLE_12732)) BOUND_VARIABLE_12730))))) (let ((_let_751 (forall ((BOUND_VARIABLE_12719 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12720 tptp.a) (BOUND_VARIABLE_12721 tptp.a)) (= (ho_156 (ho_213 (ho_212 k_460 BOUND_VARIABLE_12719) BOUND_VARIABLE_12720) BOUND_VARIABLE_12721) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_12720) BOUND_VARIABLE_12721)) BOUND_VARIABLE_12719))))) (let ((_let_752 (forall ((BOUND_VARIABLE_12708 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12709 tptp.a) (BOUND_VARIABLE_12710 tptp.a)) (= (ho_156 (ho_213 (ho_212 k_461 BOUND_VARIABLE_12708) BOUND_VARIABLE_12709) BOUND_VARIABLE_12710) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_12709) BOUND_VARIABLE_12710)) BOUND_VARIABLE_12708))))) (let ((_let_753 (forall ((BOUND_VARIABLE_12693 tptp.set_a) (BOUND_VARIABLE_12694 tptp.a) (BOUND_VARIABLE_12695 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12696 tptp.a)) (= (ho_156 (ho_191 (ho_190 (ho_189 k_462 BOUND_VARIABLE_12693) BOUND_VARIABLE_12694) BOUND_VARIABLE_12695) BOUND_VARIABLE_12696) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_12696) BOUND_VARIABLE_12693) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_12696) BOUND_VARIABLE_12694)) BOUND_VARIABLE_12695)))))) (let ((_let_754 (forall ((BOUND_VARIABLE_12678 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12679 tptp.product_prod_a_a) (BOUND_VARIABLE_12680 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12681 tptp.product_prod_a_a)) (= (ho_163 (ho_183 (ho_182 (ho_181 k_463 BOUND_VARIABLE_12678) BOUND_VARIABLE_12679) BOUND_VARIABLE_12680) BOUND_VARIABLE_12681) (and (ho_166 (ho_165 k_164 BOUND_VARIABLE_12681) BOUND_VARIABLE_12678) (ho_152 (ho_151 k_150 (ho_186 (ho_185 k_184 BOUND_VARIABLE_12681) BOUND_VARIABLE_12679)) BOUND_VARIABLE_12680)))))) (let ((_let_755 (forall ((BOUND_VARIABLE_12663 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12664 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12665 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12666 tptp.produc1572603623od_a_a)) (= (ho_149 (ho_199 (ho_198 (ho_197 k_464 BOUND_VARIABLE_12663) BOUND_VARIABLE_12664) BOUND_VARIABLE_12665) BOUND_VARIABLE_12666) (and (ho_152 (ho_151 k_150 BOUND_VARIABLE_12666) BOUND_VARIABLE_12663) (ho_205 (ho_204 k_203 (ho_202 (ho_201 k_200 BOUND_VARIABLE_12666) BOUND_VARIABLE_12664)) BOUND_VARIABLE_12665)))))) (let ((_let_756 (forall ((BOUND_VARIABLE_12651 tptp.a)) (= (ho_156 k_465 BOUND_VARIABLE_12651) (and (ho_159 (ho_158 k_157 BOUND_VARIABLE_12651) tptp.b) (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 BOUND_VARIABLE_12651) tptp.y)) tptp.pr)))))) (let ((_let_757 (forall ((BOUND_VARIABLE_14474 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14475 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14475) BOUND_VARIABLE_14474) (ll_146 BOUND_VARIABLE_14474 BOUND_VARIABLE_14475))))) (let ((_let_758 (forall ((BOUND_VARIABLE_14466 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14467 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14467) BOUND_VARIABLE_14466) (ll_145 BOUND_VARIABLE_14466 BOUND_VARIABLE_14467))))) (let ((_let_759 (forall ((BOUND_VARIABLE_14458 tptp.set_a) (BOUND_VARIABLE_14459 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_14459) BOUND_VARIABLE_14458) (ll_144 BOUND_VARIABLE_14458 BOUND_VARIABLE_14459))))) (let ((_let_760 (forall ((BOUND_VARIABLE_14450 tptp.set_a) (BOUND_VARIABLE_14451 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_14451) BOUND_VARIABLE_14450) (ll_143 BOUND_VARIABLE_14450 BOUND_VARIABLE_14451))))) (let ((_let_761 (forall ((BOUND_VARIABLE_14442 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14443 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14443) BOUND_VARIABLE_14442) (ll_142 BOUND_VARIABLE_14442 BOUND_VARIABLE_14443))))) (let ((_let_762 (forall ((BOUND_VARIABLE_14434 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14435 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14435) BOUND_VARIABLE_14434) (ll_141 BOUND_VARIABLE_14434 BOUND_VARIABLE_14435))))) (let ((_let_763 (forall ((BOUND_VARIABLE_14426 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14427 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14427) BOUND_VARIABLE_14426) (ll_140 BOUND_VARIABLE_14426 BOUND_VARIABLE_14427))))) (let ((_let_764 (forall ((BOUND_VARIABLE_14418 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14419 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14419) BOUND_VARIABLE_14418) (ll_139 BOUND_VARIABLE_14418 BOUND_VARIABLE_14419))))) (let ((_let_765 (forall ((BOUND_VARIABLE_14406 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14407 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14408 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14408))) (= (and (@ _let_1 BOUND_VARIABLE_14406) (not (@ _let_1 BOUND_VARIABLE_14407))) (ll_138 BOUND_VARIABLE_14406 BOUND_VARIABLE_14407 BOUND_VARIABLE_14408)))))) (let ((_let_766 (forall ((BOUND_VARIABLE_14398 tptp.set_a) (BOUND_VARIABLE_14399 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_14399) BOUND_VARIABLE_14398) (ll_137 BOUND_VARIABLE_14398 BOUND_VARIABLE_14399))))) (let ((_let_767 (forall ((BOUND_VARIABLE_14390 tptp.set_a) (BOUND_VARIABLE_14391 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_14391) BOUND_VARIABLE_14390) (ll_136 BOUND_VARIABLE_14390 BOUND_VARIABLE_14391))))) (let ((_let_768 (forall ((BOUND_VARIABLE_14378 tptp.set_a) (BOUND_VARIABLE_14379 tptp.set_a) (BOUND_VARIABLE_14380 tptp.a)) (let ((_let_1 (@ tptp.member_a BOUND_VARIABLE_14380))) (= (and (@ _let_1 BOUND_VARIABLE_14378) (not (@ _let_1 BOUND_VARIABLE_14379))) (ll_135 BOUND_VARIABLE_14378 BOUND_VARIABLE_14379 BOUND_VARIABLE_14380)))))) (let ((_let_769 (forall ((BOUND_VARIABLE_14370 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14371 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14371) BOUND_VARIABLE_14370) (ll_134 BOUND_VARIABLE_14370 BOUND_VARIABLE_14371))))) (let ((_let_770 (forall ((BOUND_VARIABLE_14362 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14363 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14363) BOUND_VARIABLE_14362) (ll_133 BOUND_VARIABLE_14362 BOUND_VARIABLE_14363))))) (let ((_let_771 (forall ((BOUND_VARIABLE_14350 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14351 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14352 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a BOUND_VARIABLE_14352))) (= (and (@ _let_1 BOUND_VARIABLE_14350) (not (@ _let_1 BOUND_VARIABLE_14351))) (ll_132 BOUND_VARIABLE_14350 BOUND_VARIABLE_14351 BOUND_VARIABLE_14352)))))) (let ((_let_772 (forall ((BOUND_VARIABLE_14335 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14336 tptp.product_prod_a_a) (BOUND_VARIABLE_14337 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14338 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14338) BOUND_VARIABLE_14335) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_14338) BOUND_VARIABLE_14336)) BOUND_VARIABLE_14337)) (ll_131 BOUND_VARIABLE_14335 BOUND_VARIABLE_14336 BOUND_VARIABLE_14337 BOUND_VARIABLE_14338))))) (let ((_let_773 (forall ((BOUND_VARIABLE_14316 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14317 tptp.product_prod_a_a) (BOUND_VARIABLE_14318 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14319 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14319) BOUND_VARIABLE_14316) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_14317) BOUND_VARIABLE_14319)) BOUND_VARIABLE_14318) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_14319) BOUND_VARIABLE_14317)) BOUND_VARIABLE_14318)) (ll_130 BOUND_VARIABLE_14316 BOUND_VARIABLE_14317 BOUND_VARIABLE_14318 BOUND_VARIABLE_14319))))) (let ((_let_774 (forall ((BOUND_VARIABLE_14301 tptp.set_a) (BOUND_VARIABLE_14302 tptp.a) (BOUND_VARIABLE_14303 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14304 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_14304) BOUND_VARIABLE_14301) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_14304) BOUND_VARIABLE_14302)) BOUND_VARIABLE_14303)) (ll_129 BOUND_VARIABLE_14301 BOUND_VARIABLE_14302 BOUND_VARIABLE_14303 BOUND_VARIABLE_14304))))) (let ((_let_775 (forall ((BOUND_VARIABLE_14282 tptp.set_a) (BOUND_VARIABLE_14283 tptp.a) (BOUND_VARIABLE_14284 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14285 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_14285) BOUND_VARIABLE_14282) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_14283) BOUND_VARIABLE_14285)) BOUND_VARIABLE_14284) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_14285) BOUND_VARIABLE_14283)) BOUND_VARIABLE_14284)) (ll_128 BOUND_VARIABLE_14282 BOUND_VARIABLE_14283 BOUND_VARIABLE_14284 BOUND_VARIABLE_14285))))) (let ((_let_776 (forall ((BOUND_VARIABLE_14267 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14268 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_14269 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_14270 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14270) BOUND_VARIABLE_14267) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a BOUND_VARIABLE_14270) BOUND_VARIABLE_14268)) BOUND_VARIABLE_14269)) (ll_127 BOUND_VARIABLE_14267 BOUND_VARIABLE_14268 BOUND_VARIABLE_14269 BOUND_VARIABLE_14270))))) (let ((_let_777 (forall ((BOUND_VARIABLE_14248 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14249 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_14250 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_14251 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14251) BOUND_VARIABLE_14248) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a BOUND_VARIABLE_14249) BOUND_VARIABLE_14251)) BOUND_VARIABLE_14250) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a BOUND_VARIABLE_14251) BOUND_VARIABLE_14249)) BOUND_VARIABLE_14250)) (ll_126 BOUND_VARIABLE_14248 BOUND_VARIABLE_14249 BOUND_VARIABLE_14250 BOUND_VARIABLE_14251))))) (let ((_let_778 (forall ((BOUND_VARIABLE_14237 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14238 tptp.product_prod_a_a) (BOUND_VARIABLE_14239 tptp.product_prod_a_a)) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_14238) BOUND_VARIABLE_14239)) BOUND_VARIABLE_14237) (ll_125 BOUND_VARIABLE_14237 BOUND_VARIABLE_14238 BOUND_VARIABLE_14239))))) (let ((_let_779 (forall ((BOUND_VARIABLE_14226 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14227 tptp.product_prod_a_a) (BOUND_VARIABLE_14228 tptp.product_prod_a_a)) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_14227) BOUND_VARIABLE_14228)) BOUND_VARIABLE_14226) (ll_124 BOUND_VARIABLE_14226 BOUND_VARIABLE_14227 BOUND_VARIABLE_14228))))) (let ((_let_780 (forall ((BOUND_VARIABLE_14215 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14216 tptp.a) (BOUND_VARIABLE_14217 tptp.a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_14216) BOUND_VARIABLE_14217)) BOUND_VARIABLE_14215) (ll_123 BOUND_VARIABLE_14215 BOUND_VARIABLE_14216 BOUND_VARIABLE_14217))))) (let ((_let_781 (forall ((BOUND_VARIABLE_14204 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14205 tptp.a) (BOUND_VARIABLE_14206 tptp.a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_14205) BOUND_VARIABLE_14206)) BOUND_VARIABLE_14204) (ll_122 BOUND_VARIABLE_14204 BOUND_VARIABLE_14205 BOUND_VARIABLE_14206))))) (let ((_let_782 (forall ((BOUND_VARIABLE_14176 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14177 tptp.set_Pr1948701895od_a_a)) (= (ll_121 BOUND_VARIABLE_14176 BOUND_VARIABLE_14177) (@ (@ tptp.ord_le1525442358_a_a_o (@ ll_146 BOUND_VARIABLE_14176)) (@ ll_145 BOUND_VARIABLE_14177)))))) (let ((_let_783 (forall ((BOUND_VARIABLE_14148 tptp.set_a) (BOUND_VARIABLE_14149 tptp.set_a)) (= (ll_120 BOUND_VARIABLE_14148 BOUND_VARIABLE_14149) (@ (@ tptp.ord_less_eq_a_o (@ ll_144 BOUND_VARIABLE_14148)) (@ ll_143 BOUND_VARIABLE_14149)))))) (let ((_let_784 (forall ((BOUND_VARIABLE_14120 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14121 tptp.set_Product_prod_a_a)) (= (ll_119 BOUND_VARIABLE_14120 BOUND_VARIABLE_14121) (@ (@ tptp.ord_le1347718902_a_a_o (@ ll_142 BOUND_VARIABLE_14120)) (@ ll_141 BOUND_VARIABLE_14121)))))) (let ((_let_785 (forall ((BOUND_VARIABLE_14112 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14113 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14113) BOUND_VARIABLE_14112) (ll_118 BOUND_VARIABLE_14112 BOUND_VARIABLE_14113))))) (let ((_let_786 (forall ((BOUND_VARIABLE_14104 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14105 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14105) BOUND_VARIABLE_14104) (ll_117 BOUND_VARIABLE_14104 BOUND_VARIABLE_14105))))) (let ((_let_787 (forall ((BOUND_VARIABLE_14096 tptp.set_a) (BOUND_VARIABLE_14097 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_14097) BOUND_VARIABLE_14096) (ll_116 BOUND_VARIABLE_14096 BOUND_VARIABLE_14097))))) (let ((_let_788 (forall ((BOUND_VARIABLE_14088 tptp.set_a) (BOUND_VARIABLE_14089 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_14089) BOUND_VARIABLE_14088) (ll_115 BOUND_VARIABLE_14088 BOUND_VARIABLE_14089))))) (let ((_let_789 (forall ((BOUND_VARIABLE_14080 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14081 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14081) BOUND_VARIABLE_14080) (ll_114 BOUND_VARIABLE_14080 BOUND_VARIABLE_14081))))) (let ((_let_790 (forall ((BOUND_VARIABLE_14072 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14073 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14073) BOUND_VARIABLE_14072) (ll_113 BOUND_VARIABLE_14072 BOUND_VARIABLE_14073))))) (let ((_let_791 (forall ((BOUND_VARIABLE_14061 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14062 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_14063 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14063) BOUND_VARIABLE_14061) (@ BOUND_VARIABLE_14062 BOUND_VARIABLE_14063)) (ll_112 BOUND_VARIABLE_14061 BOUND_VARIABLE_14062 BOUND_VARIABLE_14063))))) (let ((_let_792 (forall ((BOUND_VARIABLE_14050 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_14051 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_14052 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_14052) BOUND_VARIABLE_14050) (@ BOUND_VARIABLE_14051 BOUND_VARIABLE_14052)) (ll_111 BOUND_VARIABLE_14050 BOUND_VARIABLE_14051 BOUND_VARIABLE_14052))))) (let ((_let_793 (forall ((BOUND_VARIABLE_14039 tptp.set_a) (BOUND_VARIABLE_14040 (-> tptp.a Bool)) (BOUND_VARIABLE_14041 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_14041) BOUND_VARIABLE_14039) (@ BOUND_VARIABLE_14040 BOUND_VARIABLE_14041)) (ll_110 BOUND_VARIABLE_14039 BOUND_VARIABLE_14040 BOUND_VARIABLE_14041))))) (let ((_let_794 (forall ((BOUND_VARIABLE_14028 tptp.set_a) (BOUND_VARIABLE_14029 (-> tptp.a Bool)) (BOUND_VARIABLE_14030 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_14030) BOUND_VARIABLE_14028) (@ BOUND_VARIABLE_14029 BOUND_VARIABLE_14030)) (ll_109 BOUND_VARIABLE_14028 BOUND_VARIABLE_14029 BOUND_VARIABLE_14030))))) (let ((_let_795 (forall ((BOUND_VARIABLE_14017 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14018 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_14019 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14019) BOUND_VARIABLE_14017) (@ BOUND_VARIABLE_14018 BOUND_VARIABLE_14019)) (ll_108 BOUND_VARIABLE_14017 BOUND_VARIABLE_14018 BOUND_VARIABLE_14019))))) (let ((_let_796 (forall ((BOUND_VARIABLE_14006 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_14007 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_14008 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_14008) BOUND_VARIABLE_14006) (@ BOUND_VARIABLE_14007 BOUND_VARIABLE_14008)) (ll_107 BOUND_VARIABLE_14006 BOUND_VARIABLE_14007 BOUND_VARIABLE_14008))))) (let ((_let_797 (forall ((BOUND_VARIABLE_13995 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13996 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13997 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13997) BOUND_VARIABLE_13995) (@ BOUND_VARIABLE_13996 BOUND_VARIABLE_13997)) (ll_106 BOUND_VARIABLE_13995 BOUND_VARIABLE_13996 BOUND_VARIABLE_13997))))) (let ((_let_798 (forall ((BOUND_VARIABLE_13984 tptp.set_a) (BOUND_VARIABLE_13985 (-> tptp.a Bool)) (BOUND_VARIABLE_13986 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13986) BOUND_VARIABLE_13984) (@ BOUND_VARIABLE_13985 BOUND_VARIABLE_13986)) (ll_105 BOUND_VARIABLE_13984 BOUND_VARIABLE_13985 BOUND_VARIABLE_13986))))) (let ((_let_799 (forall ((BOUND_VARIABLE_13973 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13974 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13975 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13975) BOUND_VARIABLE_13973) (@ BOUND_VARIABLE_13974 BOUND_VARIABLE_13975)) (ll_104 BOUND_VARIABLE_13973 BOUND_VARIABLE_13974 BOUND_VARIABLE_13975))))) (let ((_let_800 (forall ((BOUND_VARIABLE_13962 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13963 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13964 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13964) BOUND_VARIABLE_13962) (@ BOUND_VARIABLE_13963 BOUND_VARIABLE_13964)) (ll_103 BOUND_VARIABLE_13962 BOUND_VARIABLE_13963 BOUND_VARIABLE_13964))))) (let ((_let_801 (forall ((BOUND_VARIABLE_13951 tptp.set_a) (BOUND_VARIABLE_13952 (-> tptp.a Bool)) (BOUND_VARIABLE_13953 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13953) BOUND_VARIABLE_13951) (@ BOUND_VARIABLE_13952 BOUND_VARIABLE_13953)) (ll_102 BOUND_VARIABLE_13951 BOUND_VARIABLE_13952 BOUND_VARIABLE_13953))))) (let ((_let_802 (forall ((BOUND_VARIABLE_13940 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13941 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13942 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13942) BOUND_VARIABLE_13940) (@ BOUND_VARIABLE_13941 BOUND_VARIABLE_13942)) (ll_101 BOUND_VARIABLE_13940 BOUND_VARIABLE_13941 BOUND_VARIABLE_13942))))) (let ((_let_803 (forall ((BOUND_VARIABLE_13929 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13930 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13931 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13931) BOUND_VARIABLE_13929) (@ BOUND_VARIABLE_13930 BOUND_VARIABLE_13931)) (ll_100 BOUND_VARIABLE_13929 BOUND_VARIABLE_13930 BOUND_VARIABLE_13931))))) (let ((_let_804 (forall ((BOUND_VARIABLE_13918 tptp.set_a) (BOUND_VARIABLE_13919 (-> tptp.a Bool)) (BOUND_VARIABLE_13920 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13920) BOUND_VARIABLE_13918) (@ BOUND_VARIABLE_13919 BOUND_VARIABLE_13920)) (ll_99 BOUND_VARIABLE_13918 BOUND_VARIABLE_13919 BOUND_VARIABLE_13920))))) (let ((_let_805 (forall ((BOUND_VARIABLE_13907 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13908 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13909 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13909) BOUND_VARIABLE_13907) (@ BOUND_VARIABLE_13908 BOUND_VARIABLE_13909)) (ll_98 BOUND_VARIABLE_13907 BOUND_VARIABLE_13908 BOUND_VARIABLE_13909))))) (let ((_let_806 (forall ((BOUND_VARIABLE_13896 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13897 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13898 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13898) BOUND_VARIABLE_13896) (@ BOUND_VARIABLE_13897 BOUND_VARIABLE_13898)) (ll_97 BOUND_VARIABLE_13896 BOUND_VARIABLE_13897 BOUND_VARIABLE_13898))))) (let ((_let_807 (forall ((BOUND_VARIABLE_13885 tptp.set_a) (BOUND_VARIABLE_13886 (-> tptp.a Bool)) (BOUND_VARIABLE_13887 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13887) BOUND_VARIABLE_13885) (@ BOUND_VARIABLE_13886 BOUND_VARIABLE_13887)) (ll_96 BOUND_VARIABLE_13885 BOUND_VARIABLE_13886 BOUND_VARIABLE_13887))))) (let ((_let_808 (forall ((BOUND_VARIABLE_13874 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13875 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13876 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13876) BOUND_VARIABLE_13874) (@ BOUND_VARIABLE_13875 BOUND_VARIABLE_13876)) (ll_95 BOUND_VARIABLE_13874 BOUND_VARIABLE_13875 BOUND_VARIABLE_13876))))) (let ((_let_809 (forall ((BOUND_VARIABLE_13863 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13864 tptp.set_Pr1948701895od_a_a)) (= (forall ((T2 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a T2))) (or (not (@ _let_1 BOUND_VARIABLE_13863)) (@ _let_1 BOUND_VARIABLE_13864)))) (ll_94 BOUND_VARIABLE_13863 BOUND_VARIABLE_13864))))) (let ((_let_810 (forall ((BOUND_VARIABLE_13852 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13853 tptp.set_Pr1948701895od_a_a)) (= (forall ((X4 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X4))) (or (not (@ _let_1 BOUND_VARIABLE_13852)) (@ _let_1 BOUND_VARIABLE_13853)))) (ll_93 BOUND_VARIABLE_13852 BOUND_VARIABLE_13853))))) (let ((_let_811 (forall ((BOUND_VARIABLE_13841 tptp.set_a) (BOUND_VARIABLE_13842 tptp.set_a)) (= (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (or (not (@ _let_1 BOUND_VARIABLE_13841)) (@ _let_1 BOUND_VARIABLE_13842)))) (ll_92 BOUND_VARIABLE_13841 BOUND_VARIABLE_13842))))) (let ((_let_812 (forall ((BOUND_VARIABLE_13830 tptp.set_a) (BOUND_VARIABLE_13831 tptp.set_a)) (= (forall ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (or (not (@ _let_1 BOUND_VARIABLE_13830)) (@ _let_1 BOUND_VARIABLE_13831)))) (ll_91 BOUND_VARIABLE_13830 BOUND_VARIABLE_13831))))) (let ((_let_813 (forall ((BOUND_VARIABLE_13819 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13820 tptp.set_Product_prod_a_a)) (= (forall ((T2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a T2))) (or (not (@ _let_1 BOUND_VARIABLE_13819)) (@ _let_1 BOUND_VARIABLE_13820)))) (ll_90 BOUND_VARIABLE_13819 BOUND_VARIABLE_13820))))) (let ((_let_814 (forall ((BOUND_VARIABLE_13808 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13809 tptp.set_Product_prod_a_a)) (= (forall ((X4 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X4))) (or (not (@ _let_1 BOUND_VARIABLE_13808)) (@ _let_1 BOUND_VARIABLE_13809)))) (ll_89 BOUND_VARIABLE_13808 BOUND_VARIABLE_13809))))) (let ((_let_815 (forall ((BOUND_VARIABLE_13802 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13803 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13802 (ll_88 BOUND_VARIABLE_13802 BOUND_VARIABLE_13803))))) (let ((_let_816 (forall ((BOUND_VARIABLE_13796 tptp.set_a) (BOUND_VARIABLE_13797 tptp.a)) (= BOUND_VARIABLE_13796 (ll_87 BOUND_VARIABLE_13796 BOUND_VARIABLE_13797))))) (let ((_let_817 (forall ((BOUND_VARIABLE_13790 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13791 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13790 (ll_86 BOUND_VARIABLE_13790 BOUND_VARIABLE_13791))))) (let ((_let_818 (forall ((BOUND_VARIABLE_13784 tptp.set_a) (BOUND_VARIABLE_13785 tptp.a)) (= BOUND_VARIABLE_13784 (ll_85 BOUND_VARIABLE_13784 BOUND_VARIABLE_13785))))) (let ((_let_819 (forall ((BOUND_VARIABLE_13778 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13779 tptp.produc1572603623od_a_a)) (= BOUND_VARIABLE_13778 (ll_84 BOUND_VARIABLE_13778 BOUND_VARIABLE_13779))))) (let ((_let_820 (forall ((BOUND_VARIABLE_13772 tptp.set_a) (BOUND_VARIABLE_13773 tptp.produc1572603623od_a_a)) (= BOUND_VARIABLE_13772 (ll_83 BOUND_VARIABLE_13772 BOUND_VARIABLE_13773))))) (let ((_let_821 (forall ((BOUND_VARIABLE_13766 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13767 tptp.produc1572603623od_a_a)) (= BOUND_VARIABLE_13766 (ll_82 BOUND_VARIABLE_13766 BOUND_VARIABLE_13767))))) (let ((_let_822 (forall ((BOUND_VARIABLE_13760 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13761 tptp.a)) (= BOUND_VARIABLE_13760 (ll_81 BOUND_VARIABLE_13760 BOUND_VARIABLE_13761))))) (let ((_let_823 (forall ((BOUND_VARIABLE_13754 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13755 tptp.a)) (= BOUND_VARIABLE_13754 (ll_80 BOUND_VARIABLE_13754 BOUND_VARIABLE_13755))))) (let ((_let_824 (forall ((BOUND_VARIABLE_13748 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13749 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13748 (ll_79 BOUND_VARIABLE_13748 BOUND_VARIABLE_13749))))) (let ((_let_825 (forall ((BOUND_VARIABLE_13742 tptp.set_a) (BOUND_VARIABLE_13743 tptp.product_prod_a_a)) (= BOUND_VARIABLE_13742 (ll_78 BOUND_VARIABLE_13742 BOUND_VARIABLE_13743))))) (let ((_let_826 (forall ((BOUND_VARIABLE_13712 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13713 tptp.set_Pr1948701895od_a_a)) (= (ll_77 BOUND_VARIABLE_13712 BOUND_VARIABLE_13713) (@ tptp.collec1635618130od_a_a (@ (@ tptp.minus_107310383_a_a_o (@ ll_140 BOUND_VARIABLE_13712)) (@ ll_139 BOUND_VARIABLE_13713))))))) (let ((_let_827 (forall ((BOUND_VARIABLE_13685 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13686 tptp.set_Pr1948701895od_a_a)) (= (ll_76 BOUND_VARIABLE_13685 BOUND_VARIABLE_13686) (@ tptp.collec1635618130od_a_a (@ (@ ll_138 BOUND_VARIABLE_13685) BOUND_VARIABLE_13686)))))) (let ((_let_828 (forall ((BOUND_VARIABLE_13655 tptp.set_a) (BOUND_VARIABLE_13656 tptp.set_a)) (= (ll_75 BOUND_VARIABLE_13655 BOUND_VARIABLE_13656) (@ tptp.collect_a (@ (@ tptp.minus_minus_a_o (@ ll_137 BOUND_VARIABLE_13655)) (@ ll_136 BOUND_VARIABLE_13656))))))) (let ((_let_829 (forall ((BOUND_VARIABLE_13628 tptp.set_a) (BOUND_VARIABLE_13629 tptp.set_a)) (= (ll_74 BOUND_VARIABLE_13628 BOUND_VARIABLE_13629) (@ tptp.collect_a (@ (@ ll_135 BOUND_VARIABLE_13628) BOUND_VARIABLE_13629)))))) (let ((_let_830 (forall ((BOUND_VARIABLE_13598 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13599 tptp.set_Product_prod_a_a)) (= (ll_73 BOUND_VARIABLE_13598 BOUND_VARIABLE_13599) (@ tptp.collec645855634od_a_a (@ (@ tptp.minus_1797478127_a_a_o (@ ll_134 BOUND_VARIABLE_13598)) (@ ll_133 BOUND_VARIABLE_13599))))))) (let ((_let_831 (forall ((BOUND_VARIABLE_13571 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13572 tptp.set_Product_prod_a_a)) (= (ll_72 BOUND_VARIABLE_13571 BOUND_VARIABLE_13572) (@ tptp.collec645855634od_a_a (@ (@ ll_132 BOUND_VARIABLE_13571) BOUND_VARIABLE_13572)))))) (let ((_let_832 (forall ((BOUND_VARIABLE_13557 (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (BOUND_VARIABLE_13558 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13559 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13560 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13560) (@ (@ tptp.image_236793797od_a_a BOUND_VARIABLE_13557) BOUND_VARIABLE_13558)) (@ BOUND_VARIABLE_13559 BOUND_VARIABLE_13560)) (ll_71 BOUND_VARIABLE_13557 BOUND_VARIABLE_13558 BOUND_VARIABLE_13559 BOUND_VARIABLE_13560))))) (let ((_let_833 (forall ((BOUND_VARIABLE_13544 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13545 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13546 (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (BOUND_VARIABLE_13547 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13547) BOUND_VARIABLE_13544) (@ BOUND_VARIABLE_13545 (@ BOUND_VARIABLE_13546 BOUND_VARIABLE_13547))) (ll_70 BOUND_VARIABLE_13544 BOUND_VARIABLE_13545 BOUND_VARIABLE_13546 BOUND_VARIABLE_13547))))) (let ((_let_834 (forall ((BOUND_VARIABLE_13530 (-> tptp.a tptp.produc1572603623od_a_a)) (BOUND_VARIABLE_13531 tptp.set_a) (BOUND_VARIABLE_13532 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13533 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13533) (@ (@ tptp.image_1763923566od_a_a BOUND_VARIABLE_13530) BOUND_VARIABLE_13531)) (@ BOUND_VARIABLE_13532 BOUND_VARIABLE_13533)) (ll_69 BOUND_VARIABLE_13530 BOUND_VARIABLE_13531 BOUND_VARIABLE_13532 BOUND_VARIABLE_13533))))) (let ((_let_835 (forall ((BOUND_VARIABLE_13517 tptp.set_a) (BOUND_VARIABLE_13518 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13519 (-> tptp.a tptp.produc1572603623od_a_a)) (BOUND_VARIABLE_13520 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13520) BOUND_VARIABLE_13517) (@ BOUND_VARIABLE_13518 (@ BOUND_VARIABLE_13519 BOUND_VARIABLE_13520))) (ll_68 BOUND_VARIABLE_13517 BOUND_VARIABLE_13518 BOUND_VARIABLE_13519 BOUND_VARIABLE_13520))))) (let ((_let_836 (forall ((BOUND_VARIABLE_13503 (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (BOUND_VARIABLE_13504 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13505 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13506 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13506) (@ (@ tptp.image_1765377413od_a_a BOUND_VARIABLE_13503) BOUND_VARIABLE_13504)) (@ BOUND_VARIABLE_13505 BOUND_VARIABLE_13506)) (ll_67 BOUND_VARIABLE_13503 BOUND_VARIABLE_13504 BOUND_VARIABLE_13505 BOUND_VARIABLE_13506))))) (let ((_let_837 (forall ((BOUND_VARIABLE_13490 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13491 (-> tptp.produc1572603623od_a_a Bool)) (BOUND_VARIABLE_13492 (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (BOUND_VARIABLE_13493 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13493) BOUND_VARIABLE_13490) (@ BOUND_VARIABLE_13491 (@ BOUND_VARIABLE_13492 BOUND_VARIABLE_13493))) (ll_66 BOUND_VARIABLE_13490 BOUND_VARIABLE_13491 BOUND_VARIABLE_13492 BOUND_VARIABLE_13493))))) (let ((_let_838 (forall ((BOUND_VARIABLE_13476 (-> tptp.produc1572603623od_a_a tptp.a)) (BOUND_VARIABLE_13477 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13478 (-> tptp.a Bool)) (BOUND_VARIABLE_13479 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13479) (@ (@ tptp.image_1105229276_a_a_a BOUND_VARIABLE_13476) BOUND_VARIABLE_13477)) (@ BOUND_VARIABLE_13478 BOUND_VARIABLE_13479)) (ll_65 BOUND_VARIABLE_13476 BOUND_VARIABLE_13477 BOUND_VARIABLE_13478 BOUND_VARIABLE_13479))))) (let ((_let_839 (forall ((BOUND_VARIABLE_13463 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13464 (-> tptp.a Bool)) (BOUND_VARIABLE_13465 (-> tptp.produc1572603623od_a_a tptp.a)) (BOUND_VARIABLE_13466 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13466) BOUND_VARIABLE_13463) (@ BOUND_VARIABLE_13464 (@ BOUND_VARIABLE_13465 BOUND_VARIABLE_13466))) (ll_64 BOUND_VARIABLE_13463 BOUND_VARIABLE_13464 BOUND_VARIABLE_13465 BOUND_VARIABLE_13466))))) (let ((_let_840 (forall ((BOUND_VARIABLE_13449 (-> tptp.a tptp.a)) (BOUND_VARIABLE_13450 tptp.set_a) (BOUND_VARIABLE_13451 (-> tptp.a Bool)) (BOUND_VARIABLE_13452 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13452) (@ (@ tptp.image_a_a BOUND_VARIABLE_13449) BOUND_VARIABLE_13450)) (@ BOUND_VARIABLE_13451 BOUND_VARIABLE_13452)) (ll_63 BOUND_VARIABLE_13449 BOUND_VARIABLE_13450 BOUND_VARIABLE_13451 BOUND_VARIABLE_13452))))) (let ((_let_841 (forall ((BOUND_VARIABLE_13436 tptp.set_a) (BOUND_VARIABLE_13437 (-> tptp.a Bool)) (BOUND_VARIABLE_13438 (-> tptp.a tptp.a)) (BOUND_VARIABLE_13439 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13439) BOUND_VARIABLE_13436) (@ BOUND_VARIABLE_13437 (@ BOUND_VARIABLE_13438 BOUND_VARIABLE_13439))) (ll_62 BOUND_VARIABLE_13436 BOUND_VARIABLE_13437 BOUND_VARIABLE_13438 BOUND_VARIABLE_13439))))) (let ((_let_842 (forall ((BOUND_VARIABLE_13422 (-> tptp.product_prod_a_a tptp.a)) (BOUND_VARIABLE_13423 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13424 (-> tptp.a Bool)) (BOUND_VARIABLE_13425 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13425) (@ (@ tptp.image_340790172_a_a_a BOUND_VARIABLE_13422) BOUND_VARIABLE_13423)) (@ BOUND_VARIABLE_13424 BOUND_VARIABLE_13425)) (ll_61 BOUND_VARIABLE_13422 BOUND_VARIABLE_13423 BOUND_VARIABLE_13424 BOUND_VARIABLE_13425))))) (let ((_let_843 (forall ((BOUND_VARIABLE_13409 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13410 (-> tptp.a Bool)) (BOUND_VARIABLE_13411 (-> tptp.product_prod_a_a tptp.a)) (BOUND_VARIABLE_13412 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13412) BOUND_VARIABLE_13409) (@ BOUND_VARIABLE_13410 (@ BOUND_VARIABLE_13411 BOUND_VARIABLE_13412))) (ll_60 BOUND_VARIABLE_13409 BOUND_VARIABLE_13410 BOUND_VARIABLE_13411 BOUND_VARIABLE_13412))))) (let ((_let_844 (forall ((BOUND_VARIABLE_13395 (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (BOUND_VARIABLE_13396 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13397 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13398 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13398) (@ (@ tptp.image_734753285od_a_a BOUND_VARIABLE_13395) BOUND_VARIABLE_13396)) (@ BOUND_VARIABLE_13397 BOUND_VARIABLE_13398)) (ll_59 BOUND_VARIABLE_13395 BOUND_VARIABLE_13396 BOUND_VARIABLE_13397 BOUND_VARIABLE_13398))))) (let ((_let_845 (forall ((BOUND_VARIABLE_13382 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13383 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13384 (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (BOUND_VARIABLE_13385 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13385) BOUND_VARIABLE_13382) (@ BOUND_VARIABLE_13383 (@ BOUND_VARIABLE_13384 BOUND_VARIABLE_13385))) (ll_58 BOUND_VARIABLE_13382 BOUND_VARIABLE_13383 BOUND_VARIABLE_13384 BOUND_VARIABLE_13385))))) (let ((_let_846 (forall ((BOUND_VARIABLE_13368 (-> tptp.a tptp.product_prod_a_a)) (BOUND_VARIABLE_13369 tptp.set_a) (BOUND_VARIABLE_13370 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13371 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13371) (@ (@ tptp.image_1725938350od_a_a BOUND_VARIABLE_13368) BOUND_VARIABLE_13369)) (@ BOUND_VARIABLE_13370 BOUND_VARIABLE_13371)) (ll_57 BOUND_VARIABLE_13368 BOUND_VARIABLE_13369 BOUND_VARIABLE_13370 BOUND_VARIABLE_13371))))) (let ((_let_847 (forall ((BOUND_VARIABLE_13355 tptp.set_a) (BOUND_VARIABLE_13356 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13357 (-> tptp.a tptp.product_prod_a_a)) (BOUND_VARIABLE_13358 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_13358) BOUND_VARIABLE_13355) (@ BOUND_VARIABLE_13356 (@ BOUND_VARIABLE_13357 BOUND_VARIABLE_13358))) (ll_56 BOUND_VARIABLE_13355 BOUND_VARIABLE_13356 BOUND_VARIABLE_13357 BOUND_VARIABLE_13358))))) (let ((_let_848 (forall ((BOUND_VARIABLE_13341 (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (BOUND_VARIABLE_13342 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13343 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13344 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13344) (@ (@ tptp.image_794773445od_a_a BOUND_VARIABLE_13341) BOUND_VARIABLE_13342)) (@ BOUND_VARIABLE_13343 BOUND_VARIABLE_13344)) (ll_55 BOUND_VARIABLE_13341 BOUND_VARIABLE_13342 BOUND_VARIABLE_13343 BOUND_VARIABLE_13344))))) (let ((_let_849 (forall ((BOUND_VARIABLE_13328 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13329 (-> tptp.product_prod_a_a Bool)) (BOUND_VARIABLE_13330 (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (BOUND_VARIABLE_13331 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13331) BOUND_VARIABLE_13328) (@ BOUND_VARIABLE_13329 (@ BOUND_VARIABLE_13330 BOUND_VARIABLE_13331))) (ll_54 BOUND_VARIABLE_13328 BOUND_VARIABLE_13329 BOUND_VARIABLE_13330 BOUND_VARIABLE_13331))))) (let ((_let_850 (forall ((BOUND_VARIABLE_13320 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13321 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13321) BOUND_VARIABLE_13320) (ll_53 BOUND_VARIABLE_13320 BOUND_VARIABLE_13321))))) (let ((_let_851 (forall ((BOUND_VARIABLE_13312 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13313 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13313) BOUND_VARIABLE_13312) (ll_52 BOUND_VARIABLE_13312 BOUND_VARIABLE_13313))))) (let ((_let_852 (forall ((BOUND_VARIABLE_13304 tptp.set_a) (BOUND_VARIABLE_13305 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13305) BOUND_VARIABLE_13304) (ll_51 BOUND_VARIABLE_13304 BOUND_VARIABLE_13305))))) (let ((_let_853 (forall ((BOUND_VARIABLE_13296 tptp.set_a) (BOUND_VARIABLE_13297 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13297) BOUND_VARIABLE_13296) (ll_50 BOUND_VARIABLE_13296 BOUND_VARIABLE_13297))))) (let ((_let_854 (forall ((BOUND_VARIABLE_13288 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13289 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13289) BOUND_VARIABLE_13288) (ll_49 BOUND_VARIABLE_13288 BOUND_VARIABLE_13289))))) (let ((_let_855 (forall ((BOUND_VARIABLE_13280 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13281 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13281) BOUND_VARIABLE_13280) (ll_48 BOUND_VARIABLE_13280 BOUND_VARIABLE_13281))))) (let ((_let_856 (forall ((BOUND_VARIABLE_13272 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13273 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13273) BOUND_VARIABLE_13272) (ll_47 BOUND_VARIABLE_13272 BOUND_VARIABLE_13273))))) (let ((_let_857 (forall ((BOUND_VARIABLE_13264 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13265 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13265) BOUND_VARIABLE_13264) (ll_46 BOUND_VARIABLE_13264 BOUND_VARIABLE_13265))))) (let ((_let_858 (forall ((BOUND_VARIABLE_13256 tptp.set_a) (BOUND_VARIABLE_13257 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13257) BOUND_VARIABLE_13256) (ll_45 BOUND_VARIABLE_13256 BOUND_VARIABLE_13257))))) (let ((_let_859 (forall ((BOUND_VARIABLE_13248 tptp.set_a) (BOUND_VARIABLE_13249 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13249) BOUND_VARIABLE_13248) (ll_44 BOUND_VARIABLE_13248 BOUND_VARIABLE_13249))))) (let ((_let_860 (forall ((BOUND_VARIABLE_13240 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13241 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13241) BOUND_VARIABLE_13240) (ll_43 BOUND_VARIABLE_13240 BOUND_VARIABLE_13241))))) (let ((_let_861 (forall ((BOUND_VARIABLE_13232 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13233 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13233) BOUND_VARIABLE_13232) (ll_42 BOUND_VARIABLE_13232 BOUND_VARIABLE_13233))))) (let ((_let_862 (forall ((BOUND_VARIABLE_13224 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13225 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13225) BOUND_VARIABLE_13224) (ll_41 BOUND_VARIABLE_13224 BOUND_VARIABLE_13225))))) (let ((_let_863 (forall ((BOUND_VARIABLE_13216 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13217 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13217) BOUND_VARIABLE_13216) (ll_40 BOUND_VARIABLE_13216 BOUND_VARIABLE_13217))))) (let ((_let_864 (forall ((BOUND_VARIABLE_13208 tptp.set_a) (BOUND_VARIABLE_13209 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13209) BOUND_VARIABLE_13208) (ll_39 BOUND_VARIABLE_13208 BOUND_VARIABLE_13209))))) (let ((_let_865 (forall ((BOUND_VARIABLE_13200 tptp.set_a) (BOUND_VARIABLE_13201 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13201) BOUND_VARIABLE_13200) (ll_38 BOUND_VARIABLE_13200 BOUND_VARIABLE_13201))))) (let ((_let_866 (forall ((BOUND_VARIABLE_13192 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13193 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13193) BOUND_VARIABLE_13192) (ll_37 BOUND_VARIABLE_13192 BOUND_VARIABLE_13193))))) (let ((_let_867 (forall ((BOUND_VARIABLE_13184 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13185 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13185) BOUND_VARIABLE_13184) (ll_36 BOUND_VARIABLE_13184 BOUND_VARIABLE_13185))))) (let ((_let_868 (forall ((BOUND_VARIABLE_13176 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13177 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13177) BOUND_VARIABLE_13176) (ll_35 BOUND_VARIABLE_13176 BOUND_VARIABLE_13177))))) (let ((_let_869 (forall ((BOUND_VARIABLE_13168 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13169 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13169) BOUND_VARIABLE_13168) (ll_34 BOUND_VARIABLE_13168 BOUND_VARIABLE_13169))))) (let ((_let_870 (forall ((BOUND_VARIABLE_13160 tptp.set_a) (BOUND_VARIABLE_13161 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13161) BOUND_VARIABLE_13160) (ll_33 BOUND_VARIABLE_13160 BOUND_VARIABLE_13161))))) (let ((_let_871 (forall ((BOUND_VARIABLE_13152 tptp.set_a) (BOUND_VARIABLE_13153 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13153) BOUND_VARIABLE_13152) (ll_32 BOUND_VARIABLE_13152 BOUND_VARIABLE_13153))))) (let ((_let_872 (forall ((BOUND_VARIABLE_13144 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13145 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13145) BOUND_VARIABLE_13144) (ll_31 BOUND_VARIABLE_13144 BOUND_VARIABLE_13145))))) (let ((_let_873 (forall ((BOUND_VARIABLE_13136 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13137 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13137) BOUND_VARIABLE_13136) (ll_30 BOUND_VARIABLE_13136 BOUND_VARIABLE_13137))))) (let ((_let_874 (forall ((BOUND_VARIABLE_13128 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13129 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13129) BOUND_VARIABLE_13128) (ll_29 BOUND_VARIABLE_13128 BOUND_VARIABLE_13129))))) (let ((_let_875 (forall ((BOUND_VARIABLE_13120 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13121 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13121) BOUND_VARIABLE_13120) (ll_28 BOUND_VARIABLE_13120 BOUND_VARIABLE_13121))))) (let ((_let_876 (forall ((BOUND_VARIABLE_13112 tptp.set_a) (BOUND_VARIABLE_13113 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13113) BOUND_VARIABLE_13112) (ll_27 BOUND_VARIABLE_13112 BOUND_VARIABLE_13113))))) (let ((_let_877 (forall ((BOUND_VARIABLE_13104 tptp.set_a) (BOUND_VARIABLE_13105 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13105) BOUND_VARIABLE_13104) (ll_26 BOUND_VARIABLE_13104 BOUND_VARIABLE_13105))))) (let ((_let_878 (forall ((BOUND_VARIABLE_13096 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13097 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13097) BOUND_VARIABLE_13096) (ll_25 BOUND_VARIABLE_13096 BOUND_VARIABLE_13097))))) (let ((_let_879 (forall ((BOUND_VARIABLE_13088 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13089 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13089) BOUND_VARIABLE_13088) (ll_24 BOUND_VARIABLE_13088 BOUND_VARIABLE_13089))))) (let ((_let_880 (forall ((BOUND_VARIABLE_13080 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13081 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_13081) BOUND_VARIABLE_13080) (ll_23 BOUND_VARIABLE_13080 BOUND_VARIABLE_13081))))) (let ((_let_881 (forall ((BOUND_VARIABLE_13072 tptp.set_a) (BOUND_VARIABLE_13073 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_13073) BOUND_VARIABLE_13072) (ll_22 BOUND_VARIABLE_13072 BOUND_VARIABLE_13073))))) (let ((_let_882 (forall ((BOUND_VARIABLE_13064 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13065 tptp.product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13065) BOUND_VARIABLE_13064) (ll_21 BOUND_VARIABLE_13064 BOUND_VARIABLE_13065))))) (let ((_let_883 (forall ((BOUND_VARIABLE_13044 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13045 tptp.product_prod_a_a) (BOUND_VARIABLE_13046 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13047 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13047) BOUND_VARIABLE_13044) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_13047) BOUND_VARIABLE_13045)) BOUND_VARIABLE_13046) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_13045) BOUND_VARIABLE_13047)) BOUND_VARIABLE_13046))) (ll_20 BOUND_VARIABLE_13044 BOUND_VARIABLE_13045 BOUND_VARIABLE_13046 BOUND_VARIABLE_13047))))) (let ((_let_884 (forall ((BOUND_VARIABLE_13009 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_13010 tptp.product_prod_a_a) (BOUND_VARIABLE_13011 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_13012 tptp.product_prod_a_a)) (= (ll_19 BOUND_VARIABLE_13009 BOUND_VARIABLE_13010 BOUND_VARIABLE_13011 BOUND_VARIABLE_13012) (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_13012) (@ tptp.collec645855634od_a_a (@ (@ (@ ll_131 BOUND_VARIABLE_13009) BOUND_VARIABLE_13010) BOUND_VARIABLE_13011))))))) (let ((_let_885 (forall ((BOUND_VARIABLE_12966 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12967 tptp.product_prod_a_a) (BOUND_VARIABLE_12968 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12969 tptp.product_prod_a_a)) (= (ll_18 BOUND_VARIABLE_12966 BOUND_VARIABLE_12967 BOUND_VARIABLE_12968 BOUND_VARIABLE_12969) (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_12969) (@ tptp.collec645855634od_a_a (@ (@ (@ ll_130 BOUND_VARIABLE_12966) BOUND_VARIABLE_12967) BOUND_VARIABLE_12968))))))) (let ((_let_886 (forall ((BOUND_VARIABLE_12946 tptp.set_a) (BOUND_VARIABLE_12947 tptp.a) (BOUND_VARIABLE_12948 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12949 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_12949) BOUND_VARIABLE_12946) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_12949) BOUND_VARIABLE_12947)) BOUND_VARIABLE_12948) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_12947) BOUND_VARIABLE_12949)) BOUND_VARIABLE_12948))) (ll_17 BOUND_VARIABLE_12946 BOUND_VARIABLE_12947 BOUND_VARIABLE_12948 BOUND_VARIABLE_12949))))) (let ((_let_887 (forall ((BOUND_VARIABLE_12911 tptp.set_a) (BOUND_VARIABLE_12912 tptp.a) (BOUND_VARIABLE_12913 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12914 tptp.a)) (= (ll_16 BOUND_VARIABLE_12911 BOUND_VARIABLE_12912 BOUND_VARIABLE_12913 BOUND_VARIABLE_12914) (@ (@ tptp.member_a BOUND_VARIABLE_12914) (@ tptp.collect_a (@ (@ (@ ll_129 BOUND_VARIABLE_12911) BOUND_VARIABLE_12912) BOUND_VARIABLE_12913))))))) (let ((_let_888 (forall ((BOUND_VARIABLE_12868 tptp.set_a) (BOUND_VARIABLE_12869 tptp.a) (BOUND_VARIABLE_12870 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12871 tptp.a)) (= (ll_15 BOUND_VARIABLE_12868 BOUND_VARIABLE_12869 BOUND_VARIABLE_12870 BOUND_VARIABLE_12871) (@ (@ tptp.member_a BOUND_VARIABLE_12871) (@ tptp.collect_a (@ (@ (@ ll_128 BOUND_VARIABLE_12868) BOUND_VARIABLE_12869) BOUND_VARIABLE_12870))))))) (let ((_let_889 (forall ((BOUND_VARIABLE_12848 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12849 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12850 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12851 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_12851) BOUND_VARIABLE_12848) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a BOUND_VARIABLE_12851) BOUND_VARIABLE_12849)) BOUND_VARIABLE_12850) (not (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a BOUND_VARIABLE_12849) BOUND_VARIABLE_12851)) BOUND_VARIABLE_12850))) (ll_14 BOUND_VARIABLE_12848 BOUND_VARIABLE_12849 BOUND_VARIABLE_12850 BOUND_VARIABLE_12851))))) (let ((_let_890 (forall ((BOUND_VARIABLE_12813 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12814 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12815 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12816 tptp.produc1572603623od_a_a)) (= (ll_13 BOUND_VARIABLE_12813 BOUND_VARIABLE_12814 BOUND_VARIABLE_12815 BOUND_VARIABLE_12816) (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_12816) (@ tptp.collec1635618130od_a_a (@ (@ (@ ll_127 BOUND_VARIABLE_12813) BOUND_VARIABLE_12814) BOUND_VARIABLE_12815))))))) (let ((_let_891 (forall ((BOUND_VARIABLE_12770 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12771 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12772 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12773 tptp.produc1572603623od_a_a)) (= (ll_12 BOUND_VARIABLE_12770 BOUND_VARIABLE_12771 BOUND_VARIABLE_12772 BOUND_VARIABLE_12773) (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_12773) (@ tptp.collec1635618130od_a_a (@ (@ (@ ll_126 BOUND_VARIABLE_12770) BOUND_VARIABLE_12771) BOUND_VARIABLE_12772))))))) (let ((_let_892 (forall ((BOUND_VARIABLE_12761 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc368344197od_a_a BOUND_VARIABLE_12761)) (@ tptp.produc2115494211od_a_a BOUND_VARIABLE_12761)) (ll_11 BOUND_VARIABLE_12761))))) (let ((_let_893 (forall ((BOUND_VARIABLE_12752 tptp.product_prod_a_a)) (= (@ (@ tptp.product_Pair_a_a (@ tptp.product_snd_a_a BOUND_VARIABLE_12752)) (@ tptp.product_fst_a_a BOUND_VARIABLE_12752)) (ll_10 BOUND_VARIABLE_12752))))) (let ((_let_894 (forall ((BOUND_VARIABLE_12741 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12742 tptp.product_prod_a_a) (BOUND_VARIABLE_12743 tptp.product_prod_a_a)) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_12742) BOUND_VARIABLE_12743)) BOUND_VARIABLE_12741) (ll_9 BOUND_VARIABLE_12741 BOUND_VARIABLE_12742 BOUND_VARIABLE_12743))))) (let ((_let_895 (forall ((BOUND_VARIABLE_12730 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12731 tptp.product_prod_a_a) (BOUND_VARIABLE_12732 tptp.product_prod_a_a)) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_12731) BOUND_VARIABLE_12732)) BOUND_VARIABLE_12730) (ll_8 BOUND_VARIABLE_12730 BOUND_VARIABLE_12731 BOUND_VARIABLE_12732))))) (let ((_let_896 (forall ((BOUND_VARIABLE_12719 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12720 tptp.a) (BOUND_VARIABLE_12721 tptp.a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_12720) BOUND_VARIABLE_12721)) BOUND_VARIABLE_12719) (ll_7 BOUND_VARIABLE_12719 BOUND_VARIABLE_12720 BOUND_VARIABLE_12721))))) (let ((_let_897 (forall ((BOUND_VARIABLE_12708 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12709 tptp.a) (BOUND_VARIABLE_12710 tptp.a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_12709) BOUND_VARIABLE_12710)) BOUND_VARIABLE_12708) (ll_6 BOUND_VARIABLE_12708 BOUND_VARIABLE_12709 BOUND_VARIABLE_12710))))) (let ((_let_898 (forall ((BOUND_VARIABLE_12693 tptp.set_a) (BOUND_VARIABLE_12694 tptp.a) (BOUND_VARIABLE_12695 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12696 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_12696) BOUND_VARIABLE_12693) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_12696) BOUND_VARIABLE_12694)) BOUND_VARIABLE_12695)) (ll_5 BOUND_VARIABLE_12693 BOUND_VARIABLE_12694 BOUND_VARIABLE_12695 BOUND_VARIABLE_12696))))) (let ((_let_899 (forall ((BOUND_VARIABLE_12678 tptp.set_Product_prod_a_a) (BOUND_VARIABLE_12679 tptp.product_prod_a_a) (BOUND_VARIABLE_12680 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12681 tptp.product_prod_a_a)) (= (and (@ (@ tptp.member449909584od_a_a BOUND_VARIABLE_12681) BOUND_VARIABLE_12678) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a BOUND_VARIABLE_12681) BOUND_VARIABLE_12679)) BOUND_VARIABLE_12680)) (ll_4 BOUND_VARIABLE_12678 BOUND_VARIABLE_12679 BOUND_VARIABLE_12680 BOUND_VARIABLE_12681))))) (let ((_let_900 (forall ((BOUND_VARIABLE_12663 tptp.set_Pr1948701895od_a_a) (BOUND_VARIABLE_12664 tptp.produc1572603623od_a_a) (BOUND_VARIABLE_12665 tptp.set_Pr1295299783od_a_a) (BOUND_VARIABLE_12666 tptp.produc1572603623od_a_a)) (= (and (@ (@ tptp.member2057358096od_a_a BOUND_VARIABLE_12666) BOUND_VARIABLE_12663) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a BOUND_VARIABLE_12666) BOUND_VARIABLE_12664)) BOUND_VARIABLE_12665)) (ll_3 BOUND_VARIABLE_12663 BOUND_VARIABLE_12664 BOUND_VARIABLE_12665 BOUND_VARIABLE_12666))))) (let ((_let_901 (forall ((BOUND_VARIABLE_12651 tptp.a)) (= (and (@ (@ tptp.member_a BOUND_VARIABLE_12651) tptp.b) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a BOUND_VARIABLE_12651) tptp.y)) tptp.pr)) (ll_2 BOUND_VARIABLE_12651))))) (let ((_let_902 (@ _let_28 (@ tptp.collect_a ll_2)))) (let ((_let_903 (and _let_902 _let_901 _let_900 _let_899 _let_898 _let_897 _let_896 _let_895 _let_894 _let_893 _let_892 _let_891 _let_890 _let_889 _let_888 _let_887 _let_886 _let_885 _let_884 _let_883 _let_882 _let_881 _let_880 _let_879 _let_878 _let_877 _let_876 _let_875 _let_874 _let_873 _let_872 _let_871 _let_870 _let_869 _let_868 _let_867 _let_866 _let_865 _let_864 _let_863 _let_862 _let_861 _let_860 _let_859 _let_858 _let_857 _let_856 _let_855 _let_854 _let_853 _let_852 _let_851 _let_850 _let_849 _let_848 _let_847 _let_846 _let_845 _let_844 _let_843 _let_842 _let_841 _let_840 _let_839 _let_838 _let_837 _let_836 _let_835 _let_834 _let_833 _let_832 _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757))) (let ((_let_904 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_29)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_5)) (ASSUME :args (_let_6)) (ASSUME :args (_let_7)) (ASSUME :args (_let_8)) (ASSUME :args (_let_9)) (ASSUME :args (_let_10)) (ASSUME :args (_let_11)) (ASSUME :args (_let_12)) (ASSUME :args (_let_13)) (ASSUME :args (_let_14)) (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_19)) (ASSUME :args (_let_20)) (ASSUME :args (_let_21)) (ASSUME :args (_let_22)) (ASSUME :args (_let_23)) (ASSUME :args (_let_24)) (ASSUME :args (_let_25)) (ASSUME :args (_let_26)) (ASSUME :args (_let_27))) :args (_let_29 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ _let_28 (@ tptp.collect_a (lambda ((Y4 tptp.a)) (and (@ (@ tptp.member_a Y4) tptp.b) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y4) tptp.y)) tptp.pr))))) _let_902))))) (PREPROCESS :args ((and _let_901 _let_900 _let_899 _let_898 _let_897 _let_896 _let_895 _let_894 _let_893 _let_892 _let_891 _let_890 _let_889 _let_888 _let_887 _let_886 _let_885 _let_884 _let_883 _let_882 _let_881 _let_880 _let_879 _let_878 _let_877 _let_876 _let_875 _let_874 _let_873 _let_872 _let_871 _let_870 _let_869 _let_868 _let_867 _let_866 _let_865 _let_864 _let_863 _let_862 _let_861 _let_860 _let_859 _let_858 _let_857 _let_856 _let_855 _let_854 _let_853 _let_852 _let_851 _let_850 _let_849 _let_848 _let_847 _let_846 _let_845 _let_844 _let_843 _let_842 _let_841 _let_840 _let_839 _let_838 _let_837 _let_836 _let_835 _let_834 _let_833 _let_832 _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757)))) :args (_let_903)) (PREPROCESS :args ((= _let_903 (and _let_31 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612))))) (PREPROCESS :args ((and _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34)))) :args ((and _let_31 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34))))) (let ((_let_905 (forall ((A tptp.a) (BOUND_VARIABLE_18735 |u_(-> tptp.a Bool)|)) (= (ho_156 BOUND_VARIABLE_18735 A) (ho_159 (ho_158 k_157 A) (ho_306 k_305 BOUND_VARIABLE_18735)))))) (let ((_let_906 (EQ_RESOLVE (ASSUME :args (_let_15)) (PREPROCESS :args ((= _let_15 _let_905)))))) (let ((_let_907 (ho_166 (ho_165 k_164 (ho_194 (ho_193 k_192 tptp.z) tptp.y)) tptp.pr))) (let ((_let_908 (and (ho_159 _let_30 tptp.b) _let_907))) (let ((_let_909 (= _let_32 _let_908))) (let ((_let_910 (not _let_32))) (let ((_let_911 (_let_756))) (let ((_let_912 (not _let_908))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or (not _let_31) _let_32 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_909)) :args ((or _let_908 _let_910 (not _let_909)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_908 1)) :args ((or _let_907 _let_912))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_907))))) :args (_let_912 true _let_907)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_911) :args (tptp.z QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_158 k_157 BOUND_VARIABLE_12651)))) :args _let_911)) (AND_ELIM _let_904 :args (1)) :args (_let_909 false _let_756)) :args (_let_910 true _let_908 false _let_909)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_906 :args (tptp.z k_465 QUANTIFIERS_INST_E_MATCHING ((ho_159 (ho_158 k_157 A) (ho_306 k_305 BOUND_VARIABLE_18735))))) :args (_let_905)))) _let_906 :args (_let_33 false _let_905)) (AND_ELIM _let_904 :args (0)) :args (false true _let_32 false _let_33 false _let_31)) :args (_let_29 (forall ((X tptp.produc2010915495od_a_a) (Y tptp.produc2010915495od_a_a) (B tptp.set_Pr231806599od_a_a) (Pr tptp.set_Pr532616391od_a_a)) (=> (@ (@ tptp.member1361298640od_a_a X) (@ (@ (@ tptp.prefer468349667od_a_a Y) B) Pr)) (@ (@ tptp.member180906768od_a_a (@ (@ tptp.produc539587415od_a_a X) Y)) Pr))) (forall ((X tptp.produc772425383od_a_a) (Y tptp.produc772425383od_a_a) (B tptp.set_Pr1194146439od_a_a) (Pr tptp.set_Pr2081559751od_a_a)) (=> (@ (@ tptp.member122808528od_a_a X) (@ (@ (@ tptp.prefer1377343203od_a_a Y) B) Pr)) (@ (@ tptp.member547056400od_a_a (@ (@ tptp.produc852390743od_a_a X) Y)) Pr))) (forall ((X tptp.produc1016684094_a_a_a) (Y tptp.produc1016684094_a_a_a) (B tptp.set_Pr1689873822_a_a_a) (Pr tptp.set_Pr729215751_a_a_a)) (=> (@ (@ tptp.member1403138919_a_a_a X) (@ (@ (@ tptp.prefer1944486522_a_a_a Y) B) Pr)) (@ (@ tptp.member470802768_a_a_a (@ (@ tptp.produc2054708503_a_a_a X) Y)) Pr))) (forall ((X tptp.produc1555800720od_a_a) (Y tptp.produc1555800720od_a_a) (B tptp.set_Pr195866352od_a_a) (Pr tptp.set_Pr660101255od_a_a)) (=> (@ (@ tptp.member448091577od_a_a X) (@ (@ (@ tptp.prefer445484748od_a_a Y) B) Pr)) (@ (@ tptp.member1424209616od_a_a (@ (@ tptp.produc1573596055od_a_a X) Y)) Pr))) (forall ((X tptp.produc1921647824od_a_a) (Y tptp.produc1921647824od_a_a) (B tptp.set_Pr681306928od_a_a) (Pr tptp.set_Pr231806599od_a_a)) (=> (@ (@ tptp.member160619001od_a_a X) (@ (@ (@ tptp.prefer701966604od_a_a Y) B) Pr)) (@ (@ tptp.member1361298640od_a_a (@ (@ tptp.produc563767703od_a_a X) Y)) Pr))) (forall ((X tptp.produc1572603623od_a_a) (Y tptp.produc1572603623od_a_a) (B tptp.set_Pr1948701895od_a_a) (Pr tptp.set_Pr1295299783od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X) (@ (@ (@ 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(@ tptp.product_Pair_a_a A3) B4))) (@ P2 Prod))) (forall ((P2 (-> tptp.produc1572603623od_a_a Bool)) (Prod tptp.produc1572603623od_a_a)) (=> (forall ((A3 tptp.product_prod_a_a) (B4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.produc1474507607od_a_a A3) B4))) (@ P2 Prod))) (forall ((Y tptp.product_prod_a_a)) (not (forall ((A3 tptp.a) (B4 tptp.a)) (not (= Y (@ (@ tptp.product_Pair_a_a A3) B4)))))) (forall ((Y tptp.produc1572603623od_a_a)) (not (forall ((A3 tptp.product_prod_a_a) (B4 tptp.product_prod_a_a)) (not (= Y (@ (@ tptp.produc1474507607od_a_a A3) B4)))))) _let_27 _let_26 _let_25 (forall ((R tptp.a) (S tptp.a) (R2 tptp.set_Product_prod_a_a) (S2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a R))) (=> (@ (@ tptp.member449909584od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member449909584od_a_a (@ _let_1 S2)) R2))))) (forall ((R tptp.product_prod_a_a) (S tptp.product_prod_a_a) (R2 tptp.set_Pr1948701895od_a_a) (S2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.produc1474507607od_a_a R))) (=> (@ (@ tptp.member2057358096od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member2057358096od_a_a (@ _let_1 S2)) R2))))) (forall ((F (-> tptp.product_prod_a_a Bool)) (A tptp.a) (B2 tptp.a)) (=> (@ F (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ (@ tptp.product_curry_a_a_o F) A) B2))) (forall ((F (-> tptp.produc1572603623od_a_a Bool)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (=> (@ F (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ (@ tptp.produc94438221_a_a_o F) A) B2))) (forall ((Carrier tptp.set_a) (Relation tptp.set_Product_prod_a_a) (X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a Z))) (let ((_let_2 (@ tptp.product_Pair_a_a X))) (let ((_let_3 (@ tptp.product_Pair_a_a Y))) (=> (@ (@ tptp.prefer1292084992ence_a Carrier) Relation) (=> (and (@ (@ tptp.member449909584od_a_a (@ _let_2 Y)) Relation) (@ (@ tptp.member449909584od_a_a (@ _let_3 X)) Relation)) (=> (and (@ (@ tptp.member449909584od_a_a (@ _let_3 Z)) Relation) (@ (@ 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tptp.set_Pr1295299783od_a_a) (X tptp.produc1572603623od_a_a) (Y tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.prefer1409946857od_a_a Carrier) Relation) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X) Y)) Relation) (@ (@ tptp.member2057358096od_a_a X) Carrier)))) (forall ((Carrier tptp.set_a) (Relation tptp.set_Product_prod_a_a) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.prefer1292084992ence_a Carrier) Relation) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) Relation) (@ (@ tptp.member_a X) Carrier)))) (forall ((Carrier tptp.set_Product_prod_a_a) (Relation tptp.set_Pr1948701895od_a_a) (X tptp.product_prod_a_a) (Y tptp.product_prod_a_a)) (=> (@ (@ tptp.prefer1338892073od_a_a Carrier) Relation) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) Relation) (@ (@ tptp.member449909584od_a_a X) Carrier)))) (forall ((X tptp.a) (Y tptp.a)) (= (@ tptp.product_swap_a_a (@ (@ tptp.product_Pair_a_a X) Y)) (@ (@ tptp.product_Pair_a_a Y) X))) (forall ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a)) (= (@ tptp.produc1641853175od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) (@ (@ tptp.produc1474507607od_a_a Y) X))) (forall ((F (-> tptp.product_prod_a_a Bool)) (A tptp.a) (B2 tptp.a)) (=> (@ (@ (@ tptp.product_curry_a_a_o F) A) B2) (@ F (@ (@ tptp.product_Pair_a_a A) B2)))) (forall ((F (-> tptp.produc1572603623od_a_a Bool)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (=> (@ (@ (@ tptp.produc94438221_a_a_o F) A) B2) (@ F (@ (@ tptp.produc1474507607od_a_a A) B2)))) (forall ((F (-> tptp.product_prod_a_a Bool)) (A tptp.a) (B2 tptp.a)) (=> (@ (@ (@ tptp.product_curry_a_a_o F) A) B2) (@ F (@ (@ tptp.product_Pair_a_a A) B2)))) (forall ((F (-> tptp.produc1572603623od_a_a Bool)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (=> (@ (@ (@ tptp.produc94438221_a_a_o F) A) B2) (@ F (@ (@ tptp.produc1474507607od_a_a A) B2)))) _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 (forall ((R2 tptp.set_Product_prod_a_a) (S3 tptp.set_Product_prod_a_a)) (= (= (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R2)) (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) S3))) (= R2 S3))) (forall ((R2 tptp.set_Pr1948701895od_a_a) (S3 tptp.set_Pr1948701895od_a_a)) (= (= (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R2)) (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) S3))) (= R2 S3))) _let_18 _let_17 _let_16 (forall ((Relation tptp.set_Pr1295299783od_a_a) (Carrier tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a) (Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) Relation) (@ (@ tptp.member2057358096od_a_a X3) Carrier))) (=> (forall ((X3 tptp.produc1572603623od_a_a) (Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) Relation) (@ (@ tptp.member2057358096od_a_a Y3) Carrier))) (=> (@ (@ tptp.order_491428350od_a_a Carrier) Relation) (@ (@ tptp.prefer1409946857od_a_a Carrier) Relation))))) (forall ((Relation tptp.set_Product_prod_a_a) (Carrier tptp.set_a)) (=> (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) Relation) (@ (@ tptp.member_a X3) Carrier))) (=> (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) Relation) (@ (@ tptp.member_a Y3) Carrier))) (=> (@ (@ tptp.order_preorder_on_a Carrier) Relation) (@ (@ tptp.prefer1292084992ence_a Carrier) Relation))))) (forall ((Relation tptp.set_Pr1948701895od_a_a) (Carrier tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) Relation) (@ (@ tptp.member449909584od_a_a X3) Carrier))) (=> (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) Relation) (@ (@ tptp.member449909584od_a_a Y3) Carrier))) (=> (@ (@ tptp.order_359341630od_a_a Carrier) Relation) (@ (@ tptp.prefer1338892073od_a_a Carrier) Relation))))) (forall ((Y tptp.a) (X tptp.a) (A4 tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y) X)) (@ (@ tptp.image_794773445od_a_a tptp.product_swap_a_a) A4)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) A4))) (forall ((Y tptp.product_prod_a_a) (X tptp.product_prod_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y) X)) (@ (@ tptp.image_236793797od_a_a tptp.produc1641853175od_a_a) A4)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) A4))) (forall ((B tptp.set_Pr1948701895od_a_a) (Y tptp.produc1572603623od_a_a) (Pr tptp.set_Pr1295299783od_a_a)) (= (@ tptp.collec1635618130od_a_a (lambda ((A5 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a A5) B) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A5) Y)) Pr) (not (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a Y) A5)) Pr))))) (@ (@ tptp.minus_1034916142od_a_a (@ (@ (@ tptp.prefer55414563od_a_a Y) B) Pr)) (@ (@ (@ tptp.prefer1867335523od_a_a Y) B) Pr)))) (forall ((B tptp.set_a) (Y tptp.a) (Pr tptp.set_Product_prod_a_a)) (= (@ tptp.collect_a (lambda ((A5 tptp.a)) (and (@ (@ tptp.member_a A5) B) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A5) Y)) Pr) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y) A5)) Pr))))) (@ (@ tptp.minus_minus_set_a (@ (@ (@ tptp.prefer161218362good_a Y) B) Pr)) (@ (@ (@ tptp.prefer436369274d_as_a Y) B) Pr)))) (forall ((B tptp.set_Product_prod_a_a) (Y tptp.product_prod_a_a) (Pr tptp.set_Pr1948701895od_a_a)) (= (@ tptp.collec645855634od_a_a (lambda ((A5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a A5) B) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A5) Y)) Pr) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y) A5)) Pr))))) (@ (@ tptp.minus_1507102574od_a_a (@ (@ (@ tptp.prefer477097315od_a_a Y) B) Pr)) (@ (@ (@ tptp.prefer74720675od_a_a Y) B) Pr)))) (forall ((A tptp.product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ (@ tptp.member449909584od_a_a A) (@ tptp.collec645855634od_a_a P2)) (@ P2 A))) _let_15 (forall ((A tptp.produc1572603623od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ (@ tptp.member2057358096od_a_a A) (@ tptp.collec1635618130od_a_a P2)) (@ P2 A))) (forall ((A4 tptp.set_Product_prod_a_a)) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A4))) A4)) (forall ((A4 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A4))) A4)) (forall ((A4 tptp.set_Pr1948701895od_a_a)) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A4))) A4)) (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)))))) (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)))))) (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_794773445od_a_a F) A4))))) (forall ((B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a)) (X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member_a B2) (@ (@ tptp.image_340790172_a_a_a F) A4))))) (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1765377413od_a_a F) A4))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (X tptp.a) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_1725938350od_a_a F) A4))))) (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (X tptp.a) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A4))))) (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.produc1572603623od_a_a)) (X tptp.a) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1763923566od_a_a F) A4))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_734753285od_a_a F) A4))))) (forall ((B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member_a B2) (@ (@ tptp.image_1105229276_a_a_a F) A4))))) (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_236793797od_a_a F) A4))))) (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (= (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (and (@ _let_1 A4) (not (@ _let_1 B)))))) (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (and (@ _let_1 A4) (not (@ _let_1 B)))))) (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (= (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (and (@ _let_1 A4) (not (@ _let_1 B)))))) _let_14 _let_13 _let_12 (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_794773445od_a_a F) A4))))) (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member_a B2) (@ (@ tptp.image_340790172_a_a_a F) A4))))) (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1765377413od_a_a F) A4))))) (forall ((X tptp.a) (A4 tptp.set_a) (B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a))) (=> (@ (@ tptp.member_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_1725938350od_a_a F) A4))))) (forall ((X tptp.a) (A4 tptp.set_a) (B2 tptp.a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A4))))) (forall ((X tptp.a) (A4 tptp.set_a) (B2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1763923566od_a_a F) A4))))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_734753285od_a_a F) A4))))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member_a B2) (@ (@ tptp.image_1105229276_a_a_a F) A4))))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B2 tptp.produc1572603623od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (=> (= B2 (@ F X)) (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_236793797od_a_a F) A4))))) (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ F X)) (@ (@ tptp.image_794773445od_a_a F) A4)))) (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member_a (@ F X)) (@ (@ tptp.image_340790172_a_a_a F) A4)))) (forall ((X tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ F X)) (@ (@ tptp.image_1765377413od_a_a F) A4)))) (forall ((X tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.product_prod_a_a))) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member449909584od_a_a (@ F X)) (@ (@ tptp.image_1725938350od_a_a F) A4)))) (forall ((X tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member_a (@ F X)) (@ (@ tptp.image_a_a F) A4)))) (forall ((X tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ F X)) (@ (@ tptp.image_1763923566od_a_a F) A4)))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ F X)) (@ (@ tptp.image_734753285od_a_a F) A4)))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member_a (@ F X)) (@ (@ tptp.image_1105229276_a_a_a F) A4)))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a))) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ F X)) (@ (@ tptp.image_236793797od_a_a F) A4)))) (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (not (@ _let_1 B))))) (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (not (@ _let_1 B))))) (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (not (@ _let_1 B))))) (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (@ _let_1 A4)))) (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (@ _let_1 A4)))) (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (@ _let_1 A4)))) (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1507102574od_a_a A4) B)) (not (=> (@ _let_1 A4) (@ _let_1 B)))))) (forall ((C2 tptp.a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_a A4) B)) (not (=> (@ _let_1 A4) (@ _let_1 B)))))) (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ _let_1 (@ (@ tptp.minus_1034916142od_a_a A4) B)) (not (=> (@ _let_1 A4) (@ _let_1 B)))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_794773445od_a_a F) A4)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member449909584od_a_a X3) A4))))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (A4 tptp.set_a)) (=> (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_1725938350od_a_a F) A4)) (not (forall ((X3 tptp.a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member_a X3) A4))))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member449909584od_a_a B2) (@ (@ tptp.image_734753285od_a_a F) A4)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member2057358096od_a_a X3) A4))))))) (forall ((B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a)) (A4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member_a B2) (@ (@ tptp.image_340790172_a_a_a F) A4)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member449909584od_a_a X3) A4))))))) (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (A4 tptp.set_a)) (=> (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A4)) (not (forall ((X3 tptp.a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member_a X3) A4))))))) (forall ((B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member_a B2) (@ (@ tptp.image_1105229276_a_a_a F) A4)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member2057358096od_a_a X3) A4))))))) (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1765377413od_a_a F) A4)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member449909584od_a_a X3) A4))))))) (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.produc1572603623od_a_a)) (A4 tptp.set_a)) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_1763923566od_a_a F) A4)) (not (forall ((X3 tptp.a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member_a X3) A4))))))) (forall ((B2 tptp.produc1572603623od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a B2) (@ (@ tptp.image_236793797od_a_a F) A4)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (= B2 (@ F X3)) (not (@ (@ tptp.member2057358096od_a_a X3) A4))))))) (forall ((F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) (@ (@ tptp.image_794773445od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_794773445od_a_a F) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.a tptp.product_prod_a_a)) (A4 tptp.set_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) (@ (@ tptp.image_1725938350od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1725938350od_a_a F) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) (@ (@ tptp.image_734753285od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_734753285od_a_a F) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.product_prod_a_a tptp.a)) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.a Bool))) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) (@ (@ tptp.image_340790172_a_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_340790172_a_a_a F) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.a tptp.a)) (A4 tptp.set_a) (P2 (-> tptp.a Bool))) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) (@ (@ tptp.image_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_a_a F) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.produc1572603623od_a_a tptp.a)) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.a Bool))) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) (@ (@ tptp.image_1105229276_a_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1105229276_a_a_a F) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) (@ (@ tptp.image_1765377413od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1765377413od_a_a F) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.a tptp.produc1572603623od_a_a)) (A4 tptp.set_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) (@ (@ tptp.image_1763923566od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_1763923566od_a_a F) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 (@ F X4)))))))) (forall ((F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (= (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) (@ (@ tptp.image_236793797od_a_a F) A4)) (@ P2 X4)))) (@ (@ tptp.image_236793797od_a_a F) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 (@ F X4)))))))) (= tptp.minus_1507102574od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X4))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))) (= tptp.minus_minus_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (@ tptp.collect_a (lambda ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))) (= tptp.minus_1034916142od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X4))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))) (forall ((X tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X) tptp.top_to398455383od_a_a)) (forall ((X tptp.a)) (@ (@ tptp.member_a X) tptp.top_top_set_a)) (forall ((X tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X) tptp.top_to52711959od_a_a)) (exists ((X3 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X3) tptp.top_to398455383od_a_a)) (exists ((X3 tptp.a)) (@ (@ tptp.member_a X3) tptp.top_top_set_a)) (exists ((X3 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X3) tptp.top_to52711959od_a_a)) (forall ((A4 tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X3) A4)) (= tptp.top_to398455383od_a_a A4))) (forall ((A4 tptp.set_a)) (=> (forall ((X3 tptp.a)) (@ (@ tptp.member_a X3) A4)) (= tptp.top_top_set_a A4))) (forall ((A4 tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X3) A4)) (= tptp.top_to52711959od_a_a A4))) (forall ((X tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X) tptp.top_to398455383od_a_a)) (forall ((X tptp.a)) (@ (@ tptp.member_a X) tptp.top_top_set_a)) (forall ((X tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X) tptp.top_to52711959od_a_a)) (forall ((P2 (-> tptp.a Bool)) (X tptp.a) (Y5 tptp.a) (Y tptp.a) (R2 (-> tptp.a tptp.set_Product_prod_a_a))) (let ((_let_1 (@ tptp.product_Pair_a_a X))) (=> (@ P2 X) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y5) Y)) (@ R2 X)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ _let_1 Y5)) (@ _let_1 Y))) (@ (@ tptp.same_fst_a_a P2) R2)))))) (forall ((P2 (-> tptp.product_prod_a_a Bool)) (X tptp.product_prod_a_a) (Y5 tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (R2 (-> tptp.product_prod_a_a tptp.set_Pr1948701895od_a_a))) (let ((_let_1 (@ tptp.produc1474507607od_a_a X))) (=> (@ P2 X) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y5) Y)) (@ R2 X)) (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a (@ _let_1 Y5)) (@ _let_1 Y))) (@ (@ tptp.same_f1138477100od_a_a P2) R2)))))) (forall ((F (-> tptp.a tptp.a)) (G (-> tptp.a tptp.a)) (A tptp.a) (B2 tptp.a)) (= (@ (@ (@ tptp.produc700022774_a_a_a F) G) (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2)))) (forall ((F (-> tptp.a tptp.product_prod_a_a)) (G (-> tptp.a tptp.product_prod_a_a)) (A tptp.a) (B2 tptp.a)) (= (@ (@ (@ tptp.produc2012818120od_a_a F) G) (@ (@ tptp.product_Pair_a_a A) B2)) (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2)))) (forall ((F (-> tptp.product_prod_a_a tptp.a)) (G (-> tptp.product_prod_a_a tptp.a)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (= (@ (@ (@ tptp.produc363290532_a_a_a F) G) (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2)))) (forall ((F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a)) (= (@ (@ (@ tptp.produc1779756150od_a_a F) G) (@ (@ tptp.produc1474507607od_a_a A) B2)) (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2)))) (forall ((A tptp.a) (B2 tptp.a) (R2 tptp.set_Product_prod_a_a) (F (-> tptp.a tptp.a)) (G (-> tptp.a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) R2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_794773445od_a_a (@ (@ tptp.produc700022774_a_a_a F) G)) R2)))) (forall ((A tptp.a) (B2 tptp.a) (R2 tptp.set_Product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (G (-> tptp.a tptp.product_prod_a_a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B2)) R2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_1765377413od_a_a (@ (@ tptp.produc2012818120od_a_a F) G)) R2)))) (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (R2 tptp.set_Pr1948701895od_a_a) (F (-> tptp.product_prod_a_a tptp.a)) (G (-> tptp.product_prod_a_a tptp.a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) R2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_734753285od_a_a (@ (@ tptp.produc363290532_a_a_a F) G)) R2)))) (forall ((A tptp.product_prod_a_a) (B2 tptp.product_prod_a_a) (R2 tptp.set_Pr1948701895od_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B2)) R2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ F A)) (@ G B2))) (@ (@ tptp.image_236793797od_a_a (@ (@ tptp.produc1779756150od_a_a F) G)) R2)))) _let_11 _let_10 _let_9 (forall ((X tptp.a) (Y tptp.a) (A tptp.a)) (=> (= (@ tptp.product_fst_a_a (@ (@ tptp.product_Pair_a_a X) Y)) A) (= X A))) (forall ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (A tptp.product_prod_a_a)) (=> (= (@ tptp.produc2115494211od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) A) (= X A))) (forall ((X1 tptp.a) (X2 tptp.a)) (= (@ tptp.product_fst_a_a (@ (@ tptp.product_Pair_a_a X1) X2)) X1)) (forall ((X1 tptp.product_prod_a_a) (X2 tptp.product_prod_a_a)) (= (@ tptp.produc2115494211od_a_a (@ (@ tptp.produc1474507607od_a_a X1) X2)) X1)) (forall ((C2 tptp.product_prod_a_a) (F (-> tptp.a tptp.a)) (G (-> tptp.a tptp.a)) (R2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a C2) (@ (@ tptp.image_794773445od_a_a (@ (@ tptp.produc700022774_a_a_a F) G)) R2)) (not (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (= C2 (@ (@ tptp.product_Pair_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R2))))))) (forall ((C2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.a)) (G (-> tptp.product_prod_a_a tptp.a)) (R2 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member449909584od_a_a C2) (@ (@ tptp.image_734753285od_a_a (@ (@ tptp.produc363290532_a_a_a F) G)) R2)) (not (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (= C2 (@ (@ tptp.product_Pair_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R2))))))) (forall ((C2 tptp.produc1572603623od_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (G (-> tptp.a tptp.product_prod_a_a)) (R2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a C2) (@ (@ tptp.image_1765377413od_a_a (@ (@ tptp.produc2012818120od_a_a F) G)) R2)) (not (forall ((X3 tptp.a) (Y3 tptp.a)) (=> (= C2 (@ (@ tptp.produc1474507607od_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R2))))))) (forall ((C2 tptp.produc1572603623od_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (R2 tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a C2) (@ (@ tptp.image_236793797od_a_a (@ (@ tptp.produc1779756150od_a_a F) G)) R2)) (not (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (=> (= C2 (@ (@ tptp.produc1474507607od_a_a (@ F X3)) (@ G Y3))) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R2))))))) _let_8 _let_7 (forall ((A tptp.a) (P tptp.product_prod_a_a)) (= (= A (@ tptp.product_fst_a_a P)) (exists ((B6 tptp.a)) (= P (@ (@ tptp.product_Pair_a_a A) B6))))) (forall ((A tptp.product_prod_a_a) (P tptp.produc1572603623od_a_a)) (= (= A (@ tptp.produc2115494211od_a_a P)) (exists ((B6 tptp.product_prod_a_a)) (= P (@ (@ tptp.produc1474507607od_a_a A) B6))))) (forall ((X tptp.product_prod_a_a) (Y tptp.a) (Z tptp.a)) (=> (= X (@ (@ tptp.product_Pair_a_a Y) Z)) (= (@ tptp.product_fst_a_a X) Y))) (forall ((X tptp.produc1572603623od_a_a) (Y tptp.product_prod_a_a) (Z tptp.product_prod_a_a)) (=> (= X (@ (@ tptp.produc1474507607od_a_a Y) Z)) (= (@ tptp.produc2115494211od_a_a X) Y))) (forall ((Prod tptp.product_prod_a_a)) (= (@ (@ tptp.product_Pair_a_a (@ tptp.product_fst_a_a Prod)) (@ tptp.product_snd_a_a Prod)) Prod)) (forall ((Prod tptp.produc1572603623od_a_a)) (= (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc2115494211od_a_a Prod)) (@ tptp.produc368344197od_a_a Prod)) Prod)) (forall ((B2 tptp.a) (P tptp.product_prod_a_a)) (= (= B2 (@ tptp.product_snd_a_a P)) (exists ((A5 tptp.a)) (= P (@ (@ tptp.product_Pair_a_a A5) B2))))) (forall ((B2 tptp.product_prod_a_a) (P tptp.produc1572603623od_a_a)) (= (= B2 (@ tptp.produc368344197od_a_a P)) (exists ((A5 tptp.product_prod_a_a)) (= P (@ (@ tptp.produc1474507607od_a_a A5) B2))))) (forall ((X tptp.product_prod_a_a) (Y tptp.a) (Z tptp.a)) (=> (= X (@ (@ tptp.product_Pair_a_a Y) Z)) (= (@ tptp.product_snd_a_a X) Z))) (forall ((X tptp.produc1572603623od_a_a) (Y tptp.product_prod_a_a) (Z tptp.product_prod_a_a)) (=> (= X (@ (@ tptp.produc1474507607od_a_a Y) Z)) (= (@ tptp.produc368344197od_a_a X) Z))) (forall ((X tptp.a) (Y tptp.a) (A tptp.a)) (=> (= (@ tptp.product_snd_a_a (@ (@ tptp.product_Pair_a_a X) Y)) A) (= Y A))) (forall ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (A tptp.product_prod_a_a)) (=> (= (@ tptp.produc368344197od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) A) (= Y A))) (forall ((X1 tptp.a) (X2 tptp.a)) (= (@ tptp.product_snd_a_a (@ (@ tptp.product_Pair_a_a X1) X2)) X2)) (forall ((X1 tptp.product_prod_a_a) (X2 tptp.product_prod_a_a)) (= (@ tptp.produc368344197od_a_a (@ (@ tptp.produc1474507607od_a_a X1) X2)) X2)) (forall ((T tptp.product_prod_a_a)) (= T (@ (@ tptp.product_Pair_a_a (@ tptp.product_fst_a_a T)) (@ tptp.product_snd_a_a T)))) (forall ((T tptp.produc1572603623od_a_a)) (= T (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc2115494211od_a_a T)) (@ tptp.produc368344197od_a_a T)))) (forall ((Prod tptp.product_prod_a_a)) (= Prod (@ (@ tptp.product_Pair_a_a (@ tptp.product_fst_a_a Prod)) (@ tptp.product_snd_a_a Prod)))) (forall ((Prod tptp.produc1572603623od_a_a)) (= Prod (@ (@ tptp.produc1474507607od_a_a (@ tptp.produc2115494211od_a_a Prod)) (@ tptp.produc368344197od_a_a Prod)))) _let_6 _let_5 (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (A tptp.product_prod_a_a)) (=> (@ (@ P2 X) Y) (=> (= A (@ (@ tptp.product_Pair_a_a X) Y)) (@ (@ P2 (@ tptp.product_fst_a_a A)) (@ tptp.product_snd_a_a A))))) (forall ((P2 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (A tptp.produc1572603623od_a_a)) (=> (@ (@ P2 X) Y) (=> (= A (@ (@ tptp.produc1474507607od_a_a X) Y)) (@ (@ P2 (@ tptp.produc2115494211od_a_a A)) (@ tptp.produc368344197od_a_a A))))) (forall ((P2 (-> tptp.a Bool)) (P tptp.a) (Q (-> tptp.a Bool)) (Q2 tptp.a)) (let ((_let_1 (@ (@ tptp.product_Pair_a_a P) Q2))) (=> (@ P2 P) (=> (@ Q Q2) (and (@ P2 (@ tptp.product_fst_a_a _let_1)) (@ Q (@ tptp.product_snd_a_a _let_1))))))) (forall ((P2 (-> tptp.product_prod_a_a Bool)) (P tptp.product_prod_a_a) (Q (-> tptp.product_prod_a_a Bool)) (Q2 tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.produc1474507607od_a_a P) Q2))) (=> (@ P2 P) (=> (@ Q Q2) (and (@ P2 (@ tptp.produc2115494211od_a_a _let_1)) (@ Q (@ tptp.produc368344197od_a_a _let_1))))))) (forall ((P2 (-> tptp.a tptp.a Bool)) (Y tptp.a) (X tptp.a)) (let ((_let_1 (@ (@ tptp.product_Pair_a_a X) Y))) (=> (@ (@ P2 Y) X) (@ (@ P2 (@ tptp.product_snd_a_a _let_1)) (@ tptp.product_fst_a_a _let_1))))) (forall ((P2 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (Y tptp.product_prod_a_a) (X tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.produc1474507607od_a_a X) Y))) (=> (@ (@ P2 Y) X) (@ (@ P2 (@ tptp.produc368344197od_a_a _let_1)) (@ tptp.produc2115494211od_a_a _let_1))))) (forall ((B2 tptp.a) (F (-> tptp.product_prod_a_a tptp.a)) (X tptp.product_prod_a_a) (C2 tptp.a) (G (-> tptp.product_prod_a_a tptp.a)) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr1853143117_a_a_a A4) F) G)))))) (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (X tptp.a) (C2 tptp.a) (G (-> tptp.a tptp.a)) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr423046308_a_a_a A4) F) G)))))) (forall ((B2 tptp.a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (X tptp.produc1572603623od_a_a) (C2 tptp.a) (G (-> tptp.produc1572603623od_a_a tptp.a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr356189709_a_a_a A4) F) G)))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (X tptp.product_prod_a_a) (C2 tptp.product_prod_a_a) (G (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A4 tptp.set_Product_prod_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member449909584od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr200450189od_a_a A4) F) G)))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.a tptp.product_prod_a_a)) (X tptp.a) (C2 tptp.product_prod_a_a) (G (-> tptp.a tptp.product_prod_a_a)) (A4 tptp.set_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr1715025636od_a_a A4) F) G)))))) (forall ((B2 tptp.product_prod_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (X tptp.produc1572603623od_a_a) (C2 tptp.product_prod_a_a) (G (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (A4 tptp.set_Pr1948701895od_a_a)) (=> (= B2 (@ F X)) (=> (= C2 (@ G X)) (=> (@ (@ tptp.member2057358096od_a_a X) A4) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) C2)) (@ (@ (@ tptp.bNF_Gr533818957od_a_a A4) F) G)))))) (forall ((A tptp.a) (B2 tptp.product_prod_a_a) (A2 tptp.a) (B3 tptp.product_prod_a_a) (R tptp.set_Product_prod_a_a) (S tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1361298640od_a_a (@ (@ tptp.produc563767703od_a_a (@ (@ 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((_let_1 (@ tptp.produc1474507607od_a_a A))) (= (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a (@ _let_1 B2)) (@ (@ tptp.produc1474507607od_a_a A2) B3))) (@ (@ tptp.lex_pr942790511od_a_a R) S)) (or (@ (@ tptp.member2057358096od_a_a (@ _let_1 A2)) R) (and (= A A2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B2) B3)) S)))))) (forall ((A tptp.a) (B2 tptp.a) (A2 tptp.a) (B3 tptp.a) (R tptp.set_Product_prod_a_a) (S tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.product_Pair_a_a A))) (= (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a (@ _let_1 B2)) (@ (@ tptp.product_Pair_a_a A2) B3))) (@ (@ tptp.lex_prod_a_a R) S)) (or (@ (@ tptp.member449909584od_a_a (@ _let_1 A2)) R) (and (= A A2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B2) B3)) S)))))) (forall ((A tptp.product_prod_a_a) (B2 tptp.a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_a))) (= (@ (@ tptp.member1403138919_a_a_a (@ (@ 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tptp.produc1460477704od_a_a A4) B)) (not (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (forall ((Y3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc1935643479od_a_a X3) Y3)))))))))) (forall ((C2 tptp.product_prod_a_a) (A4 tptp.set_a) (B (-> tptp.a tptp.set_a))) (=> (@ (@ tptp.member449909584od_a_a C2) (@ (@ tptp.product_Sigma_a_a A4) B)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.product_Pair_a_a X3) Y3)))))))))) (forall ((C2 tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a C2) (@ (@ tptp.produc304751368od_a_a A4) B)) (not (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (forall ((Y3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Y3) (@ B X3)) (not (= C2 (@ (@ tptp.produc1474507607od_a_a X3) Y3)))))))))) (forall ((X tptp.produc1016684094_a_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_a)) (= (@ (@ tptp.member1403138919_a_a_a X) (@ (@ tptp.produc1282482655_a_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B))) (and (@ (@ tptp.member449909584od_a_a (@ tptp.produc1805832986_a_a_a X)) A4) (@ (@ tptp.member_a (@ tptp.produc1954021468_a_a_a X)) B)))) (forall ((X tptp.produc772425383od_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member122808528od_a_a X) (@ (@ tptp.produc1227942600od_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B))) (and (@ (@ tptp.member449909584od_a_a (@ tptp.produc1775747843od_a_a X)) A4) (@ (@ tptp.member2057358096od_a_a (@ tptp.produc1055472197od_a_a X)) B)))) (forall ((X tptp.produc1921647824od_a_a) (A4 tptp.set_a) (B tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member160619001od_a_a X) (@ (@ tptp.produc520147185od_a_a A4) (lambda ((Uu tptp.a)) B))) (and (@ (@ tptp.member_a (@ tptp.produc1043497516od_a_a X)) A4) (@ (@ tptp.member449909584od_a_a (@ tptp.produc1191685998od_a_a X)) B)))) (forall ((X tptp.produc1555800720od_a_a) (A4 tptp.set_a) (B tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member448091577od_a_a X) (@ (@ tptp.produc663418545od_a_a A4) (lambda ((Uu tptp.a)) B))) (and (@ (@ tptp.member_a (@ tptp.produc530563564od_a_a X)) A4) (@ (@ tptp.member2057358096od_a_a (@ tptp.produc921029422od_a_a X)) B)))) (forall ((X tptp.produc47586087od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member1545452880od_a_a X) (@ (@ tptp.produc197318472od_a_a A4) (lambda ((Uu tptp.produc1572603623od_a_a)) B))) (and (@ (@ tptp.member2057358096od_a_a (@ tptp.produc745123715od_a_a X)) A4) (@ (@ tptp.member449909584od_a_a (@ tptp.produc24848069od_a_a X)) B)))) (forall ((X tptp.produc1683075710_a_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_a)) (= (@ (@ tptp.member575366567_a_a_a X) (@ (@ tptp.produc4724255_a_a_a A4) (lambda ((Uu tptp.produc1572603623od_a_a)) B))) (and (@ (@ tptp.member2057358096od_a_a (@ tptp.produc2019352922_a_a_a X)) A4) (@ (@ tptp.member_a (@ tptp.produc262335132_a_a_a X)) B)))) (forall ((X tptp.produc1990712039od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1899387664od_a_a X) (@ (@ tptp.produc1460477704od_a_a A4) (lambda ((Uu tptp.produc1572603623od_a_a)) B))) (and (@ (@ tptp.member2057358096od_a_a (@ tptp.produc303632707od_a_a X)) A4) (@ (@ tptp.member2057358096od_a_a (@ tptp.produc1441227909od_a_a X)) B)))) (forall ((X tptp.product_prod_a_a) (A4 tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.member449909584od_a_a X) (@ (@ tptp.product_Sigma_a_a A4) (lambda ((Uu tptp.a)) B))) (and (@ (@ tptp.member_a (@ tptp.product_fst_a_a X)) A4) (@ (@ tptp.member_a (@ tptp.product_snd_a_a X)) B)))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member2057358096od_a_a X) (@ (@ tptp.produc304751368od_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B))) (and (@ (@ tptp.member449909584od_a_a (@ tptp.produc2115494211od_a_a X)) A4) (@ (@ tptp.member449909584od_a_a (@ tptp.produc368344197od_a_a X)) B)))) (forall ((X tptp.product_prod_a_a) (A4 tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X))) (= (@ _let_1 (@ (@ tptp.product_product_a_a A4) B)) (@ _let_1 (@ (@ tptp.product_Sigma_a_a A4) (lambda ((Uu tptp.a)) B)))))) (forall ((X tptp.produc1572603623od_a_a) (A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X))) (= (@ _let_1 (@ (@ tptp.produc905674258od_a_a A4) B)) (@ _let_1 (@ (@ tptp.produc304751368od_a_a A4) (lambda ((Uu tptp.product_prod_a_a)) B)))))) (forall ((A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X3))) (=> (@ _let_1 A4) (@ _let_1 B)))) (@ (@ tptp.ord_le1824328871od_a_a A4) B))) (forall ((A4 tptp.set_a) (B tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A4) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a A4) B))) (forall ((A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X3))) (=> (@ _let_1 A4) (@ _let_1 B)))) (@ (@ tptp.ord_le456379495od_a_a A4) B))) (forall ((A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (@ (@ tptp.member449909584od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.image_794773445od_a_a F) A4)) B))) (forall ((A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.a)) (B tptp.set_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (@ (@ tptp.member_a (@ F X3)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_340790172_a_a_a F) A4)) B))) (forall ((A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) A4) (@ (@ tptp.member2057358096od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.image_1765377413od_a_a F) A4)) B))) (forall ((A4 tptp.set_a) (F (-> tptp.a tptp.product_prod_a_a)) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (@ (@ tptp.member449909584od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.image_1725938350od_a_a F) A4)) B))) (forall ((A4 tptp.set_a) (F (-> tptp.a tptp.a)) (B tptp.set_a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (@ (@ tptp.member_a (@ F X3)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A4)) B))) (forall ((A4 tptp.set_a) (F (-> tptp.a tptp.produc1572603623od_a_a)) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A4) (@ (@ tptp.member2057358096od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.image_1763923566od_a_a F) A4)) B))) (forall ((A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.product_prod_a_a)) (B tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (@ (@ tptp.member449909584od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.image_734753285od_a_a F) A4)) B))) (forall ((A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.a)) (B tptp.set_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (@ (@ tptp.member_a (@ F X3)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_1105229276_a_a_a F) A4)) B))) (forall ((A4 tptp.set_Pr1948701895od_a_a) (F (-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a)) (B tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) A4) (@ (@ tptp.member2057358096od_a_a (@ F X3)) B))) (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.image_236793797od_a_a F) A4)) B))) (forall ((R tptp.set_Product_prod_a_a) (S tptp.set_Product_prod_a_a)) (=> (forall ((X3 tptp.a) (Y3 tptp.a)) (let ((_let_1 (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le1824328871od_a_a R) S))) (forall ((R tptp.set_Pr1948701895od_a_a) (S tptp.set_Pr1948701895od_a_a)) (=> (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le456379495od_a_a R) S))) _let_4 _let_3 _let_2 (= tptp.ord_le1824328871od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (forall ((X4 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X4))) (=> (@ _let_1 A6) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (forall ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ _let_1 A6) (@ _let_1 B5)))))) (= tptp.ord_le456379495od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (forall ((X4 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X4))) (=> (@ _let_1 A6) (@ _let_1 B5)))))) (forall ((A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a) (C2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ (@ tptp.ord_le1824328871od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))) (forall ((A4 tptp.set_a) (B tptp.set_a) (C2 tptp.a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))) (forall ((A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a) (C2 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a C2))) (=> (@ (@ tptp.ord_le456379495od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))) (forall ((A4 tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a) (X tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X))) (=> (@ (@ tptp.ord_le1824328871od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))) (forall ((A4 tptp.set_a) (B tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))) (forall ((A4 tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a) (X tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.member2057358096od_a_a X))) (=> (@ (@ tptp.ord_le456379495od_a_a A4) B) (=> (@ _let_1 A4) (@ _let_1 B))))) (forall ((X tptp.product_prod_a_a) (Z2 tptp.set_Product_prod_a_a) (X5 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (@ (@ tptp.member449909584od_a_a X) Z2) (=> (@ (@ tptp.ord_le1824328871od_a_a Z2) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) X5) (@ P2 X4))))) (@ P2 X)))) (forall ((X tptp.a) (Z2 tptp.set_a) (X5 tptp.set_a) (P2 (-> tptp.a Bool))) (=> (@ (@ tptp.member_a X) Z2) (=> (@ (@ tptp.ord_less_eq_set_a Z2) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) X5) (@ P2 X4))))) (@ P2 X)))) (forall ((X tptp.produc1572603623od_a_a) (Z2 tptp.set_Pr1948701895od_a_a) (X5 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (=> (@ (@ tptp.member2057358096od_a_a X) Z2) (=> (@ (@ tptp.ord_le456379495od_a_a Z2) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) X5) (@ P2 X4))))) (@ P2 X)))) (forall ((X5 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) X5) (@ P2 X4))))) X5)) (forall ((X5 tptp.set_a) (P2 (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) X5) (@ P2 X4))))) X5)) (forall ((X5 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (@ (@ tptp.ord_le456379495od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) X5) (@ P2 X4))))) X5)) (forall ((A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 X4))))) A4)) (forall ((A4 tptp.set_a) (P2 (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 X4))))) A4)) (forall ((A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (@ (@ tptp.ord_le456379495od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 X4))))) A4)) (forall ((B tptp.set_Product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a B))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 X4))))) (forall ((X4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X4) B) (@ P2 X4))))))) (forall ((B tptp.set_a) (A4 tptp.set_a) (P2 (-> tptp.a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_a B))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 X4))))) (forall ((X4 tptp.a)) (=> (@ (@ tptp.member_a X4) B) (@ P2 X4))))))) (forall ((B tptp.set_Pr1948701895od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.produc1572603623od_a_a Bool))) (let ((_let_1 (@ tptp.ord_le456379495od_a_a B))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 X4))))) (forall ((X4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X4) B) (@ P2 X4))))))) (forall ((B tptp.set_Product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (Q (-> tptp.product_prod_a_a Bool)) (P2 (-> tptp.product_prod_a_a Bool))) (=> (@ (@ tptp.ord_le1824328871od_a_a B) A4) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) B) (=> (@ Q X3) (@ P2 X3)))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) B) (@ Q X4))))) (@ tptp.collec645855634od_a_a (lambda ((X4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X4) A4) (@ P2 X4)))))))) (forall ((B tptp.set_a) (A4 tptp.set_a) (Q (-> tptp.a Bool)) (P2 (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_set_a B) A4) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) B) (=> (@ Q X3) (@ P2 X3)))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) B) (@ Q X4))))) (@ tptp.collect_a (lambda ((X4 tptp.a)) (and (@ (@ tptp.member_a X4) A4) (@ P2 X4)))))))) (forall ((B tptp.set_Pr1948701895od_a_a) (A4 tptp.set_Pr1948701895od_a_a) (Q (-> tptp.produc1572603623od_a_a Bool)) (P2 (-> tptp.produc1572603623od_a_a Bool))) (=> (@ (@ tptp.ord_le456379495od_a_a B) A4) (=> (forall ((X3 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a X3) B) (=> (@ Q X3) (@ P2 X3)))) (@ (@ tptp.ord_le456379495od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) B) (@ Q X4))))) (@ tptp.collec1635618130od_a_a (lambda ((X4 tptp.produc1572603623od_a_a)) (and (@ (@ tptp.member2057358096od_a_a X4) A4) (@ P2 X4)))))))) (forall ((R2 tptp.set_Product_prod_a_a) (S3 tptp.set_Product_prod_a_a)) (= (@ (@ tptp.ord_le1347718902_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) R2))) (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) S3))) (@ (@ tptp.ord_le1824328871od_a_a R2) S3))) (forall ((R2 tptp.set_a) (S3 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) R2))) (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) S3))) (@ (@ tptp.ord_less_eq_set_a R2) S3))) (forall ((R2 tptp.set_Pr1948701895od_a_a) (S3 tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.ord_le1525442358_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) R2))) (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) S3))) (@ (@ tptp.ord_le456379495od_a_a R2) S3))) (= tptp.ord_le1824328871od_a_a (lambda ((A6 tptp.set_Product_prod_a_a) (B5 tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1347718902_a_a_o (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A6))) (lambda ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) B5))))) (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B5 tptp.set_a)) (@ (@ tptp.ord_less_eq_a_o (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A6))) (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) B5))))) (= tptp.ord_le456379495od_a_a (lambda ((A6 tptp.set_Pr1948701895od_a_a) (B5 tptp.set_Pr1948701895od_a_a)) (@ (@ tptp.ord_le1525442358_a_a_o (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A6))) (lambda ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) B5))))) (forall ((R2 tptp.set_Product_prod_a_a) (S3 tptp.set_Product_prod_a_a)) (= (@ (@ tptp.ord_less_eq_a_a_o (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R2))) (lambda ((X4 tptp.a) (Y4 tptp.a)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) S3))) (@ (@ tptp.ord_le1824328871od_a_a R2) S3))) (forall ((R2 tptp.set_Pr1948701895od_a_a) (S3 tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.ord_le252190158_a_a_o (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R2))) (lambda ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) S3))) (@ (@ tptp.ord_le456379495od_a_a R2) S3))) (forall ((X tptp.a) (Fx tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Fx)) (@ (@ tptp.bNF_Gr_a_a A4) F)) (@ (@ tptp.member_a X) A4))) (forall ((X tptp.product_prod_a_a) (Fx tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Fx)) (@ (@ tptp.bNF_Gr1372473186od_a_a A4) F)) (@ (@ tptp.member449909584od_a_a X) A4))) (forall ((X tptp.a) (Fx tptp.a) (A4 tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Fx)) (@ (@ tptp.bNF_Gr_a_a A4) F)) (= (@ F X) Fx))) (forall ((X tptp.product_prod_a_a) (Fx tptp.product_prod_a_a) (A4 tptp.set_Product_prod_a_a) (F (-> tptp.product_prod_a_a tptp.product_prod_a_a))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Fx)) (@ (@ tptp.bNF_Gr1372473186od_a_a A4) F)) (= (@ F X) Fx))) (forall ((A4 tptp.set_Product_prod_a_a)) (= (forall ((X4 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a X4) A4))) (= A4 tptp.bot_bo2131659635od_a_a))) (forall ((A4 tptp.set_a)) (= (forall ((X4 tptp.a)) (not (@ (@ tptp.member_a X4) A4))) (= A4 tptp.bot_bot_set_a))) (forall ((A4 tptp.set_Pr1948701895od_a_a)) (= (forall ((X4 tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a X4) A4))) (= A4 tptp.bot_bo1116205875od_a_a))) (forall ((C2 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a C2) tptp.bot_bo2131659635od_a_a))) (forall ((C2 tptp.a)) (not (@ (@ tptp.member_a C2) tptp.bot_bot_set_a))) (forall ((C2 tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a C2) tptp.bot_bo1116205875od_a_a))) (forall ((A4 tptp.set_Product_prod_a_a)) (= (exists ((X4 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X4) A4)) (not (= A4 tptp.bot_bo2131659635od_a_a)))) (forall ((A4 tptp.set_a)) (= (exists ((X4 tptp.a)) (@ (@ tptp.member_a X4) A4)) (not (= A4 tptp.bot_bot_set_a)))) (forall ((A4 tptp.set_Pr1948701895od_a_a)) (= (exists ((X4 tptp.produc1572603623od_a_a)) (@ (@ tptp.member2057358096od_a_a X4) A4)) (not (= A4 tptp.bot_bo1116205875od_a_a)))) (forall ((A4 tptp.set_Product_prod_a_a)) (=> (forall ((Y3 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a Y3) A4))) (= A4 tptp.bot_bo2131659635od_a_a))) (forall ((A4 tptp.set_a)) (=> (forall ((Y3 tptp.a)) (not (@ (@ tptp.member_a Y3) A4))) (= A4 tptp.bot_bot_set_a))) (forall ((A4 tptp.set_Pr1948701895od_a_a)) (=> (forall ((Y3 tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a Y3) A4))) (= A4 tptp.bot_bo1116205875od_a_a))) (forall ((A4 tptp.set_Product_prod_a_a) (A tptp.product_prod_a_a)) (=> (= A4 tptp.bot_bo2131659635od_a_a) (not (@ (@ tptp.member449909584od_a_a A) A4)))) (forall ((A4 tptp.set_a) (A tptp.a)) (=> (= A4 tptp.bot_bot_set_a) (not (@ (@ tptp.member_a A) A4)))) (forall ((A4 tptp.set_Pr1948701895od_a_a) (A tptp.produc1572603623od_a_a)) (=> (= A4 tptp.bot_bo1116205875od_a_a) (not (@ (@ tptp.member2057358096od_a_a A) A4)))) (forall ((A tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a A) tptp.bot_bo2131659635od_a_a))) (forall ((A tptp.a)) (not (@ (@ tptp.member_a A) tptp.bot_bot_set_a))) (forall ((A tptp.produc1572603623od_a_a)) (not (@ (@ tptp.member2057358096od_a_a A) tptp.bot_bo1116205875od_a_a))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.55/1.23 )
% 0.55/1.23 % SZS output end Proof for ITP157^1
% 0.55/1.23 % cvc5---1.0.5 exiting
% 0.55/1.23 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------