TSTP Solution File: ITP028^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP028^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 03:17:35 EDT 2023
% Result : Theorem 0.81s 1.06s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.19 % Problem : ITP028^1 : TPTP v8.1.2. Released v7.5.0.
% 0.14/0.20 % Command : do_cvc5 %s %d
% 0.21/0.42 % Computer : n013.cluster.edu
% 0.21/0.42 % Model : x86_64 x86_64
% 0.21/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.42 % Memory : 8042.1875MB
% 0.21/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.42 % CPULimit : 300
% 0.21/0.42 % WCLimit : 300
% 0.21/0.42 % DateTime : Sun Aug 27 12:52:47 EDT 2023
% 0.21/0.42 % CPUTime :
% 0.27/0.61 %----Proving TH0
% 0.27/0.62 %------------------------------------------------------------------------------
% 0.27/0.62 % File : ITP028^1 : TPTP v8.1.2. Released v7.5.0.
% 0.27/0.62 % Domain : Interactive Theorem Proving
% 0.27/0.62 % Problem : Sledgehammer Algebra8 problem prob_962__6421504_1
% 0.27/0.62 % Version : Especial.
% 0.27/0.62 % English :
% 0.27/0.62
% 0.27/0.62 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.62 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.62 % Source : [Des21]
% 0.27/0.62 % Names : Algebra8/prob_962__6421504_1 [Des21]
% 0.27/0.62
% 0.27/0.62 % Status : Theorem
% 0.27/0.62 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.27/0.62 % Syntax : Number of formulae : 456 ( 120 unt; 102 typ; 0 def)
% 0.27/0.62 % Number of atoms : 1002 ( 288 equ; 0 cnn)
% 0.27/0.62 % Maximal formula atoms : 8 ( 2 avg)
% 0.27/0.62 % Number of connectives : 2874 ( 78 ~; 10 |; 54 &;2255 @)
% 0.27/0.62 % ( 0 <=>; 477 =>; 0 <=; 0 <~>)
% 0.27/0.62 % Maximal formula depth : 16 ( 7 avg)
% 0.27/0.62 % Number of types : 16 ( 15 usr)
% 0.27/0.62 % Number of type conns : 618 ( 618 >; 0 *; 0 +; 0 <<)
% 0.27/0.62 % Number of symbols : 90 ( 87 usr; 12 con; 0-5 aty)
% 0.27/0.62 % Number of variables : 1103 ( 97 ^; 962 !; 44 ?;1103 :)
% 0.27/0.62 % SPC : TH0_THM_EQU_NAR
% 0.27/0.62
% 0.27/0.62 % Comments : This file was generated by Sledgehammer 2021-02-23 15:45:55.322
% 0.27/0.62 %------------------------------------------------------------------------------
% 0.27/0.62 % Could-be-implicit typings (15)
% 0.27/0.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J_J,type,
% 0.27/0.62 set_Pr1710391469_a_a_e: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J,type,
% 0.27/0.62 produc169085773_a_a_e: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J_J,type,
% 0.27/0.62 set_se821189730_a_a_e: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J_J,type,
% 0.27/0.62 set_Pr2045688071_set_a: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J,type,
% 0.27/0.62 set_Pr204296108_a_a_e: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__a_Mtf__e_J_Mt__Set__Oset_Itf__a_J_J_J,type,
% 0.27/0.62 set_Pr305929312_set_a: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 produc1691597095_set_a: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 produc715398134_a_a_e: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_Mtf__e_J_Mt__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 produc1965228714_set_a: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.27/0.62 set_set_set_a: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 set_set_a: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_I_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 set_a_e: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 set_a: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_tf__e,type,
% 0.27/0.62 e: $tType ).
% 0.27/0.62
% 0.27/0.62 thf(ty_n_tf__a,type,
% 0.27/0.62 a: $tType ).
% 0.27/0.62
% 0.27/0.62 % Explicit typings (87)
% 0.27/0.62 thf(sy_c_BNF__Def_OfstOp_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 bNF_fs1024561536_e_a_e: ( set_a > ( a > e ) > $o ) > ( ( a > e ) > ( a > e ) > $o ) > produc715398134_a_a_e > produc715398134_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_BNF__Def_Opick__middlep_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 bNF_pi1175744974_e_a_e: ( set_a > ( a > e ) > $o ) > ( ( a > e ) > ( a > e ) > $o ) > set_a > ( a > e ) > a > e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_BNF__Def_Opick__middlep_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 bNF_pi929741261_a_a_e: ( set_a > set_a > $o ) > ( set_a > ( a > e ) > $o ) > set_a > ( a > e ) > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_BNF__Def_OsndOp_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 bNF_sn375433437_a_a_e: ( set_a > set_a > $o ) > ( set_a > ( a > e ) > $o ) > produc715398134_a_a_e > produc715398134_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 bNF_Gr2072183031_a_a_e: set_Pr204296108_a_a_e > ( produc715398134_a_a_e > set_a ) > ( produc715398134_a_a_e > a > e ) > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 bNF_Gr1872575811_a_a_e: set_set_a > ( set_a > set_a ) > ( set_a > a > e ) > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Finite__Set_OFpow_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 finite33065488_a_a_e: set_Pr204296108_a_a_e > set_se821189730_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Finite__Set_OFpow_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 finite_Fpow_set_a: set_set_a > set_set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Finite__Set_OFpow_001tf__a,type,
% 0.27/0.62 finite_Fpow_a: set_a > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Fun__Def_Oin__rel_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 fun_in_rel_set_a_a_e: set_Pr204296108_a_a_e > set_a > ( a > e ) > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 ord_less_eq_o_set_a: ( $o > set_a ) > ( $o > set_a ) > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 ord_less_eq_set_a_e: set_a_e > set_a_e > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__a_Mtf__e_J_Mt__Set__Oset_Itf__a_J_J_J,type,
% 0.27/0.62 ord_le802356416_set_a: set_Pr305929312_set_a > set_Pr305929312_set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J,type,
% 0.27/0.62 ord_le700723212_a_a_e: set_Pr204296108_a_a_e > set_Pr204296108_a_a_e > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.27/0.62 ord_le2103863998_set_a: set_set_set_a > set_set_set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 ord_le318720350_set_a: set_set_a > set_set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 order_Greatest_set_a: ( set_a > $o ) > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_M_Eo_J,type,
% 0.27/0.62 top_to2000253225_a_e_o: produc715398134_a_a_e > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
% 0.27/0.62 top_top_set_a_o: set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J_J,type,
% 0.27/0.62 top_to970499581_a_a_e: set_Pr1710391469_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J,type,
% 0.27/0.62 top_to1601855068_a_a_e: set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J_J,type,
% 0.27/0.62 top_to144004695_set_a: set_Pr2045688071_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 top_top_set_set_a: set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 top_top_set_a: set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_OPair_001_062_Itf__a_Mtf__e_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 produc479206876_set_a: ( a > e ) > set_a > produc1965228714_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 produc1134456688_a_a_e: set_a > ( a > e ) > produc715398134_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Ocurry_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001_Eo,type,
% 0.27/0.62 produc952037978_a_e_o: ( produc715398134_a_a_e > $o ) > set_a > ( a > e ) > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001t__Set__Oset_Itf__a_J_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 produc387505142_set_a: ( produc715398134_a_a_e > set_a ) > ( produc715398134_a_a_e > set_a ) > produc169085773_a_a_e > produc1691597095_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Omap__prod_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 produc1443219402_e_a_e: ( set_a > set_a ) > ( ( a > e ) > a > e ) > produc715398134_a_a_e > produc715398134_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001_Eo,type,
% 0.27/0.62 produc1341862587_a_e_o: ( set_a > ( a > e ) > $o ) > produc715398134_a_a_e > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J,type,
% 0.27/0.62 produc1096319049_a_a_e: ( set_a > ( a > e ) > set_Pr204296108_a_a_e ) > produc715398134_a_a_e > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 produc1620938593_set_a: ( set_a > ( a > e ) > set_set_a ) > produc715398134_a_a_e > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Ofst_001_062_Itf__a_Mtf__e_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 produc385678576_set_a: produc1965228714_set_a > a > e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 produc1040928388_a_a_e: produc715398134_a_a_e > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Osnd_001_062_Itf__a_Mtf__e_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 produc1809800494_set_a: produc1965228714_set_a > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 produc317566658_a_a_e: produc715398134_a_a_e > a > e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Oswap_001_062_Itf__a_Mtf__e_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 produc100464700_set_a: produc1965228714_set_a > produc715398134_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_Oprod_Oswap_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 produc755714512_a_a_e: produc715398134_a_a_e > produc1965228714_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_ODomain_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 domain_set_a_a_e: set_Pr204296108_a_a_e > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_ORange_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 range_set_a_a_e: set_Pr204296108_a_a_e > set_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_Oconverse_001_062_Itf__a_Mtf__e_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 converse_a_e_set_a: set_Pr305929312_set_a > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_Oconverse_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 converse_set_a_a_e: set_Pr204296108_a_a_e > set_Pr305929312_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_Orelcompp_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 relcom658603713_e_a_e: ( set_a > ( a > e ) > $o ) > ( ( a > e ) > ( a > e ) > $o ) > set_a > ( a > e ) > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_Orelcompp_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 relcom779348378_a_a_e: ( set_a > set_a > $o ) > ( set_a > ( a > e ) > $o ) > set_a > ( a > e ) > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 collec1369693387_a_a_e: ( produc715398134_a_a_e > $o ) > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 collect_set_a: ( set_a > $o ) > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.27/0.62 collect_a: ( a > $o ) > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_OPow_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 pow_Pr328302361_a_a_e: set_Pr204296108_a_a_e > set_se821189730_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_OPow_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 pow_set_a: set_set_a > set_set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_OPow_001tf__a,type,
% 0.27/0.62 pow_a: set_a > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001_062_Itf__a_Mtf__e_J_001tf__a,type,
% 0.27/0.62 image_a_e_a: ( ( a > e ) > a ) > set_a_e > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_Itf__a_Mtf__e_J_Mt__Set__Oset_Itf__a_J_J_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 image_376979367_a_a_e: ( produc1965228714_set_a > produc715398134_a_a_e ) > set_Pr305929312_set_a > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 image_2101504031_set_a: ( produc169085773_a_a_e > produc1691597095_set_a ) > set_Pr1710391469_a_a_e > set_Pr2045688071_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 image_1149879910_e_a_e: ( produc715398134_a_a_e > a > e ) > set_Pr204296108_a_a_e > set_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001t__Product____Type__Oprod_I_062_Itf__a_Mtf__e_J_Mt__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 image_1875450791_set_a: ( produc715398134_a_a_e > produc1965228714_set_a ) > set_Pr204296108_a_a_e > set_Pr305929312_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 image_625620211_a_a_e: ( produc715398134_a_a_e > produc715398134_a_a_e ) > set_Pr204296108_a_a_e > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 image_64240033_set_a: ( produc715398134_a_a_e > set_a ) > set_Pr204296108_a_a_e > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_001tf__a,type,
% 0.27/0.62 image_2116492353_a_e_a: ( produc715398134_a_a_e > a ) > set_Pr204296108_a_a_e > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 image_1441218763_set_a: ( set_Pr204296108_a_a_e > set_set_a ) > set_se821189730_a_a_e > set_set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Set__Oset_Itf__a_J_J_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 image_1956910981_set_a: ( set_set_a > set_set_a ) > set_set_set_a > set_set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Set__Oset_Itf__a_J_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 image_402591269_set_a: ( set_set_a > set_a ) > set_set_set_a > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Set__Oset_Itf__a_J_J_001tf__a,type,
% 0.27/0.62 image_set_set_a_a: ( set_set_a > a ) > set_set_set_a > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__a_J_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 image_set_a_a_e: ( set_a > a > e ) > set_set_a > set_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__a_J_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 image_210900495_a_a_e: ( set_a > produc715398134_a_a_e ) > set_set_a > set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__a_J_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 image_1930509541_set_a: ( set_a > set_set_a ) > set_set_a > set_set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 image_set_a_set_a: ( set_a > set_a ) > set_set_a > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__a_J_001tf__a,type,
% 0.27/0.62 image_set_a_a: ( set_a > a ) > set_set_a > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001tf__a_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 image_a_a_e: ( a > a > e ) > set_a > set_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 image_a_set_set_a: ( a > set_set_a ) > set_a > set_set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 image_a_set_a: ( a > set_a ) > set_a > set_set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
% 0.27/0.62 image_a_a: ( a > a ) > set_a > set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001_062_Itf__a_Mtf__e_J,type,
% 0.27/0.62 member_a_e: ( a > e ) > set_a_e > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__a_Mtf__e_J_Mt__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 member360729153_set_a: produc1965228714_set_a > set_Pr305929312_set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J,type,
% 0.27/0.62 member1258382221_a_a_e: produc715398134_a_a_e > set_Pr204296108_a_a_e > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_Mtf__e_J_J_J,type,
% 0.27/0.62 member1437121347_a_a_e: set_Pr204296108_a_a_e > set_se821189730_a_a_e > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.27/0.62 member_set_set_a: set_set_a > set_set_set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.62 member_set_a: set_a > set_set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001tf__a,type,
% 0.27/0.62 member_a: a > set_a > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_C,type,
% 0.27/0.62 c: set_Pr204296108_a_a_e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_a1,type,
% 0.27/0.62 a1: set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_a2,type,
% 0.27/0.62 a2: set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_a3,type,
% 0.27/0.62 a3: set_a ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_b1,type,
% 0.27/0.62 b1: a > e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_b2,type,
% 0.27/0.62 b2: a > e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_b3,type,
% 0.27/0.62 b3: a > e ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_thesis____,type,
% 0.27/0.62 thesis: $o ).
% 0.27/0.62
% 0.27/0.62 % Relevant facts (352)
% 0.27/0.62 thf(fact_0__092_060open_062_092_060forall_062a_092_060in_062C_O_A_092_060forall_062b_092_060in_062C_O_Afst_Aa_A_092_060subseteq_062_Afst_Ab_A_092_060or_062_Afst_Ab_A_092_060subseteq_062_Afst_Aa_092_060close_062,axiom,
% 0.27/0.62 ! [X: produc715398134_a_a_e] :
% 0.27/0.62 ( ( member1258382221_a_a_e @ X @ c )
% 0.27/0.62 => ! [Xa: produc715398134_a_a_e] :
% 0.27/0.62 ( ( member1258382221_a_a_e @ Xa @ c )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ ( produc1040928388_a_a_e @ X ) @ ( produc1040928388_a_a_e @ Xa ) )
% 0.27/0.62 | ( ord_less_eq_set_a @ ( produc1040928388_a_a_e @ Xa ) @ ( produc1040928388_a_a_e @ X ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % \<open>\<forall>a\<in>C. \<forall>b\<in>C. fst a \<subseteq> fst b \<or> fst b \<subseteq> fst a\<close>
% 0.27/0.62 thf(fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062,axiom,
% 0.27/0.62 ? [X2: set_a] :
% 0.27/0.62 ( ( member_set_a @ X2 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
% 0.27/0.62 & ( ord_less_eq_set_a @ a1 @ X2 )
% 0.27/0.62 & ( ord_less_eq_set_a @ a2 @ X2 )
% 0.27/0.62 & ( ord_less_eq_set_a @ a3 @ X2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % \<open>\<exists>a\<in>fst ` C. a1 \<subseteq> a \<and> a2 \<subseteq> a \<and> a3 \<subseteq> a\<close>
% 0.27/0.62 thf(fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062,axiom,
% 0.27/0.62 ( ( ord_less_eq_set_a @ a1 @ a2 )
% 0.27/0.62 | ( ord_less_eq_set_a @ a2 @ a1 ) ) ).
% 0.27/0.62
% 0.27/0.62 % \<open>a1 \<subseteq> a2 \<or> a2 \<subseteq> a1\<close>
% 0.27/0.62 thf(fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062,axiom,
% 0.27/0.62 ( ( ord_less_eq_set_a @ a1 @ a3 )
% 0.27/0.62 | ( ord_less_eq_set_a @ a3 @ a1 ) ) ).
% 0.27/0.62
% 0.27/0.62 % \<open>a1 \<subseteq> a3 \<or> a3 \<subseteq> a1\<close>
% 0.27/0.62 thf(fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062,axiom,
% 0.27/0.62 ( ( ord_less_eq_set_a @ a2 @ a3 )
% 0.27/0.62 | ( ord_less_eq_set_a @ a3 @ a2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % \<open>a2 \<subseteq> a3 \<or> a3 \<subseteq> a2\<close>
% 0.27/0.62 thf(fact_5_A_I3_J,axiom,
% 0.27/0.62 member_set_a @ a3 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ).
% 0.27/0.62
% 0.27/0.62 % A(3)
% 0.27/0.62 thf(fact_6_A_I2_J,axiom,
% 0.27/0.62 member_set_a @ a2 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ).
% 0.27/0.62
% 0.27/0.62 % A(2)
% 0.27/0.62 thf(fact_7_A_I1_J,axiom,
% 0.27/0.62 member_set_a @ a1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ).
% 0.27/0.62
% 0.27/0.62 % A(1)
% 0.27/0.62 thf(fact_8__092_060open_062_Ia1_M_Ab1_J_A_092_060in_062_AC_092_060close_062,axiom,
% 0.27/0.62 member1258382221_a_a_e @ ( produc1134456688_a_a_e @ a1 @ b1 ) @ c ).
% 0.27/0.62
% 0.27/0.62 % \<open>(a1, b1) \<in> C\<close>
% 0.27/0.62 thf(fact_9__092_060open_062_Ia2_M_Ab2_J_A_092_060in_062_AC_092_060close_062,axiom,
% 0.27/0.62 member1258382221_a_a_e @ ( produc1134456688_a_a_e @ a2 @ b2 ) @ c ).
% 0.27/0.62
% 0.27/0.62 % \<open>(a2, b2) \<in> C\<close>
% 0.27/0.62 thf(fact_10__092_060open_062_Ia3_M_Ab3_J_A_092_060in_062_AC_092_060close_062,axiom,
% 0.27/0.62 member1258382221_a_a_e @ ( produc1134456688_a_a_e @ a3 @ b3 ) @ c ).
% 0.27/0.62
% 0.27/0.62 % \<open>(a3, b3) \<in> C\<close>
% 0.27/0.62 thf(fact_11_subsetI,axiom,
% 0.27/0.62 ! [A: set_a_e,B: set_a_e] :
% 0.27/0.62 ( ! [X2: a > e] :
% 0.27/0.62 ( ( member_a_e @ X2 @ A )
% 0.27/0.62 => ( member_a_e @ X2 @ B ) )
% 0.27/0.62 => ( ord_less_eq_set_a_e @ A @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_12_subsetI,axiom,
% 0.27/0.62 ! [A: set_Pr305929312_set_a,B: set_Pr305929312_set_a] :
% 0.27/0.62 ( ! [X2: produc1965228714_set_a] :
% 0.27/0.62 ( ( member360729153_set_a @ X2 @ A )
% 0.27/0.62 => ( member360729153_set_a @ X2 @ B ) )
% 0.27/0.62 => ( ord_le802356416_set_a @ A @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_13_subsetI,axiom,
% 0.27/0.62 ! [A: set_set_set_a,B: set_set_set_a] :
% 0.27/0.62 ( ! [X2: set_set_a] :
% 0.27/0.62 ( ( member_set_set_a @ X2 @ A )
% 0.27/0.62 => ( member_set_set_a @ X2 @ B ) )
% 0.27/0.62 => ( ord_le2103863998_set_a @ A @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_14_subsetI,axiom,
% 0.27/0.62 ! [A: set_set_a,B: set_set_a] :
% 0.27/0.62 ( ! [X2: set_a] :
% 0.27/0.62 ( ( member_set_a @ X2 @ A )
% 0.27/0.62 => ( member_set_a @ X2 @ B ) )
% 0.27/0.62 => ( ord_le318720350_set_a @ A @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_15_subsetI,axiom,
% 0.27/0.62 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.62 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.62 => ( member1258382221_a_a_e @ X2 @ B ) )
% 0.27/0.62 => ( ord_le700723212_a_a_e @ A @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_16_subsetI,axiom,
% 0.27/0.62 ! [A: set_a,B: set_a] :
% 0.27/0.62 ( ! [X2: a] :
% 0.27/0.62 ( ( member_a @ X2 @ A )
% 0.27/0.62 => ( member_a @ X2 @ B ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_17_subset__antisym,axiom,
% 0.27/0.62 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.62 => ( ( ord_le700723212_a_a_e @ B @ A )
% 0.27/0.62 => ( A = B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_antisym
% 0.27/0.62 thf(fact_18_subset__antisym,axiom,
% 0.27/0.62 ! [A: set_set_a,B: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.62 => ( ( ord_le318720350_set_a @ B @ A )
% 0.27/0.62 => ( A = B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_antisym
% 0.27/0.62 thf(fact_19_subset__antisym,axiom,
% 0.27/0.62 ! [A: set_set_set_a,B: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ A @ B )
% 0.27/0.62 => ( ( ord_le2103863998_set_a @ B @ A )
% 0.27/0.62 => ( A = B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_antisym
% 0.27/0.62 thf(fact_20_subset__antisym,axiom,
% 0.27/0.62 ! [A: set_a,B: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.62 => ( A = B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_antisym
% 0.27/0.62 thf(fact_21_image__eqI,axiom,
% 0.27/0.62 ! [B2: set_a,F: set_a > set_a,X3: set_a,A: set_set_a] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_set_a @ X3 @ A )
% 0.27/0.62 => ( member_set_a @ B2 @ ( image_set_a_set_a @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_22_image__eqI,axiom,
% 0.27/0.62 ! [B2: produc715398134_a_a_e,F: set_a > produc715398134_a_a_e,X3: set_a,A: set_set_a] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_set_a @ X3 @ A )
% 0.27/0.62 => ( member1258382221_a_a_e @ B2 @ ( image_210900495_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_23_image__eqI,axiom,
% 0.27/0.62 ! [B2: set_a,F: produc715398134_a_a_e > set_a,X3: produc715398134_a_a_e,A: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.62 => ( member_set_a @ B2 @ ( image_64240033_set_a @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_24_image__eqI,axiom,
% 0.27/0.62 ! [B2: produc715398134_a_a_e,F: produc715398134_a_a_e > produc715398134_a_a_e,X3: produc715398134_a_a_e,A: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.62 => ( member1258382221_a_a_e @ B2 @ ( image_625620211_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_25_image__eqI,axiom,
% 0.27/0.62 ! [B2: a,F: a > a,X3: a,A: set_a] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_a @ X3 @ A )
% 0.27/0.62 => ( member_a @ B2 @ ( image_a_a @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_26_image__eqI,axiom,
% 0.27/0.62 ! [B2: a,F: set_a > a,X3: set_a,A: set_set_a] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_set_a @ X3 @ A )
% 0.27/0.62 => ( member_a @ B2 @ ( image_set_a_a @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_27_image__eqI,axiom,
% 0.27/0.62 ! [B2: set_a,F: a > set_a,X3: a,A: set_a] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_a @ X3 @ A )
% 0.27/0.62 => ( member_set_a @ B2 @ ( image_a_set_a @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_28_image__eqI,axiom,
% 0.27/0.62 ! [B2: a > e,F: a > a > e,X3: a,A: set_a] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_a @ X3 @ A )
% 0.27/0.62 => ( member_a_e @ B2 @ ( image_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_29_image__eqI,axiom,
% 0.27/0.62 ! [B2: a,F: ( a > e ) > a,X3: a > e,A: set_a_e] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_a_e @ X3 @ A )
% 0.27/0.62 => ( member_a @ B2 @ ( image_a_e_a @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_30_image__eqI,axiom,
% 0.27/0.62 ! [B2: a > e,F: set_a > a > e,X3: set_a,A: set_set_a] :
% 0.27/0.62 ( ( B2
% 0.27/0.62 = ( F @ X3 ) )
% 0.27/0.62 => ( ( member_set_a @ X3 @ A )
% 0.27/0.62 => ( member_a_e @ B2 @ ( image_set_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_eqI
% 0.27/0.62 thf(fact_31_order__refl,axiom,
% 0.27/0.62 ! [X3: set_Pr204296108_a_a_e] : ( ord_le700723212_a_a_e @ X3 @ X3 ) ).
% 0.27/0.62
% 0.27/0.62 % order_refl
% 0.27/0.62 thf(fact_32_order__refl,axiom,
% 0.27/0.62 ! [X3: set_set_a] : ( ord_le318720350_set_a @ X3 @ X3 ) ).
% 0.27/0.62
% 0.27/0.62 % order_refl
% 0.27/0.62 thf(fact_33_order__refl,axiom,
% 0.27/0.62 ! [X3: set_set_set_a] : ( ord_le2103863998_set_a @ X3 @ X3 ) ).
% 0.27/0.62
% 0.27/0.62 % order_refl
% 0.27/0.62 thf(fact_34_order__refl,axiom,
% 0.27/0.62 ! [X3: $o > set_a] : ( ord_less_eq_o_set_a @ X3 @ X3 ) ).
% 0.27/0.62
% 0.27/0.62 % order_refl
% 0.27/0.62 thf(fact_35_order__refl,axiom,
% 0.27/0.62 ! [X3: set_a] : ( ord_less_eq_set_a @ X3 @ X3 ) ).
% 0.27/0.62
% 0.27/0.62 % order_refl
% 0.27/0.62 thf(fact_36_image__mono,axiom,
% 0.27/0.62 ! [A: set_a,B: set_a,F: a > a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( image_a_a @ F @ A ) @ ( image_a_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_37_image__mono,axiom,
% 0.27/0.62 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > set_a] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.62 => ( ord_le318720350_set_a @ ( image_64240033_set_a @ F @ A ) @ ( image_64240033_set_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_38_image__mono,axiom,
% 0.27/0.62 ! [A: set_a,B: set_a,F: a > set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.62 => ( ord_le318720350_set_a @ ( image_a_set_a @ F @ A ) @ ( image_a_set_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_39_image__mono,axiom,
% 0.27/0.62 ! [A: set_set_a,B: set_set_a,F: set_a > a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( image_set_a_a @ F @ A ) @ ( image_set_a_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_40_image__mono,axiom,
% 0.27/0.62 ! [A: set_a,B: set_a,F: a > set_set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.62 => ( ord_le2103863998_set_a @ ( image_a_set_set_a @ F @ A ) @ ( image_a_set_set_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_41_image__mono,axiom,
% 0.27/0.62 ! [A: set_set_a,B: set_set_a,F: set_a > set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.62 => ( ord_le318720350_set_a @ ( image_set_a_set_a @ F @ A ) @ ( image_set_a_set_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_42_image__mono,axiom,
% 0.27/0.62 ! [A: set_set_set_a,B: set_set_set_a,F: set_set_a > a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ A @ B )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( image_set_set_a_a @ F @ A ) @ ( image_set_set_a_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_43_image__mono,axiom,
% 0.27/0.62 ! [A: set_set_a,B: set_set_a,F: set_a > set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.62 => ( ord_le2103863998_set_a @ ( image_1930509541_set_a @ F @ A ) @ ( image_1930509541_set_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_44_image__mono,axiom,
% 0.27/0.62 ! [A: set_set_set_a,B: set_set_set_a,F: set_set_a > set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ A @ B )
% 0.27/0.62 => ( ord_le318720350_set_a @ ( image_402591269_set_a @ F @ A ) @ ( image_402591269_set_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_45_image__mono,axiom,
% 0.27/0.62 ! [A: set_set_set_a,B: set_set_set_a,F: set_set_a > set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ A @ B )
% 0.27/0.62 => ( ord_le2103863998_set_a @ ( image_1956910981_set_a @ F @ A ) @ ( image_1956910981_set_a @ F @ B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_mono
% 0.27/0.62 thf(fact_46_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_set_a,F: set_a > a,B: set_a] :
% 0.27/0.62 ( ! [X2: set_a] :
% 0.27/0.62 ( ( member_set_a @ X2 @ A )
% 0.27/0.62 => ( member_a @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( image_set_a_a @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_47_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_set_a,F: set_a > set_a,B: set_set_a] :
% 0.27/0.62 ( ! [X2: set_a] :
% 0.27/0.62 ( ( member_set_a @ X2 @ A )
% 0.27/0.62 => ( member_set_a @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_le318720350_set_a @ ( image_set_a_set_a @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_48_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > a,B: set_a] :
% 0.27/0.62 ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.62 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.62 => ( member_a @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( image_2116492353_a_e_a @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_49_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_set_a,F: set_a > produc715398134_a_a_e,B: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ! [X2: set_a] :
% 0.27/0.62 ( ( member_set_a @ X2 @ A )
% 0.27/0.62 => ( member1258382221_a_a_e @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_le700723212_a_a_e @ ( image_210900495_a_a_e @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_50_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > set_a,B: set_set_a] :
% 0.27/0.62 ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.62 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.62 => ( member_set_a @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_le318720350_set_a @ ( image_64240033_set_a @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_51_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > produc715398134_a_a_e,B: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.62 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.62 => ( member1258382221_a_a_e @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_le700723212_a_a_e @ ( image_625620211_a_a_e @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_52_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_a,F: a > a,B: set_a] :
% 0.27/0.62 ( ! [X2: a] :
% 0.27/0.62 ( ( member_a @ X2 @ A )
% 0.27/0.62 => ( member_a @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( image_a_a @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_53_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_a,F: a > set_a,B: set_set_a] :
% 0.27/0.62 ( ! [X2: a] :
% 0.27/0.62 ( ( member_a @ X2 @ A )
% 0.27/0.62 => ( member_set_a @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_le318720350_set_a @ ( image_a_set_a @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_54_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_a,F: a > a > e,B: set_a_e] :
% 0.27/0.62 ( ! [X2: a] :
% 0.27/0.62 ( ( member_a @ X2 @ A )
% 0.27/0.62 => ( member_a_e @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_less_eq_set_a_e @ ( image_a_a_e @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_55_image__subsetI,axiom,
% 0.27/0.62 ! [A: set_a_e,F: ( a > e ) > a,B: set_a] :
% 0.27/0.62 ( ! [X2: a > e] :
% 0.27/0.62 ( ( member_a_e @ X2 @ A )
% 0.27/0.62 => ( member_a @ ( F @ X2 ) @ B ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( image_a_e_a @ F @ A ) @ B ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subsetI
% 0.27/0.62 thf(fact_56_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_a,F: a > a,A: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B @ ( image_a_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_a_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_57_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_set_a,F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_64240033_set_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_64240033_set_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_58_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_a,F: set_a > a,A: set_set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B @ ( image_set_a_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_set_a_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_59_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_set_a,F: a > set_a,A: set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_a_set_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_a_set_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_60_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_a,F: set_set_a > a,A: set_set_set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B @ ( image_set_set_a_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_set_set_a_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_61_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_set_a,F: set_a > set_a,A: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_set_a_set_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_set_a_set_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_62_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_set_set_a,F: a > set_set_a,A: set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B @ ( image_a_set_set_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_a_set_set_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_63_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_set_a,F: set_set_a > set_a,A: set_set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_402591269_set_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_402591269_set_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_64_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_set_set_a,F: set_a > set_set_a,A: set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B @ ( image_1930509541_set_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_1930509541_set_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_65_subset__imageE,axiom,
% 0.27/0.62 ! [B: set_set_set_a,F: set_set_a > set_set_a,A: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B @ ( image_1956910981_set_a @ F @ A ) )
% 0.27/0.62 => ~ ! [C: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ C @ A )
% 0.27/0.62 => ( B
% 0.27/0.62 != ( image_1956910981_set_a @ F @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_imageE
% 0.27/0.62 thf(fact_66_image__subset__iff,axiom,
% 0.27/0.62 ! [F: set_a > a,A: set_set_a,B: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ ( image_set_a_a @ F @ A ) @ B )
% 0.27/0.62 = ( ! [X4: set_a] :
% 0.27/0.62 ( ( member_set_a @ X4 @ A )
% 0.27/0.62 => ( member_a @ ( F @ X4 ) @ B ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subset_iff
% 0.27/0.62 thf(fact_67_image__subset__iff,axiom,
% 0.27/0.62 ! [F: a > a,A: set_a,B: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ ( image_a_a @ F @ A ) @ B )
% 0.27/0.62 = ( ! [X4: a] :
% 0.27/0.62 ( ( member_a @ X4 @ A )
% 0.27/0.62 => ( member_a @ ( F @ X4 ) @ B ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subset_iff
% 0.27/0.62 thf(fact_68_image__subset__iff,axiom,
% 0.27/0.62 ! [F: set_a > produc715398134_a_a_e,A: set_set_a,B: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ ( image_210900495_a_a_e @ F @ A ) @ B )
% 0.27/0.62 = ( ! [X4: set_a] :
% 0.27/0.62 ( ( member_set_a @ X4 @ A )
% 0.27/0.62 => ( member1258382221_a_a_e @ ( F @ X4 ) @ B ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subset_iff
% 0.27/0.62 thf(fact_69_image__subset__iff,axiom,
% 0.27/0.62 ! [F: set_a > set_a,A: set_set_a,B: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ ( image_set_a_set_a @ F @ A ) @ B )
% 0.27/0.62 = ( ! [X4: set_a] :
% 0.27/0.62 ( ( member_set_a @ X4 @ A )
% 0.27/0.62 => ( member_set_a @ ( F @ X4 ) @ B ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subset_iff
% 0.27/0.62 thf(fact_70_image__subset__iff,axiom,
% 0.27/0.62 ! [F: set_Pr204296108_a_a_e > set_set_a,A: set_se821189730_a_a_e,B: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ ( image_1441218763_set_a @ F @ A ) @ B )
% 0.27/0.62 = ( ! [X4: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( member1437121347_a_a_e @ X4 @ A )
% 0.27/0.62 => ( member_set_set_a @ ( F @ X4 ) @ B ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subset_iff
% 0.27/0.62 thf(fact_71_image__subset__iff,axiom,
% 0.27/0.62 ! [F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e,B: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ ( image_64240033_set_a @ F @ A ) @ B )
% 0.27/0.62 = ( ! [X4: produc715398134_a_a_e] :
% 0.27/0.62 ( ( member1258382221_a_a_e @ X4 @ A )
% 0.27/0.62 => ( member_set_a @ ( F @ X4 ) @ B ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % image_subset_iff
% 0.27/0.62 thf(fact_72_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_a,F: a > a,A: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B @ ( image_a_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_a_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_73_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_set_a,F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_64240033_set_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_64240033_set_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_74_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_a,F: set_a > a,A: set_set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B @ ( image_set_a_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_set_a_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_75_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_set_a,F: a > set_a,A: set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_a_set_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_a_set_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_76_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_a,F: set_set_a > a,A: set_set_set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B @ ( image_set_set_a_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_set_set_a_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_77_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_set_a,F: set_a > set_a,A: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_set_a_set_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_set_a_set_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_78_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_set_set_a,F: a > set_set_a,A: set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B @ ( image_a_set_set_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_a_set_set_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_79_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_set_a,F: set_set_a > set_a,A: set_set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B @ ( image_402591269_set_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_402591269_set_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_80_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_set_set_a,F: set_a > set_set_a,A: set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B @ ( image_1930509541_set_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_1930509541_set_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_81_subset__image__iff,axiom,
% 0.27/0.62 ! [B: set_set_set_a,F: set_set_a > set_set_a,A: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B @ ( image_1956910981_set_a @ F @ A ) )
% 0.27/0.62 = ( ? [AA: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ AA @ A )
% 0.27/0.62 & ( B
% 0.27/0.62 = ( image_1956910981_set_a @ F @ AA ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_image_iff
% 0.27/0.62 thf(fact_82_PairE__lemma,axiom,
% 0.27/0.62 ! [P: produc1965228714_set_a] :
% 0.27/0.62 ? [X2: a > e,Y: set_a] :
% 0.27/0.62 ( P
% 0.27/0.62 = ( produc479206876_set_a @ X2 @ Y ) ) ).
% 0.27/0.62
% 0.27/0.62 % PairE_lemma
% 0.27/0.62 thf(fact_83_PairE__lemma,axiom,
% 0.27/0.62 ! [P: produc715398134_a_a_e] :
% 0.27/0.62 ? [X2: set_a,Y: a > e] :
% 0.27/0.62 ( P
% 0.27/0.62 = ( produc1134456688_a_a_e @ X2 @ Y ) ) ).
% 0.27/0.62
% 0.27/0.62 % PairE_lemma
% 0.27/0.62 thf(fact_84_dual__order_Oantisym,axiom,
% 0.27/0.62 ! [B2: set_Pr204296108_a_a_e,A2: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_le700723212_a_a_e @ A2 @ B2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.antisym
% 0.27/0.62 thf(fact_85_dual__order_Oantisym,axiom,
% 0.27/0.62 ! [B2: set_set_a,A2: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.antisym
% 0.27/0.62 thf(fact_86_dual__order_Oantisym,axiom,
% 0.27/0.62 ! [B2: set_set_set_a,A2: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_le2103863998_set_a @ A2 @ B2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.antisym
% 0.27/0.62 thf(fact_87_dual__order_Oantisym,axiom,
% 0.27/0.62 ! [B2: $o > set_a,A2: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_less_eq_o_set_a @ A2 @ B2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.antisym
% 0.27/0.62 thf(fact_88_dual__order_Oantisym,axiom,
% 0.27/0.62 ! [B2: set_a,A2: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.antisym
% 0.27/0.62 thf(fact_89_dual__order_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_Pr204296108_a_a_e,Z: set_Pr204296108_a_a_e] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_Pr204296108_a_a_e,B3: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ B3 @ A3 )
% 0.27/0.62 & ( ord_le700723212_a_a_e @ A3 @ B3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.eq_iff
% 0.27/0.62 thf(fact_90_dual__order_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_set_a,Z: set_set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_set_a,B3: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B3 @ A3 )
% 0.27/0.62 & ( ord_le318720350_set_a @ A3 @ B3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.eq_iff
% 0.27/0.62 thf(fact_91_dual__order_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_set_set_a,Z: set_set_set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_set_set_a,B3: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B3 @ A3 )
% 0.27/0.62 & ( ord_le2103863998_set_a @ A3 @ B3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.eq_iff
% 0.27/0.62 thf(fact_92_dual__order_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: $o > set_a,Z: $o > set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: $o > set_a,B3: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ B3 @ A3 )
% 0.27/0.62 & ( ord_less_eq_o_set_a @ A3 @ B3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.eq_iff
% 0.27/0.62 thf(fact_93_dual__order_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_a,B3: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.27/0.62 & ( ord_less_eq_set_a @ A3 @ B3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.eq_iff
% 0.27/0.62 thf(fact_94_dual__order_Otrans,axiom,
% 0.27/0.62 ! [B2: set_Pr204296108_a_a_e,A2: set_Pr204296108_a_a_e,C2: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_le700723212_a_a_e @ C2 @ B2 )
% 0.27/0.62 => ( ord_le700723212_a_a_e @ C2 @ A2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.trans
% 0.27/0.62 thf(fact_95_dual__order_Otrans,axiom,
% 0.27/0.62 ! [B2: set_set_a,A2: set_set_a,C2: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_le318720350_set_a @ C2 @ B2 )
% 0.27/0.62 => ( ord_le318720350_set_a @ C2 @ A2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.trans
% 0.27/0.62 thf(fact_96_dual__order_Otrans,axiom,
% 0.27/0.62 ! [B2: set_set_set_a,A2: set_set_set_a,C2: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_le2103863998_set_a @ C2 @ B2 )
% 0.27/0.62 => ( ord_le2103863998_set_a @ C2 @ A2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.trans
% 0.27/0.62 thf(fact_97_dual__order_Otrans,axiom,
% 0.27/0.62 ! [B2: $o > set_a,A2: $o > set_a,C2: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_less_eq_o_set_a @ C2 @ B2 )
% 0.27/0.62 => ( ord_less_eq_o_set_a @ C2 @ A2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.trans
% 0.27/0.62 thf(fact_98_dual__order_Otrans,axiom,
% 0.27/0.62 ! [B2: set_a,A2: set_a,C2: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ C2 @ B2 )
% 0.27/0.62 => ( ord_less_eq_set_a @ C2 @ A2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.trans
% 0.27/0.62 thf(fact_99_dual__order_Orefl,axiom,
% 0.27/0.62 ! [A2: set_Pr204296108_a_a_e] : ( ord_le700723212_a_a_e @ A2 @ A2 ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.refl
% 0.27/0.62 thf(fact_100_dual__order_Orefl,axiom,
% 0.27/0.62 ! [A2: set_set_a] : ( ord_le318720350_set_a @ A2 @ A2 ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.refl
% 0.27/0.62 thf(fact_101_dual__order_Orefl,axiom,
% 0.27/0.62 ! [A2: set_set_set_a] : ( ord_le2103863998_set_a @ A2 @ A2 ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.refl
% 0.27/0.62 thf(fact_102_dual__order_Orefl,axiom,
% 0.27/0.62 ! [A2: $o > set_a] : ( ord_less_eq_o_set_a @ A2 @ A2 ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.refl
% 0.27/0.62 thf(fact_103_dual__order_Orefl,axiom,
% 0.27/0.62 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.refl
% 0.27/0.62 thf(fact_104_order__trans,axiom,
% 0.27/0.62 ! [X3: set_Pr204296108_a_a_e,Y3: set_Pr204296108_a_a_e,Z2: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ X3 @ Y3 )
% 0.27/0.62 => ( ( ord_le700723212_a_a_e @ Y3 @ Z2 )
% 0.27/0.62 => ( ord_le700723212_a_a_e @ X3 @ Z2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_trans
% 0.27/0.62 thf(fact_105_order__trans,axiom,
% 0.27/0.62 ! [X3: set_set_a,Y3: set_set_a,Z2: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ X3 @ Y3 )
% 0.27/0.62 => ( ( ord_le318720350_set_a @ Y3 @ Z2 )
% 0.27/0.62 => ( ord_le318720350_set_a @ X3 @ Z2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_trans
% 0.27/0.62 thf(fact_106_order__trans,axiom,
% 0.27/0.62 ! [X3: set_set_set_a,Y3: set_set_set_a,Z2: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ X3 @ Y3 )
% 0.27/0.62 => ( ( ord_le2103863998_set_a @ Y3 @ Z2 )
% 0.27/0.62 => ( ord_le2103863998_set_a @ X3 @ Z2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_trans
% 0.27/0.62 thf(fact_107_order__trans,axiom,
% 0.27/0.62 ! [X3: $o > set_a,Y3: $o > set_a,Z2: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ X3 @ Y3 )
% 0.27/0.62 => ( ( ord_less_eq_o_set_a @ Y3 @ Z2 )
% 0.27/0.62 => ( ord_less_eq_o_set_a @ X3 @ Z2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_trans
% 0.27/0.62 thf(fact_108_order__trans,axiom,
% 0.27/0.62 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 0.27/0.62 => ( ord_less_eq_set_a @ X3 @ Z2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_trans
% 0.27/0.62 thf(fact_109_order__class_Oorder_Oantisym,axiom,
% 0.27/0.62 ! [A2: set_Pr204296108_a_a_e,B2: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ A2 @ B2 )
% 0.27/0.62 => ( ( ord_le700723212_a_a_e @ B2 @ A2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.antisym
% 0.27/0.62 thf(fact_110_order__class_Oorder_Oantisym,axiom,
% 0.27/0.62 ! [A2: set_set_a,B2: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( ord_le318720350_set_a @ B2 @ A2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.antisym
% 0.27/0.62 thf(fact_111_order__class_Oorder_Oantisym,axiom,
% 0.27/0.62 ! [A2: set_set_set_a,B2: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( ord_le2103863998_set_a @ B2 @ A2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.antisym
% 0.27/0.62 thf(fact_112_order__class_Oorder_Oantisym,axiom,
% 0.27/0.62 ! [A2: $o > set_a,B2: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( ord_less_eq_o_set_a @ B2 @ A2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.antisym
% 0.27/0.62 thf(fact_113_order__class_Oorder_Oantisym,axiom,
% 0.27/0.62 ! [A2: set_a,B2: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.62 => ( A2 = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.antisym
% 0.27/0.62 thf(fact_114_ord__le__eq__trans,axiom,
% 0.27/0.62 ! [A2: set_Pr204296108_a_a_e,B2: set_Pr204296108_a_a_e,C2: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ A2 @ B2 )
% 0.27/0.62 => ( ( B2 = C2 )
% 0.27/0.62 => ( ord_le700723212_a_a_e @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_trans
% 0.27/0.62 thf(fact_115_ord__le__eq__trans,axiom,
% 0.27/0.62 ! [A2: set_set_a,B2: set_set_a,C2: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( B2 = C2 )
% 0.27/0.62 => ( ord_le318720350_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_trans
% 0.27/0.62 thf(fact_116_ord__le__eq__trans,axiom,
% 0.27/0.62 ! [A2: set_set_set_a,B2: set_set_set_a,C2: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( B2 = C2 )
% 0.27/0.62 => ( ord_le2103863998_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_trans
% 0.27/0.62 thf(fact_117_ord__le__eq__trans,axiom,
% 0.27/0.62 ! [A2: $o > set_a,B2: $o > set_a,C2: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( B2 = C2 )
% 0.27/0.62 => ( ord_less_eq_o_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_trans
% 0.27/0.62 thf(fact_118_ord__le__eq__trans,axiom,
% 0.27/0.62 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.62 => ( ( B2 = C2 )
% 0.27/0.62 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_trans
% 0.27/0.62 thf(fact_119_ord__eq__le__trans,axiom,
% 0.27/0.62 ! [A2: set_Pr204296108_a_a_e,B2: set_Pr204296108_a_a_e,C2: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( A2 = B2 )
% 0.27/0.62 => ( ( ord_le700723212_a_a_e @ B2 @ C2 )
% 0.27/0.62 => ( ord_le700723212_a_a_e @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_trans
% 0.27/0.62 thf(fact_120_ord__eq__le__trans,axiom,
% 0.27/0.62 ! [A2: set_set_a,B2: set_set_a,C2: set_set_a] :
% 0.27/0.62 ( ( A2 = B2 )
% 0.27/0.62 => ( ( ord_le318720350_set_a @ B2 @ C2 )
% 0.27/0.62 => ( ord_le318720350_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_trans
% 0.27/0.62 thf(fact_121_ord__eq__le__trans,axiom,
% 0.27/0.62 ! [A2: set_set_set_a,B2: set_set_set_a,C2: set_set_set_a] :
% 0.27/0.62 ( ( A2 = B2 )
% 0.27/0.62 => ( ( ord_le2103863998_set_a @ B2 @ C2 )
% 0.27/0.62 => ( ord_le2103863998_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_trans
% 0.27/0.62 thf(fact_122_ord__eq__le__trans,axiom,
% 0.27/0.62 ! [A2: $o > set_a,B2: $o > set_a,C2: $o > set_a] :
% 0.27/0.62 ( ( A2 = B2 )
% 0.27/0.62 => ( ( ord_less_eq_o_set_a @ B2 @ C2 )
% 0.27/0.62 => ( ord_less_eq_o_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_trans
% 0.27/0.62 thf(fact_123_ord__eq__le__trans,axiom,
% 0.27/0.62 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.27/0.62 ( ( A2 = B2 )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.27/0.62 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_trans
% 0.27/0.62 thf(fact_124_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_Pr204296108_a_a_e,Z: set_Pr204296108_a_a_e] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_Pr204296108_a_a_e,B3: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ A3 @ B3 )
% 0.27/0.62 & ( ord_le700723212_a_a_e @ B3 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.eq_iff
% 0.27/0.62 thf(fact_125_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_set_a,Z: set_set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_set_a,B3: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ A3 @ B3 )
% 0.27/0.62 & ( ord_le318720350_set_a @ B3 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.eq_iff
% 0.27/0.62 thf(fact_126_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_set_set_a,Z: set_set_set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_set_set_a,B3: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ A3 @ B3 )
% 0.27/0.62 & ( ord_le2103863998_set_a @ B3 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.eq_iff
% 0.27/0.62 thf(fact_127_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: $o > set_a,Z: $o > set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: $o > set_a,B3: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ A3 @ B3 )
% 0.27/0.62 & ( ord_less_eq_o_set_a @ B3 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.eq_iff
% 0.27/0.62 thf(fact_128_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.62 = ( ^ [A3: set_a,B3: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.62 & ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.eq_iff
% 0.27/0.62 thf(fact_129_antisym__conv,axiom,
% 0.27/0.62 ! [Y3: set_Pr204296108_a_a_e,X3: set_Pr204296108_a_a_e] :
% 0.27/0.62 ( ( ord_le700723212_a_a_e @ Y3 @ X3 )
% 0.27/0.62 => ( ( ord_le700723212_a_a_e @ X3 @ Y3 )
% 0.27/0.62 = ( X3 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym_conv
% 0.27/0.62 thf(fact_130_antisym__conv,axiom,
% 0.27/0.62 ! [Y3: set_set_a,X3: set_set_a] :
% 0.27/0.62 ( ( ord_le318720350_set_a @ Y3 @ X3 )
% 0.27/0.62 => ( ( ord_le318720350_set_a @ X3 @ Y3 )
% 0.27/0.62 = ( X3 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym_conv
% 0.27/0.62 thf(fact_131_antisym__conv,axiom,
% 0.27/0.62 ! [Y3: set_set_set_a,X3: set_set_set_a] :
% 0.27/0.62 ( ( ord_le2103863998_set_a @ Y3 @ X3 )
% 0.27/0.62 => ( ( ord_le2103863998_set_a @ X3 @ Y3 )
% 0.27/0.62 = ( X3 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym_conv
% 0.27/0.62 thf(fact_132_antisym__conv,axiom,
% 0.27/0.62 ! [Y3: $o > set_a,X3: $o > set_a] :
% 0.27/0.62 ( ( ord_less_eq_o_set_a @ Y3 @ X3 )
% 0.27/0.62 => ( ( ord_less_eq_o_set_a @ X3 @ Y3 )
% 0.27/0.62 = ( X3 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym_conv
% 0.27/0.62 thf(fact_133_antisym__conv,axiom,
% 0.27/0.62 ! [Y3: set_a,X3: set_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 0.27/0.62 => ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.27/0.62 = ( X3 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym_conv
% 0.27/0.62 thf(fact_134_order_Otrans,axiom,
% 0.27/0.62 ! [A2: set_Pr204296108_a_a_e,B2: set_Pr204296108_a_a_e,C2: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( ord_le700723212_a_a_e @ A2 @ B2 )
% 0.27/0.63 => ( ( ord_le700723212_a_a_e @ B2 @ C2 )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ A2 @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order.trans
% 0.27/0.63 thf(fact_135_order_Otrans,axiom,
% 0.27/0.63 ! [A2: set_set_a,B2: set_set_a,C2: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ord_le318720350_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ord_le318720350_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order.trans
% 0.27/0.63 thf(fact_136_order_Otrans,axiom,
% 0.27/0.63 ! [A2: set_set_set_a,B2: set_set_set_a,C2: set_set_set_a] :
% 0.27/0.63 ( ( ord_le2103863998_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ord_le2103863998_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ord_le2103863998_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order.trans
% 0.27/0.63 thf(fact_137_order_Otrans,axiom,
% 0.27/0.63 ! [A2: $o > set_a,B2: $o > set_a,C2: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ord_less_eq_o_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order.trans
% 0.27/0.63 thf(fact_138_order_Otrans,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order.trans
% 0.27/0.63 thf(fact_139_eq__refl,axiom,
% 0.27/0.63 ! [X3: set_Pr204296108_a_a_e,Y3: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( X3 = Y3 )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ X3 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_refl
% 0.27/0.63 thf(fact_140_eq__refl,axiom,
% 0.27/0.63 ! [X3: set_set_a,Y3: set_set_a] :
% 0.27/0.63 ( ( X3 = Y3 )
% 0.27/0.63 => ( ord_le318720350_set_a @ X3 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_refl
% 0.27/0.63 thf(fact_141_eq__refl,axiom,
% 0.27/0.63 ! [X3: set_set_set_a,Y3: set_set_set_a] :
% 0.27/0.63 ( ( X3 = Y3 )
% 0.27/0.63 => ( ord_le2103863998_set_a @ X3 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_refl
% 0.27/0.63 thf(fact_142_eq__refl,axiom,
% 0.27/0.63 ! [X3: $o > set_a,Y3: $o > set_a] :
% 0.27/0.63 ( ( X3 = Y3 )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ X3 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_refl
% 0.27/0.63 thf(fact_143_eq__refl,axiom,
% 0.27/0.63 ! [X3: set_a,Y3: set_a] :
% 0.27/0.63 ( ( X3 = Y3 )
% 0.27/0.63 => ( ord_less_eq_set_a @ X3 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_refl
% 0.27/0.63 thf(fact_144_antisym,axiom,
% 0.27/0.63 ! [X3: set_Pr204296108_a_a_e,Y3: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( ord_le700723212_a_a_e @ X3 @ Y3 )
% 0.27/0.63 => ( ( ord_le700723212_a_a_e @ Y3 @ X3 )
% 0.27/0.63 => ( X3 = Y3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % antisym
% 0.27/0.63 thf(fact_145_antisym,axiom,
% 0.27/0.63 ! [X3: set_set_a,Y3: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ X3 @ Y3 )
% 0.27/0.63 => ( ( ord_le318720350_set_a @ Y3 @ X3 )
% 0.27/0.63 => ( X3 = Y3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % antisym
% 0.27/0.63 thf(fact_146_antisym,axiom,
% 0.27/0.63 ! [X3: set_set_set_a,Y3: set_set_set_a] :
% 0.27/0.63 ( ( ord_le2103863998_set_a @ X3 @ Y3 )
% 0.27/0.63 => ( ( ord_le2103863998_set_a @ Y3 @ X3 )
% 0.27/0.63 => ( X3 = Y3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % antisym
% 0.27/0.63 thf(fact_147_antisym,axiom,
% 0.27/0.63 ! [X3: $o > set_a,Y3: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ X3 @ Y3 )
% 0.27/0.63 => ( ( ord_less_eq_o_set_a @ Y3 @ X3 )
% 0.27/0.63 => ( X3 = Y3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % antisym
% 0.27/0.63 thf(fact_148_antisym,axiom,
% 0.27/0.63 ! [X3: set_a,Y3: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 0.27/0.63 => ( X3 = Y3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % antisym
% 0.27/0.63 thf(fact_149_eq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y2: set_Pr204296108_a_a_e,Z: set_Pr204296108_a_a_e] : ( Y2 = Z ) )
% 0.27/0.63 = ( ^ [X4: set_Pr204296108_a_a_e,Y4: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( ord_le700723212_a_a_e @ X4 @ Y4 )
% 0.27/0.63 & ( ord_le700723212_a_a_e @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_iff
% 0.27/0.63 thf(fact_150_eq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y2: set_set_a,Z: set_set_a] : ( Y2 = Z ) )
% 0.27/0.63 = ( ^ [X4: set_set_a,Y4: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ X4 @ Y4 )
% 0.27/0.63 & ( ord_le318720350_set_a @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_iff
% 0.27/0.63 thf(fact_151_eq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y2: set_set_set_a,Z: set_set_set_a] : ( Y2 = Z ) )
% 0.27/0.63 = ( ^ [X4: set_set_set_a,Y4: set_set_set_a] :
% 0.27/0.63 ( ( ord_le2103863998_set_a @ X4 @ Y4 )
% 0.27/0.63 & ( ord_le2103863998_set_a @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_iff
% 0.27/0.63 thf(fact_152_eq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y2: $o > set_a,Z: $o > set_a] : ( Y2 = Z ) )
% 0.27/0.63 = ( ^ [X4: $o > set_a,Y4: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ X4 @ Y4 )
% 0.27/0.63 & ( ord_less_eq_o_set_a @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_iff
% 0.27/0.63 thf(fact_153_eq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.63 = ( ^ [X4: set_a,Y4: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X4 @ Y4 )
% 0.27/0.63 & ( ord_less_eq_set_a @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_iff
% 0.27/0.63 thf(fact_154_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_a,Y: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_155_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,F: set_a > set_set_a,C2: set_set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_a,Y: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_le318720350_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_le318720350_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_156_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_set_a,B2: set_set_a,F: set_set_a > set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_set_a,Y: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_157_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,F: set_a > set_set_set_a,C2: set_set_set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_a,Y: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_le2103863998_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_le2103863998_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_158_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,F: set_a > $o > set_a,C2: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_a,Y: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_159_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_set_a,B2: set_set_a,F: set_set_a > set_set_a,C2: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_set_a,Y: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_le318720350_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_le318720350_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_160_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_set_set_a,B2: set_set_set_a,F: set_set_set_a > set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_le2103863998_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_set_set_a,Y: set_set_set_a] :
% 0.27/0.63 ( ( ord_le2103863998_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_161_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: $o > set_a,B2: $o > set_a,F: ( $o > set_a ) > set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: $o > set_a,Y: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_162_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_set_a,B2: set_set_a,F: set_set_a > set_set_set_a,C2: set_set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_set_a,Y: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_le2103863998_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_le2103863998_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_163_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A2: set_set_a,B2: set_set_a,F: set_set_a > $o > set_a,C2: $o > set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ( F @ B2 )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X2: set_set_a,Y: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_164_ord__eq__le__subst,axiom,
% 0.27/0.63 ! [A2: set_Pr204296108_a_a_e,F: ( $o > set_a ) > set_Pr204296108_a_a_e,B2: $o > set_a,C2: $o > set_a] :
% 0.27/0.63 ( ( A2
% 0.27/0.63 = ( F @ B2 ) )
% 0.27/0.63 => ( ( ord_less_eq_o_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ! [X2: $o > set_a,Y: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_eq_le_subst
% 0.27/0.63 thf(fact_165_ord__eq__le__subst,axiom,
% 0.27/0.63 ! [A2: set_set_a,F: ( $o > set_a ) > set_set_a,B2: $o > set_a,C2: $o > set_a] :
% 0.27/0.63 ( ( A2
% 0.27/0.63 = ( F @ B2 ) )
% 0.27/0.63 => ( ( ord_less_eq_o_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ! [X2: $o > set_a,Y: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_le318720350_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_le318720350_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_eq_le_subst
% 0.27/0.63 thf(fact_166_ord__eq__le__subst,axiom,
% 0.27/0.63 ! [A2: set_set_set_a,F: ( $o > set_a ) > set_set_set_a,B2: $o > set_a,C2: $o > set_a] :
% 0.27/0.63 ( ( A2
% 0.27/0.63 = ( F @ B2 ) )
% 0.27/0.63 => ( ( ord_less_eq_o_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ! [X2: $o > set_a,Y: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_le2103863998_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_le2103863998_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_eq_le_subst
% 0.27/0.63 thf(fact_167_ord__eq__le__subst,axiom,
% 0.27/0.63 ! [A2: $o > set_a,F: ( $o > set_a ) > $o > set_a,B2: $o > set_a,C2: $o > set_a] :
% 0.27/0.63 ( ( A2
% 0.27/0.63 = ( F @ B2 ) )
% 0.27/0.63 => ( ( ord_less_eq_o_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ! [X2: $o > set_a,Y: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_o_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_o_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_eq_le_subst
% 0.27/0.63 thf(fact_168_ord__eq__le__subst,axiom,
% 0.27/0.63 ! [A2: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
% 0.27/0.63 ( ( A2
% 0.27/0.63 = ( F @ B2 ) )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ! [X2: set_a,Y: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_eq_le_subst
% 0.27/0.63 thf(fact_169_order__subst2,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
% 0.27/0.63 => ( ! [X2: set_a,Y: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order_subst2
% 0.27/0.63 thf(fact_170_order__subst1,axiom,
% 0.27/0.63 ! [A2: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.27/0.63 => ( ! [X2: set_a,Y: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ X2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y ) ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order_subst1
% 0.27/0.63 thf(fact_171_mem__Collect__eq,axiom,
% 0.27/0.63 ! [A2: set_a,P2: set_a > $o] :
% 0.27/0.63 ( ( member_set_a @ A2 @ ( collect_set_a @ P2 ) )
% 0.27/0.63 = ( P2 @ A2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_Collect_eq
% 0.27/0.63 thf(fact_172_mem__Collect__eq,axiom,
% 0.27/0.63 ! [A2: produc715398134_a_a_e,P2: produc715398134_a_a_e > $o] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ A2 @ ( collec1369693387_a_a_e @ P2 ) )
% 0.27/0.63 = ( P2 @ A2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_Collect_eq
% 0.27/0.63 thf(fact_173_Collect__mem__eq,axiom,
% 0.27/0.63 ! [A: set_set_a] :
% 0.27/0.63 ( ( collect_set_a
% 0.27/0.63 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A ) )
% 0.27/0.63 = A ) ).
% 0.27/0.63
% 0.27/0.63 % Collect_mem_eq
% 0.27/0.63 thf(fact_174_Collect__mem__eq,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( collec1369693387_a_a_e
% 0.27/0.63 @ ^ [X4: produc715398134_a_a_e] : ( member1258382221_a_a_e @ X4 @ A ) )
% 0.27/0.63 = A ) ).
% 0.27/0.63
% 0.27/0.63 % Collect_mem_eq
% 0.27/0.63 thf(fact_175_rev__image__eqI,axiom,
% 0.27/0.63 ! [X3: set_a,A: set_set_a,B2: set_a,F: set_a > set_a] :
% 0.27/0.63 ( ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( ( B2
% 0.27/0.63 = ( F @ X3 ) )
% 0.27/0.63 => ( member_set_a @ B2 @ ( image_set_a_set_a @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % rev_image_eqI
% 0.27/0.63 thf(fact_176_rev__image__eqI,axiom,
% 0.27/0.63 ! [X3: set_a,A: set_set_a,B2: produc715398134_a_a_e,F: set_a > produc715398134_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( ( B2
% 0.27/0.63 = ( F @ X3 ) )
% 0.27/0.63 => ( member1258382221_a_a_e @ B2 @ ( image_210900495_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % rev_image_eqI
% 0.27/0.63 thf(fact_177_rev__image__eqI,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e,A: set_Pr204296108_a_a_e,B2: set_a,F: produc715398134_a_a_e > set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( ( B2
% 0.27/0.63 = ( F @ X3 ) )
% 0.27/0.63 => ( member_set_a @ B2 @ ( image_64240033_set_a @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % rev_image_eqI
% 0.27/0.63 thf(fact_178_rev__image__eqI,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e,A: set_Pr204296108_a_a_e,B2: produc715398134_a_a_e,F: produc715398134_a_a_e > produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( ( B2
% 0.27/0.63 = ( F @ X3 ) )
% 0.27/0.63 => ( member1258382221_a_a_e @ B2 @ ( image_625620211_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % rev_image_eqI
% 0.27/0.63 thf(fact_179_ball__imageD,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e,P2: set_a > $o] :
% 0.27/0.63 ( ! [X2: set_a] :
% 0.27/0.63 ( ( member_set_a @ X2 @ ( image_64240033_set_a @ F @ A ) )
% 0.27/0.63 => ( P2 @ X2 ) )
% 0.27/0.63 => ! [X: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X @ A )
% 0.27/0.63 => ( P2 @ ( F @ X ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ball_imageD
% 0.27/0.63 thf(fact_180_image__cong,axiom,
% 0.27/0.63 ! [M: set_Pr204296108_a_a_e,N: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > set_a,G: produc715398134_a_a_e > set_a] :
% 0.27/0.63 ( ( M = N )
% 0.27/0.63 => ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ N )
% 0.27/0.63 => ( ( F @ X2 )
% 0.27/0.63 = ( G @ X2 ) ) )
% 0.27/0.63 => ( ( image_64240033_set_a @ F @ M )
% 0.27/0.63 = ( image_64240033_set_a @ G @ N ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % image_cong
% 0.27/0.63 thf(fact_181_bex__imageD,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e,P2: set_a > $o] :
% 0.27/0.63 ( ? [X: set_a] :
% 0.27/0.63 ( ( member_set_a @ X @ ( image_64240033_set_a @ F @ A ) )
% 0.27/0.63 & ( P2 @ X ) )
% 0.27/0.63 => ? [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.63 & ( P2 @ ( F @ X2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % bex_imageD
% 0.27/0.63 thf(fact_182_image__iff,axiom,
% 0.27/0.63 ! [Z2: set_a,F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ Z2 @ ( image_64240033_set_a @ F @ A ) )
% 0.27/0.63 = ( ? [X4: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X4 @ A )
% 0.27/0.63 & ( Z2
% 0.27/0.63 = ( F @ X4 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % image_iff
% 0.27/0.63 thf(fact_183_imageI,axiom,
% 0.27/0.63 ! [X3: set_a,A: set_set_a,F: set_a > set_a] :
% 0.27/0.63 ( ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ X3 ) @ ( image_set_a_set_a @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % imageI
% 0.27/0.63 thf(fact_184_imageI,axiom,
% 0.27/0.63 ! [X3: set_a,A: set_set_a,F: set_a > produc715398134_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ X3 ) @ ( image_210900495_a_a_e @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % imageI
% 0.27/0.63 thf(fact_185_imageI,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e,A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ X3 ) @ ( image_64240033_set_a @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % imageI
% 0.27/0.63 thf(fact_186_imageI,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e,A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ X3 ) @ ( image_625620211_a_a_e @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % imageI
% 0.27/0.63 thf(fact_187_Collect__mono__iff,axiom,
% 0.27/0.63 ! [P2: a > $o,Q: a > $o] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ ( collect_a @ P2 ) @ ( collect_a @ Q ) )
% 0.27/0.63 = ( ! [X4: a] :
% 0.27/0.63 ( ( P2 @ X4 )
% 0.27/0.63 => ( Q @ X4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Collect_mono_iff
% 0.27/0.63 thf(fact_188_set__eq__subset,axiom,
% 0.27/0.63 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.63 = ( ^ [A4: set_a,B4: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A4 @ B4 )
% 0.27/0.63 & ( ord_less_eq_set_a @ B4 @ A4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % set_eq_subset
% 0.27/0.63 thf(fact_189_subset__trans,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a,C3: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ B @ C3 )
% 0.27/0.63 => ( ord_less_eq_set_a @ A @ C3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_trans
% 0.27/0.63 thf(fact_190_Collect__mono,axiom,
% 0.27/0.63 ! [P2: a > $o,Q: a > $o] :
% 0.27/0.63 ( ! [X2: a] :
% 0.27/0.63 ( ( P2 @ X2 )
% 0.27/0.63 => ( Q @ X2 ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ ( collect_a @ P2 ) @ ( collect_a @ Q ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Collect_mono
% 0.27/0.63 thf(fact_191_subset__iff,axiom,
% 0.27/0.63 ( ord_le318720350_set_a
% 0.27/0.63 = ( ^ [A4: set_set_a,B4: set_set_a] :
% 0.27/0.63 ! [T: set_a] :
% 0.27/0.63 ( ( member_set_a @ T @ A4 )
% 0.27/0.63 => ( member_set_a @ T @ B4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_iff
% 0.27/0.63 thf(fact_192_subset__iff,axiom,
% 0.27/0.63 ( ord_le700723212_a_a_e
% 0.27/0.63 = ( ^ [A4: set_Pr204296108_a_a_e,B4: set_Pr204296108_a_a_e] :
% 0.27/0.63 ! [T: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ T @ A4 )
% 0.27/0.63 => ( member1258382221_a_a_e @ T @ B4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_iff
% 0.27/0.63 thf(fact_193_subset__iff,axiom,
% 0.27/0.63 ( ord_less_eq_set_a
% 0.27/0.63 = ( ^ [A4: set_a,B4: set_a] :
% 0.27/0.63 ! [T: a] :
% 0.27/0.63 ( ( member_a @ T @ A4 )
% 0.27/0.63 => ( member_a @ T @ B4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_iff
% 0.27/0.63 thf(fact_194_equalityD2,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( A = B )
% 0.27/0.63 => ( ord_less_eq_set_a @ B @ A ) ) ).
% 0.27/0.63
% 0.27/0.63 % equalityD2
% 0.27/0.63 thf(fact_195_subset__eq,axiom,
% 0.27/0.63 ( ord_le318720350_set_a
% 0.27/0.63 = ( ^ [A4: set_set_a,B4: set_set_a] :
% 0.27/0.63 ! [X4: set_a] :
% 0.27/0.63 ( ( member_set_a @ X4 @ A4 )
% 0.27/0.63 => ( member_set_a @ X4 @ B4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_eq
% 0.27/0.63 thf(fact_196_subset__eq,axiom,
% 0.27/0.63 ( ord_le700723212_a_a_e
% 0.27/0.63 = ( ^ [A4: set_Pr204296108_a_a_e,B4: set_Pr204296108_a_a_e] :
% 0.27/0.63 ! [X4: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X4 @ A4 )
% 0.27/0.63 => ( member1258382221_a_a_e @ X4 @ B4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_eq
% 0.27/0.63 thf(fact_197_subset__eq,axiom,
% 0.27/0.63 ( ord_less_eq_set_a
% 0.27/0.63 = ( ^ [A4: set_a,B4: set_a] :
% 0.27/0.63 ! [X4: a] :
% 0.27/0.63 ( ( member_a @ X4 @ A4 )
% 0.27/0.63 => ( member_a @ X4 @ B4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_eq
% 0.27/0.63 thf(fact_198_equalityE,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( A = B )
% 0.27/0.63 => ~ ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ~ ( ord_less_eq_set_a @ B @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % equalityE
% 0.27/0.63 thf(fact_199_subsetD,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a,C2: set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.63 => ( ( member_set_a @ C2 @ A )
% 0.27/0.63 => ( member_set_a @ C2 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subsetD
% 0.27/0.63 thf(fact_200_subsetD,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.63 => ( ( member1258382221_a_a_e @ C2 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ C2 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subsetD
% 0.27/0.63 thf(fact_201_subsetD,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a,C2: a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ( ( member_a @ C2 @ A )
% 0.27/0.63 => ( member_a @ C2 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subsetD
% 0.27/0.63 thf(fact_202_in__mono,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a,X3: set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.63 => ( ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( member_set_a @ X3 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_mono
% 0.27/0.63 thf(fact_203_in__mono,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,X3: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.63 => ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ X3 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_mono
% 0.27/0.63 thf(fact_204_in__mono,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a,X3: a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ( ( member_a @ X3 @ A )
% 0.27/0.63 => ( member_a @ X3 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_mono
% 0.27/0.63 thf(fact_205_prod_Oinject,axiom,
% 0.27/0.63 ! [X1: set_a,X22: a > e,Y1: set_a,Y22: a > e] :
% 0.27/0.63 ( ( ( produc1134456688_a_a_e @ X1 @ X22 )
% 0.27/0.63 = ( produc1134456688_a_a_e @ Y1 @ Y22 ) )
% 0.27/0.63 = ( ( X1 = Y1 )
% 0.27/0.63 & ( X22 = Y22 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod.inject
% 0.27/0.63 thf(fact_206_old_Oprod_Oinject,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,A5: set_a,B5: a > e] :
% 0.27/0.63 ( ( ( produc1134456688_a_a_e @ A2 @ B2 )
% 0.27/0.63 = ( produc1134456688_a_a_e @ A5 @ B5 ) )
% 0.27/0.63 = ( ( A2 = A5 )
% 0.27/0.63 & ( B2 = B5 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.inject
% 0.27/0.63 thf(fact_207_eq__fst__iff,axiom,
% 0.27/0.63 ! [A2: set_a,P: produc715398134_a_a_e] :
% 0.27/0.63 ( ( A2
% 0.27/0.63 = ( produc1040928388_a_a_e @ P ) )
% 0.27/0.63 = ( ? [B3: a > e] :
% 0.27/0.63 ( P
% 0.27/0.63 = ( produc1134456688_a_a_e @ A2 @ B3 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_fst_iff
% 0.27/0.63 thf(fact_208_fst__conv,axiom,
% 0.27/0.63 ! [X1: set_a,X22: a > e] :
% 0.27/0.63 ( ( produc1040928388_a_a_e @ ( produc1134456688_a_a_e @ X1 @ X22 ) )
% 0.27/0.63 = X1 ) ).
% 0.27/0.63
% 0.27/0.63 % fst_conv
% 0.27/0.63 thf(fact_209_fst__eqD,axiom,
% 0.27/0.63 ! [X3: set_a,Y3: a > e,A2: set_a] :
% 0.27/0.63 ( ( ( produc1040928388_a_a_e @ ( produc1134456688_a_a_e @ X3 @ Y3 ) )
% 0.27/0.63 = A2 )
% 0.27/0.63 => ( X3 = A2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % fst_eqD
% 0.27/0.63 thf(fact_210_fstI,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e,Y3: set_a,Z2: a > e] :
% 0.27/0.63 ( ( X3
% 0.27/0.63 = ( produc1134456688_a_a_e @ Y3 @ Z2 ) )
% 0.27/0.63 => ( ( produc1040928388_a_a_e @ X3 )
% 0.27/0.63 = Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % fstI
% 0.27/0.63 thf(fact_211_all__subset__image,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e,P2: set_set_a > $o] :
% 0.27/0.63 ( ( ! [B4: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ B4 @ ( image_64240033_set_a @ F @ A ) )
% 0.27/0.63 => ( P2 @ B4 ) ) )
% 0.27/0.63 = ( ! [B4: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( ord_le700723212_a_a_e @ B4 @ A )
% 0.27/0.63 => ( P2 @ ( image_64240033_set_a @ F @ B4 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % all_subset_image
% 0.27/0.63 thf(fact_212_all__subset__image,axiom,
% 0.27/0.63 ! [F: a > a,A: set_a,P2: set_a > $o] :
% 0.27/0.63 ( ( ! [B4: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ B4 @ ( image_a_a @ F @ A ) )
% 0.27/0.63 => ( P2 @ B4 ) ) )
% 0.27/0.63 = ( ! [B4: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ B4 @ A )
% 0.27/0.63 => ( P2 @ ( image_a_a @ F @ B4 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % all_subset_image
% 0.27/0.63 thf(fact_213_Greatest__equality,axiom,
% 0.27/0.63 ! [P2: set_a > $o,X3: set_a] :
% 0.27/0.63 ( ( P2 @ X3 )
% 0.27/0.63 => ( ! [Y: set_a] :
% 0.27/0.63 ( ( P2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ Y @ X3 ) )
% 0.27/0.63 => ( ( order_Greatest_set_a @ P2 )
% 0.27/0.63 = X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Greatest_equality
% 0.27/0.63 thf(fact_214_GreatestI2__order,axiom,
% 0.27/0.63 ! [P2: set_a > $o,X3: set_a,Q: set_a > $o] :
% 0.27/0.63 ( ( P2 @ X3 )
% 0.27/0.63 => ( ! [Y: set_a] :
% 0.27/0.63 ( ( P2 @ Y )
% 0.27/0.63 => ( ord_less_eq_set_a @ Y @ X3 ) )
% 0.27/0.63 => ( ! [X2: set_a] :
% 0.27/0.63 ( ( P2 @ X2 )
% 0.27/0.63 => ( ! [Y5: set_a] :
% 0.27/0.63 ( ( P2 @ Y5 )
% 0.27/0.63 => ( ord_less_eq_set_a @ Y5 @ X2 ) )
% 0.27/0.63 => ( Q @ X2 ) ) )
% 0.27/0.63 => ( Q @ ( order_Greatest_set_a @ P2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % GreatestI2_order
% 0.27/0.63 thf(fact_215_old_Oprod_Oinducts,axiom,
% 0.27/0.63 ! [P2: produc715398134_a_a_e > $o,Prod: produc715398134_a_a_e] :
% 0.27/0.63 ( ! [A6: set_a,B6: a > e] : ( P2 @ ( produc1134456688_a_a_e @ A6 @ B6 ) )
% 0.27/0.63 => ( P2 @ Prod ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.inducts
% 0.27/0.63 thf(fact_216_old_Oprod_Oexhaust,axiom,
% 0.27/0.63 ! [Y3: produc715398134_a_a_e] :
% 0.27/0.63 ~ ! [A6: set_a,B6: a > e] :
% 0.27/0.63 ( Y3
% 0.27/0.63 != ( produc1134456688_a_a_e @ A6 @ B6 ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.exhaust
% 0.27/0.63 thf(fact_217_Pair__inject,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,A5: set_a,B5: a > e] :
% 0.27/0.63 ( ( ( produc1134456688_a_a_e @ A2 @ B2 )
% 0.27/0.63 = ( produc1134456688_a_a_e @ A5 @ B5 ) )
% 0.27/0.63 => ~ ( ( A2 = A5 )
% 0.27/0.63 => ( B2 != B5 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Pair_inject
% 0.27/0.63 thf(fact_218_prod__cases,axiom,
% 0.27/0.63 ! [P2: produc715398134_a_a_e > $o,P: produc715398134_a_a_e] :
% 0.27/0.63 ( ! [A6: set_a,B6: a > e] : ( P2 @ ( produc1134456688_a_a_e @ A6 @ B6 ) )
% 0.27/0.63 => ( P2 @ P ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_cases
% 0.27/0.63 thf(fact_219_image__Fpow__mono,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e,B: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ ( image_64240033_set_a @ F @ A ) @ B )
% 0.27/0.63 => ( ord_le2103863998_set_a @ ( image_1441218763_set_a @ ( image_64240033_set_a @ F ) @ ( finite33065488_a_a_e @ A ) ) @ ( finite_Fpow_set_a @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % image_Fpow_mono
% 0.27/0.63 thf(fact_220_not__sub,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a] :
% 0.27/0.63 ( ~ ( ord_le318720350_set_a @ A @ B )
% 0.27/0.63 => ? [A6: set_a] :
% 0.27/0.63 ( ( member_set_a @ A6 @ A )
% 0.27/0.63 & ~ ( member_set_a @ A6 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % not_sub
% 0.27/0.63 thf(fact_221_not__sub,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ~ ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.63 => ? [A6: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ A6 @ A )
% 0.27/0.63 & ~ ( member1258382221_a_a_e @ A6 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % not_sub
% 0.27/0.63 thf(fact_222_not__sub,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ~ ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ? [A6: a] :
% 0.27/0.63 ( ( member_a @ A6 @ A )
% 0.27/0.63 & ~ ( member_a @ A6 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % not_sub
% 0.27/0.63 thf(fact_223_eqsets__sub,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( A = B )
% 0.27/0.63 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqsets_sub
% 0.27/0.63 thf(fact_224_sub__which1,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a,X3: set_a] :
% 0.27/0.63 ( ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.63 | ( ord_le318720350_set_a @ B @ A ) )
% 0.27/0.63 => ( ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( ~ ( member_set_a @ X3 @ B )
% 0.27/0.63 => ( ord_le318720350_set_a @ B @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sub_which1
% 0.27/0.63 thf(fact_225_sub__which1,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,X3: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.63 | ( ord_le700723212_a_a_e @ B @ A ) )
% 0.27/0.63 => ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( ~ ( member1258382221_a_a_e @ X3 @ B )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ B @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sub_which1
% 0.27/0.63 thf(fact_226_sub__which1,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a,X3: a] :
% 0.27/0.63 ( ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 | ( ord_less_eq_set_a @ B @ A ) )
% 0.27/0.63 => ( ( member_a @ X3 @ A )
% 0.27/0.63 => ( ~ ( member_a @ X3 @ B )
% 0.27/0.63 => ( ord_less_eq_set_a @ B @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sub_which1
% 0.27/0.63 thf(fact_227_Fpow__mono,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ( ord_le318720350_set_a @ ( finite_Fpow_a @ A ) @ ( finite_Fpow_a @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Fpow_mono
% 0.27/0.63 thf(fact_228_le__convert,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.27/0.63 ( ( A2 = B2 )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ A2 @ C2 )
% 0.27/0.63 => ( ord_less_eq_set_a @ B2 @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % le_convert
% 0.27/0.63 thf(fact_229_ge__convert,axiom,
% 0.27/0.63 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.27/0.63 ( ( A2 = B2 )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ C2 @ A2 )
% 0.27/0.63 => ( ord_less_eq_set_a @ C2 @ B2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ge_convert
% 0.27/0.63 thf(fact_230_mem__in__image3,axiom,
% 0.27/0.63 ! [B2: set_a,F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ B2 @ ( image_64240033_set_a @ F @ A ) )
% 0.27/0.63 => ? [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.63 & ( B2
% 0.27/0.63 = ( F @ X2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image3
% 0.27/0.63 thf(fact_231_mem__in__image2,axiom,
% 0.27/0.63 ! [A2: set_a,A: set_set_a,F: set_a > set_a] :
% 0.27/0.63 ( ( member_set_a @ A2 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ A2 ) @ ( image_set_a_set_a @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image2
% 0.27/0.63 thf(fact_232_mem__in__image2,axiom,
% 0.27/0.63 ! [A2: set_a,A: set_set_a,F: set_a > produc715398134_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ A2 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ A2 ) @ ( image_210900495_a_a_e @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image2
% 0.27/0.63 thf(fact_233_mem__in__image2,axiom,
% 0.27/0.63 ! [A2: produc715398134_a_a_e,A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ A2 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ A2 ) @ ( image_64240033_set_a @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image2
% 0.27/0.63 thf(fact_234_mem__in__image2,axiom,
% 0.27/0.63 ! [A2: produc715398134_a_a_e,A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ A2 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ A2 ) @ ( image_625620211_a_a_e @ F @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image2
% 0.27/0.63 thf(fact_235_mem__in__image1,axiom,
% 0.27/0.63 ! [A: set_set_a,F: set_a > set_a,B: set_set_a,A2: set_a] :
% 0.27/0.63 ( ! [X2: set_a] :
% 0.27/0.63 ( ( member_set_a @ X2 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ X2 ) @ B ) )
% 0.27/0.63 => ( ( member_set_a @ A2 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ A2 ) @ ( image_set_a_set_a @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image1
% 0.27/0.63 thf(fact_236_mem__in__image1,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > set_a,B: set_set_a,A2: produc715398134_a_a_e] :
% 0.27/0.63 ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ X2 ) @ B ) )
% 0.27/0.63 => ( ( member1258382221_a_a_e @ A2 @ A )
% 0.27/0.63 => ( member_set_a @ ( F @ A2 ) @ ( image_64240033_set_a @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image1
% 0.27/0.63 thf(fact_237_mem__in__image1,axiom,
% 0.27/0.63 ! [A: set_set_a,F: set_a > produc715398134_a_a_e,B: set_Pr204296108_a_a_e,A2: set_a] :
% 0.27/0.63 ( ! [X2: set_a] :
% 0.27/0.63 ( ( member_set_a @ X2 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ X2 ) @ B ) )
% 0.27/0.63 => ( ( member_set_a @ A2 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ A2 ) @ ( image_210900495_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image1
% 0.27/0.63 thf(fact_238_mem__in__image1,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,F: produc715398134_a_a_e > produc715398134_a_a_e,B: set_Pr204296108_a_a_e,A2: produc715398134_a_a_e] :
% 0.27/0.63 ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ X2 ) @ B ) )
% 0.27/0.63 => ( ( member1258382221_a_a_e @ A2 @ A )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( F @ A2 ) @ ( image_625620211_a_a_e @ F @ A ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_in_image1
% 0.27/0.63 thf(fact_239_proper__subset,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a,X3: set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.63 => ( ~ ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( ( member_set_a @ X3 @ B )
% 0.27/0.63 => ( A != B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % proper_subset
% 0.27/0.63 thf(fact_240_proper__subset,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,X3: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.63 => ( ~ ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( ( member1258382221_a_a_e @ X3 @ B )
% 0.27/0.63 => ( A != B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % proper_subset
% 0.27/0.63 thf(fact_241_proper__subset,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a,X3: a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ( ~ ( member_a @ X3 @ A )
% 0.27/0.63 => ( ( member_a @ X3 @ B )
% 0.27/0.63 => ( A != B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % proper_subset
% 0.27/0.63 thf(fact_242_not__subseteq,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a] :
% 0.27/0.63 ( ~ ( ord_le318720350_set_a @ A @ B )
% 0.27/0.63 => ? [X2: set_a] :
% 0.27/0.63 ( ( member_set_a @ X2 @ A )
% 0.27/0.63 & ~ ( member_set_a @ X2 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % not_subseteq
% 0.27/0.63 thf(fact_243_not__subseteq,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ~ ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.63 => ? [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.63 & ~ ( member1258382221_a_a_e @ X2 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % not_subseteq
% 0.27/0.63 thf(fact_244_not__subseteq,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ~ ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ? [X2: a] :
% 0.27/0.63 ( ( member_a @ X2 @ A )
% 0.27/0.63 & ~ ( member_a @ X2 @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % not_subseteq
% 0.27/0.63 thf(fact_245_subset__self,axiom,
% 0.27/0.63 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 0.27/0.63
% 0.27/0.63 % subset_self
% 0.27/0.63 thf(fact_246_sets__not__eq,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a] :
% 0.27/0.63 ( ( A != B )
% 0.27/0.63 => ( ( ord_le318720350_set_a @ B @ A )
% 0.27/0.63 => ? [X2: set_a] :
% 0.27/0.63 ( ( member_set_a @ X2 @ A )
% 0.27/0.63 & ~ ( member_set_a @ X2 @ B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sets_not_eq
% 0.27/0.63 thf(fact_247_sets__not__eq,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( A != B )
% 0.27/0.63 => ( ( ord_le700723212_a_a_e @ B @ A )
% 0.27/0.63 => ? [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.63 & ~ ( member1258382221_a_a_e @ X2 @ B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sets_not_eq
% 0.27/0.63 thf(fact_248_sets__not__eq,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( A != B )
% 0.27/0.63 => ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.63 => ? [X2: a] :
% 0.27/0.63 ( ( member_a @ X2 @ A )
% 0.27/0.63 & ~ ( member_a @ X2 @ B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sets_not_eq
% 0.27/0.63 thf(fact_249_sub__which2,axiom,
% 0.27/0.63 ! [A: set_set_a,B: set_set_a,X3: set_a] :
% 0.27/0.63 ( ( ( ord_le318720350_set_a @ A @ B )
% 0.27/0.63 | ( ord_le318720350_set_a @ B @ A ) )
% 0.27/0.63 => ( ~ ( member_set_a @ X3 @ A )
% 0.27/0.63 => ( ( member_set_a @ X3 @ B )
% 0.27/0.63 => ( ord_le318720350_set_a @ A @ B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sub_which2
% 0.27/0.63 thf(fact_250_sub__which2,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,X3: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ( ord_le700723212_a_a_e @ A @ B )
% 0.27/0.63 | ( ord_le700723212_a_a_e @ B @ A ) )
% 0.27/0.63 => ( ~ ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.63 => ( ( member1258382221_a_a_e @ X3 @ B )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ A @ B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sub_which2
% 0.27/0.63 thf(fact_251_sub__which2,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a,X3: a] :
% 0.27/0.63 ( ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 | ( ord_less_eq_set_a @ B @ A ) )
% 0.27/0.63 => ( ~ ( member_a @ X3 @ A )
% 0.27/0.63 => ( ( member_a @ X3 @ B )
% 0.27/0.63 => ( ord_less_eq_set_a @ A @ B ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sub_which2
% 0.27/0.63 thf(fact_252_image__Pow__mono,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e,B: set_set_a] :
% 0.27/0.63 ( ( ord_le318720350_set_a @ ( image_64240033_set_a @ F @ A ) @ B )
% 0.27/0.63 => ( ord_le2103863998_set_a @ ( image_1441218763_set_a @ ( image_64240033_set_a @ F ) @ ( pow_Pr328302361_a_a_e @ A ) ) @ ( pow_set_a @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % image_Pow_mono
% 0.27/0.63 thf(fact_253_Sup_OSUP__cong,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C3: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a,Sup: set_set_a > set_a] :
% 0.27/0.63 ( ( A = B )
% 0.27/0.63 => ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ B )
% 0.27/0.63 => ( ( C3 @ X2 )
% 0.27/0.63 = ( D @ X2 ) ) )
% 0.27/0.63 => ( ( Sup @ ( image_64240033_set_a @ C3 @ A ) )
% 0.27/0.63 = ( Sup @ ( image_64240033_set_a @ D @ B ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Sup.SUP_cong
% 0.27/0.63 thf(fact_254_Inf_OINF__cong,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C3: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a,Inf: set_set_a > set_a] :
% 0.27/0.63 ( ( A = B )
% 0.27/0.63 => ( ! [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X2 @ B )
% 0.27/0.63 => ( ( C3 @ X2 )
% 0.27/0.63 = ( D @ X2 ) ) )
% 0.27/0.63 => ( ( Inf @ ( image_64240033_set_a @ C3 @ A ) )
% 0.27/0.63 = ( Inf @ ( image_64240033_set_a @ D @ B ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Inf.INF_cong
% 0.27/0.63 thf(fact_255_subrelI,axiom,
% 0.27/0.63 ! [R: set_Pr204296108_a_a_e,S: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ! [X2: set_a,Y: a > e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ X2 @ Y ) @ R )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ X2 @ Y ) @ S ) )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ R @ S ) ) ).
% 0.27/0.63
% 0.27/0.63 % subrelI
% 0.27/0.63 thf(fact_256_ssubst__Pair__rhs,axiom,
% 0.27/0.63 ! [R: set_a,S: a > e,R2: set_Pr204296108_a_a_e,S2: a > e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ R @ S ) @ R2 )
% 0.27/0.63 => ( ( S2 = S )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ R @ S2 ) @ R2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ssubst_Pair_rhs
% 0.27/0.63 thf(fact_257_PowI,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ( member_set_a @ A @ ( pow_a @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % PowI
% 0.27/0.63 thf(fact_258_Pow__iff,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( member_set_a @ A @ ( pow_a @ B ) )
% 0.27/0.63 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.27/0.63
% 0.27/0.63 % Pow_iff
% 0.27/0.63 thf(fact_259_Pow__top,axiom,
% 0.27/0.63 ! [A: set_a] : ( member_set_a @ A @ ( pow_a @ A ) ) ).
% 0.27/0.63
% 0.27/0.63 % Pow_top
% 0.27/0.63 thf(fact_260_PowD,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( member_set_a @ A @ ( pow_a @ B ) )
% 0.27/0.63 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.27/0.63
% 0.27/0.63 % PowD
% 0.27/0.63 thf(fact_261_Pow__mono,axiom,
% 0.27/0.63 ! [A: set_a,B: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.63 => ( ord_le318720350_set_a @ ( pow_a @ A ) @ ( pow_a @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Pow_mono
% 0.27/0.63 thf(fact_262_image__Pow__surj,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,A: set_Pr204296108_a_a_e,B: set_set_a] :
% 0.27/0.63 ( ( ( image_64240033_set_a @ F @ A )
% 0.27/0.63 = B )
% 0.27/0.63 => ( ( image_1441218763_set_a @ ( image_64240033_set_a @ F ) @ ( pow_Pr328302361_a_a_e @ A ) )
% 0.27/0.63 = ( pow_set_a @ B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % image_Pow_surj
% 0.27/0.63 thf(fact_263_le__rel__bool__arg__iff,axiom,
% 0.27/0.63 ( ord_less_eq_o_set_a
% 0.27/0.63 = ( ^ [X5: $o > set_a,Y6: $o > set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.27/0.63 & ( ord_less_eq_set_a @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % le_rel_bool_arg_iff
% 0.27/0.63 thf(fact_264_curryI,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > $o,A2: set_a,B2: a > e] :
% 0.27/0.63 ( ( F @ ( produc1134456688_a_a_e @ A2 @ B2 ) )
% 0.27/0.63 => ( produc952037978_a_e_o @ F @ A2 @ B2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % curryI
% 0.27/0.63 thf(fact_265_curryD,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > $o,A2: set_a,B2: a > e] :
% 0.27/0.63 ( ( produc952037978_a_e_o @ F @ A2 @ B2 )
% 0.27/0.63 => ( F @ ( produc1134456688_a_a_e @ A2 @ B2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % curryD
% 0.27/0.63 thf(fact_266_curryE,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > $o,A2: set_a,B2: a > e] :
% 0.27/0.63 ( ( produc952037978_a_e_o @ F @ A2 @ B2 )
% 0.27/0.63 => ( F @ ( produc1134456688_a_a_e @ A2 @ B2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % curryE
% 0.27/0.63 thf(fact_267_fst__eq__Domain,axiom,
% 0.27/0.63 ! [R2: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( image_64240033_set_a @ produc1040928388_a_a_e @ R2 )
% 0.27/0.63 = ( domain_set_a_a_e @ R2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % fst_eq_Domain
% 0.27/0.63 thf(fact_268_Domain__fst,axiom,
% 0.27/0.63 ( domain_set_a_a_e
% 0.27/0.63 = ( image_64240033_set_a @ produc1040928388_a_a_e ) ) ).
% 0.27/0.63
% 0.27/0.63 % Domain_fst
% 0.27/0.63 thf(fact_269_RangeE,axiom,
% 0.27/0.63 ! [B2: a > e,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_a_e @ B2 @ ( range_set_a_a_e @ R ) )
% 0.27/0.63 => ~ ! [A6: set_a] :
% 0.27/0.63 ~ ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A6 @ B2 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % RangeE
% 0.27/0.63 thf(fact_270_Range__iff,axiom,
% 0.27/0.63 ! [A2: a > e,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_a_e @ A2 @ ( range_set_a_a_e @ R ) )
% 0.27/0.63 = ( ? [Y4: set_a] : ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ Y4 @ A2 ) @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Range_iff
% 0.27/0.63 thf(fact_271_Range_Ocases,axiom,
% 0.27/0.63 ! [A2: a > e,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_a_e @ A2 @ ( range_set_a_a_e @ R ) )
% 0.27/0.63 => ~ ! [A6: set_a] :
% 0.27/0.63 ~ ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A6 @ A2 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % Range.cases
% 0.27/0.63 thf(fact_272_Range_Osimps,axiom,
% 0.27/0.63 ! [A2: a > e,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_a_e @ A2 @ ( range_set_a_a_e @ R ) )
% 0.27/0.63 = ( ? [A3: set_a,B3: a > e] :
% 0.27/0.63 ( ( A2 = B3 )
% 0.27/0.63 & ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A3 @ B3 ) @ R ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Range.simps
% 0.27/0.63 thf(fact_273_Range_Ointros,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B2 ) @ R )
% 0.27/0.63 => ( member_a_e @ B2 @ ( range_set_a_a_e @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Range.intros
% 0.27/0.63 thf(fact_274_Range_Oinducts,axiom,
% 0.27/0.63 ! [X3: a > e,R: set_Pr204296108_a_a_e,P2: ( a > e ) > $o] :
% 0.27/0.63 ( ( member_a_e @ X3 @ ( range_set_a_a_e @ R ) )
% 0.27/0.63 => ( ! [A6: set_a,B6: a > e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A6 @ B6 ) @ R )
% 0.27/0.63 => ( P2 @ B6 ) )
% 0.27/0.63 => ( P2 @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Range.inducts
% 0.27/0.63 thf(fact_275_DomainE,axiom,
% 0.27/0.63 ! [A2: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ A2 @ ( domain_set_a_a_e @ R ) )
% 0.27/0.63 => ~ ! [B6: a > e] :
% 0.27/0.63 ~ ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B6 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % DomainE
% 0.27/0.63 thf(fact_276_Domain__iff,axiom,
% 0.27/0.63 ! [A2: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ A2 @ ( domain_set_a_a_e @ R ) )
% 0.27/0.63 = ( ? [Y4: a > e] : ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ Y4 ) @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Domain_iff
% 0.27/0.63 thf(fact_277_Domain_Ocases,axiom,
% 0.27/0.63 ! [A2: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ A2 @ ( domain_set_a_a_e @ R ) )
% 0.27/0.63 => ~ ! [B6: a > e] :
% 0.27/0.63 ~ ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B6 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % Domain.cases
% 0.27/0.63 thf(fact_278_Domain_Osimps,axiom,
% 0.27/0.63 ! [A2: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ A2 @ ( domain_set_a_a_e @ R ) )
% 0.27/0.63 = ( ? [A3: set_a,B3: a > e] :
% 0.27/0.63 ( ( A2 = A3 )
% 0.27/0.63 & ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A3 @ B3 ) @ R ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Domain.simps
% 0.27/0.63 thf(fact_279_Domain_ODomainI,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B2 ) @ R )
% 0.27/0.63 => ( member_set_a @ A2 @ ( domain_set_a_a_e @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Domain.DomainI
% 0.27/0.63 thf(fact_280_Domain_Oinducts,axiom,
% 0.27/0.63 ! [X3: set_a,R: set_Pr204296108_a_a_e,P2: set_a > $o] :
% 0.27/0.63 ( ( member_set_a @ X3 @ ( domain_set_a_a_e @ R ) )
% 0.27/0.63 => ( ! [A6: set_a,B6: a > e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A6 @ B6 ) @ R )
% 0.27/0.63 => ( P2 @ A6 ) )
% 0.27/0.63 => ( P2 @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Domain.inducts
% 0.27/0.63 thf(fact_281_pair__in__swap__image,axiom,
% 0.27/0.63 ! [Y3: a > e,X3: set_a,A: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ Y3 @ X3 ) @ ( image_1875450791_set_a @ produc755714512_a_a_e @ A ) )
% 0.27/0.63 = ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ X3 @ Y3 ) @ A ) ) ).
% 0.27/0.63
% 0.27/0.63 % pair_in_swap_image
% 0.27/0.63 thf(fact_282_pair__in__swap__image,axiom,
% 0.27/0.63 ! [Y3: set_a,X3: a > e,A: set_Pr305929312_set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ Y3 @ X3 ) @ ( image_376979367_a_a_e @ produc100464700_set_a @ A ) )
% 0.27/0.63 = ( member360729153_set_a @ ( produc479206876_set_a @ X3 @ Y3 ) @ A ) ) ).
% 0.27/0.63
% 0.27/0.63 % pair_in_swap_image
% 0.27/0.63 thf(fact_283_swap__simp,axiom,
% 0.27/0.63 ! [X3: a > e,Y3: set_a] :
% 0.27/0.63 ( ( produc100464700_set_a @ ( produc479206876_set_a @ X3 @ Y3 ) )
% 0.27/0.63 = ( produc1134456688_a_a_e @ Y3 @ X3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % swap_simp
% 0.27/0.63 thf(fact_284_swap__simp,axiom,
% 0.27/0.63 ! [X3: set_a,Y3: a > e] :
% 0.27/0.63 ( ( produc755714512_a_a_e @ ( produc1134456688_a_a_e @ X3 @ Y3 ) )
% 0.27/0.63 = ( produc479206876_set_a @ Y3 @ X3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % swap_simp
% 0.27/0.63 thf(fact_285_converse__iff,axiom,
% 0.27/0.63 ! [A2: a > e,B2: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ A2 @ B2 ) @ ( converse_set_a_a_e @ R ) )
% 0.27/0.63 = ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ B2 @ A2 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse_iff
% 0.27/0.63 thf(fact_286_converse__iff,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,R: set_Pr305929312_set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B2 ) @ ( converse_a_e_set_a @ R ) )
% 0.27/0.63 = ( member360729153_set_a @ ( produc479206876_set_a @ B2 @ A2 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse_iff
% 0.27/0.63 thf(fact_287_converse_Oinducts,axiom,
% 0.27/0.63 ! [X1: a > e,X22: set_a,R: set_Pr204296108_a_a_e,P2: ( a > e ) > set_a > $o] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ X1 @ X22 ) @ ( converse_set_a_a_e @ R ) )
% 0.27/0.63 => ( ! [A6: set_a,B6: a > e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A6 @ B6 ) @ R )
% 0.27/0.63 => ( P2 @ B6 @ A6 ) )
% 0.27/0.63 => ( P2 @ X1 @ X22 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.inducts
% 0.27/0.63 thf(fact_288_converse_Oinducts,axiom,
% 0.27/0.63 ! [X1: set_a,X22: a > e,R: set_Pr305929312_set_a,P2: set_a > ( a > e ) > $o] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ X1 @ X22 ) @ ( converse_a_e_set_a @ R ) )
% 0.27/0.63 => ( ! [A6: a > e,B6: set_a] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ A6 @ B6 ) @ R )
% 0.27/0.63 => ( P2 @ B6 @ A6 ) )
% 0.27/0.63 => ( P2 @ X1 @ X22 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.inducts
% 0.27/0.63 thf(fact_289_converse_Ointros,axiom,
% 0.27/0.63 ! [A2: a > e,B2: set_a,R: set_Pr305929312_set_a] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ A2 @ B2 ) @ R )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ B2 @ A2 ) @ ( converse_a_e_set_a @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.intros
% 0.27/0.63 thf(fact_290_converse_Ointros,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B2 ) @ R )
% 0.27/0.63 => ( member360729153_set_a @ ( produc479206876_set_a @ B2 @ A2 ) @ ( converse_set_a_a_e @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.intros
% 0.27/0.63 thf(fact_291_converse_Osimps,axiom,
% 0.27/0.63 ! [A1: a > e,A22: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ A1 @ A22 ) @ ( converse_set_a_a_e @ R ) )
% 0.27/0.63 = ( ? [A3: set_a,B3: a > e] :
% 0.27/0.63 ( ( A1 = B3 )
% 0.27/0.63 & ( A22 = A3 )
% 0.27/0.63 & ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A3 @ B3 ) @ R ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.simps
% 0.27/0.63 thf(fact_292_converse_Osimps,axiom,
% 0.27/0.63 ! [A1: set_a,A22: a > e,R: set_Pr305929312_set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A1 @ A22 ) @ ( converse_a_e_set_a @ R ) )
% 0.27/0.63 = ( ? [A3: a > e,B3: set_a] :
% 0.27/0.63 ( ( A1 = B3 )
% 0.27/0.63 & ( A22 = A3 )
% 0.27/0.63 & ( member360729153_set_a @ ( produc479206876_set_a @ A3 @ B3 ) @ R ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.simps
% 0.27/0.63 thf(fact_293_converse_Ocases,axiom,
% 0.27/0.63 ! [A1: a > e,A22: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ A1 @ A22 ) @ ( converse_set_a_a_e @ R ) )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A22 @ A1 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.cases
% 0.27/0.63 thf(fact_294_converse_Ocases,axiom,
% 0.27/0.63 ! [A1: set_a,A22: a > e,R: set_Pr305929312_set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A1 @ A22 ) @ ( converse_a_e_set_a @ R ) )
% 0.27/0.63 => ( member360729153_set_a @ ( produc479206876_set_a @ A22 @ A1 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % converse.cases
% 0.27/0.63 thf(fact_295_converseE,axiom,
% 0.27/0.63 ! [Yx: produc1965228714_set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member360729153_set_a @ Yx @ ( converse_set_a_a_e @ R ) )
% 0.27/0.63 => ~ ! [X2: set_a,Y: a > e] :
% 0.27/0.63 ( ( Yx
% 0.27/0.63 = ( produc479206876_set_a @ Y @ X2 ) )
% 0.27/0.63 => ~ ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ X2 @ Y ) @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converseE
% 0.27/0.63 thf(fact_296_converseE,axiom,
% 0.27/0.63 ! [Yx: produc715398134_a_a_e,R: set_Pr305929312_set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ Yx @ ( converse_a_e_set_a @ R ) )
% 0.27/0.63 => ~ ! [X2: a > e,Y: set_a] :
% 0.27/0.63 ( ( Yx
% 0.27/0.63 = ( produc1134456688_a_a_e @ Y @ X2 ) )
% 0.27/0.63 => ~ ( member360729153_set_a @ ( produc479206876_set_a @ X2 @ Y ) @ R ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % converseE
% 0.27/0.63 thf(fact_297_converseD,axiom,
% 0.27/0.63 ! [A2: a > e,B2: set_a,R: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member360729153_set_a @ ( produc479206876_set_a @ A2 @ B2 ) @ ( converse_set_a_a_e @ R ) )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ B2 @ A2 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % converseD
% 0.27/0.63 thf(fact_298_converseD,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,R: set_Pr305929312_set_a] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B2 ) @ ( converse_a_e_set_a @ R ) )
% 0.27/0.63 => ( member360729153_set_a @ ( produc479206876_set_a @ B2 @ A2 ) @ R ) ) ).
% 0.27/0.63
% 0.27/0.63 % converseD
% 0.27/0.63 thf(fact_299_prod_Oswap__def,axiom,
% 0.27/0.63 ( produc100464700_set_a
% 0.27/0.63 = ( ^ [P3: produc1965228714_set_a] : ( produc1134456688_a_a_e @ ( produc1809800494_set_a @ P3 ) @ ( produc385678576_set_a @ P3 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod.swap_def
% 0.27/0.63 thf(fact_300_prod_Oswap__def,axiom,
% 0.27/0.63 ( produc755714512_a_a_e
% 0.27/0.63 = ( ^ [P3: produc715398134_a_a_e] : ( produc479206876_set_a @ ( produc317566658_a_a_e @ P3 ) @ ( produc1040928388_a_a_e @ P3 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod.swap_def
% 0.27/0.63 thf(fact_301_map__prod__imageI,axiom,
% 0.27/0.63 ! [A2: set_a,B2: a > e,R2: set_Pr204296108_a_a_e,F: set_a > set_a,G: ( a > e ) > a > e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ A2 @ B2 ) @ R2 )
% 0.27/0.63 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ ( F @ A2 ) @ ( G @ B2 ) ) @ ( image_625620211_a_a_e @ ( produc1443219402_e_a_e @ F @ G ) @ R2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % map_prod_imageI
% 0.27/0.63 thf(fact_302_UNIV__I,axiom,
% 0.27/0.63 ! [X3: set_a] : ( member_set_a @ X3 @ top_top_set_set_a ) ).
% 0.27/0.63
% 0.27/0.63 % UNIV_I
% 0.27/0.63 thf(fact_303_UNIV__I,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e] : ( member1258382221_a_a_e @ X3 @ top_to1601855068_a_a_e ) ).
% 0.27/0.63
% 0.27/0.63 % UNIV_I
% 0.27/0.63 thf(fact_304_map__prod__simp,axiom,
% 0.27/0.63 ! [F: set_a > set_a,G: ( a > e ) > a > e,A2: set_a,B2: a > e] :
% 0.27/0.63 ( ( produc1443219402_e_a_e @ F @ G @ ( produc1134456688_a_a_e @ A2 @ B2 ) )
% 0.27/0.63 = ( produc1134456688_a_a_e @ ( F @ A2 ) @ ( G @ B2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % map_prod_simp
% 0.27/0.63 thf(fact_305_fst__map__prod,axiom,
% 0.27/0.63 ! [F: set_a > set_a,G: ( a > e ) > a > e,X3: produc715398134_a_a_e] :
% 0.27/0.63 ( ( produc1040928388_a_a_e @ ( produc1443219402_e_a_e @ F @ G @ X3 ) )
% 0.27/0.63 = ( F @ ( produc1040928388_a_a_e @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fst_map_prod
% 0.27/0.63 thf(fact_306_prod_Ocollapse,axiom,
% 0.27/0.63 ! [Prod: produc715398134_a_a_e] :
% 0.27/0.63 ( ( produc1134456688_a_a_e @ ( produc1040928388_a_a_e @ Prod ) @ ( produc317566658_a_a_e @ Prod ) )
% 0.27/0.63 = Prod ) ).
% 0.27/0.63
% 0.27/0.63 % prod.collapse
% 0.27/0.63 thf(fact_307_fst__swap,axiom,
% 0.27/0.63 ! [X3: produc1965228714_set_a] :
% 0.27/0.63 ( ( produc1040928388_a_a_e @ ( produc100464700_set_a @ X3 ) )
% 0.27/0.63 = ( produc1809800494_set_a @ X3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % fst_swap
% 0.27/0.63 thf(fact_308_snd__swap,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e] :
% 0.27/0.63 ( ( produc1809800494_set_a @ ( produc755714512_a_a_e @ X3 ) )
% 0.27/0.63 = ( produc1040928388_a_a_e @ X3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % snd_swap
% 0.27/0.63 thf(fact_309_range__fst,axiom,
% 0.27/0.63 ( ( image_64240033_set_a @ produc1040928388_a_a_e @ top_to1601855068_a_a_e )
% 0.27/0.63 = top_top_set_set_a ) ).
% 0.27/0.63
% 0.27/0.63 % range_fst
% 0.27/0.63 thf(fact_310_rangeI,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,X3: produc715398134_a_a_e] : ( member_set_a @ ( F @ X3 ) @ ( image_64240033_set_a @ F @ top_to1601855068_a_a_e ) ) ).
% 0.27/0.63
% 0.27/0.63 % rangeI
% 0.27/0.63 thf(fact_311_range__eqI,axiom,
% 0.27/0.63 ! [B2: set_a,F: produc715398134_a_a_e > set_a,X3: produc715398134_a_a_e] :
% 0.27/0.63 ( ( B2
% 0.27/0.63 = ( F @ X3 ) )
% 0.27/0.63 => ( member_set_a @ B2 @ ( image_64240033_set_a @ F @ top_to1601855068_a_a_e ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % range_eqI
% 0.27/0.63 thf(fact_312_surj__def,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a] :
% 0.27/0.63 ( ( ( image_64240033_set_a @ F @ top_to1601855068_a_a_e )
% 0.27/0.63 = top_top_set_set_a )
% 0.27/0.63 = ( ! [Y4: set_a] :
% 0.27/0.63 ? [X4: produc715398134_a_a_e] :
% 0.27/0.63 ( Y4
% 0.27/0.63 = ( F @ X4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % surj_def
% 0.27/0.63 thf(fact_313_surjI,axiom,
% 0.27/0.63 ! [G: produc715398134_a_a_e > set_a,F: set_a > produc715398134_a_a_e] :
% 0.27/0.63 ( ! [X2: set_a] :
% 0.27/0.63 ( ( G @ ( F @ X2 ) )
% 0.27/0.63 = X2 )
% 0.27/0.63 => ( ( image_64240033_set_a @ G @ top_to1601855068_a_a_e )
% 0.27/0.63 = top_top_set_set_a ) ) ).
% 0.27/0.63
% 0.27/0.63 % surjI
% 0.27/0.63 thf(fact_314_surjE,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,Y3: set_a] :
% 0.27/0.63 ( ( ( image_64240033_set_a @ F @ top_to1601855068_a_a_e )
% 0.27/0.63 = top_top_set_set_a )
% 0.27/0.63 => ~ ! [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( Y3
% 0.27/0.63 != ( F @ X2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % surjE
% 0.27/0.63 thf(fact_315_surjD,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,Y3: set_a] :
% 0.27/0.63 ( ( ( image_64240033_set_a @ F @ top_to1601855068_a_a_e )
% 0.27/0.63 = top_top_set_set_a )
% 0.27/0.63 => ? [X2: produc715398134_a_a_e] :
% 0.27/0.63 ( Y3
% 0.27/0.63 = ( F @ X2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % surjD
% 0.27/0.63 thf(fact_316_map__prod__surj,axiom,
% 0.27/0.63 ! [F: produc715398134_a_a_e > set_a,G: produc715398134_a_a_e > set_a] :
% 0.27/0.63 ( ( ( image_64240033_set_a @ F @ top_to1601855068_a_a_e )
% 0.27/0.63 = top_top_set_set_a )
% 0.27/0.63 => ( ( ( image_64240033_set_a @ G @ top_to1601855068_a_a_e )
% 0.27/0.63 = top_top_set_set_a )
% 0.27/0.63 => ( ( image_2101504031_set_a @ ( produc387505142_set_a @ F @ G ) @ top_to970499581_a_a_e )
% 0.27/0.63 = top_to144004695_set_a ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % map_prod_surj
% 0.27/0.63 thf(fact_317_top_Oextremum__uniqueI,axiom,
% 0.27/0.63 ! [A2: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
% 0.27/0.63 => ( A2 = top_top_set_a ) ) ).
% 0.27/0.63
% 0.27/0.63 % top.extremum_uniqueI
% 0.27/0.63 thf(fact_318_top_Oextremum__unique,axiom,
% 0.27/0.63 ! [A2: set_a] :
% 0.27/0.63 ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
% 0.27/0.63 = ( A2 = top_top_set_a ) ) ).
% 0.27/0.63
% 0.27/0.63 % top.extremum_unique
% 0.27/0.63 thf(fact_319_top__greatest,axiom,
% 0.27/0.63 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ top_top_set_a ) ).
% 0.27/0.63
% 0.27/0.63 % top_greatest
% 0.27/0.63 thf(fact_320_subset__UNIV,axiom,
% 0.27/0.63 ! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ) ).
% 0.27/0.63
% 0.27/0.63 % subset_UNIV
% 0.27/0.63 thf(fact_321_sndI,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e,Y3: set_a,Z2: a > e] :
% 0.27/0.63 ( ( X3
% 0.27/0.63 = ( produc1134456688_a_a_e @ Y3 @ Z2 ) )
% 0.27/0.63 => ( ( produc317566658_a_a_e @ X3 )
% 0.27/0.63 = Z2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % sndI
% 0.27/0.63 thf(fact_322_snd__eqD,axiom,
% 0.27/0.63 ! [X3: set_a,Y3: a > e,A2: a > e] :
% 0.27/0.63 ( ( ( produc317566658_a_a_e @ ( produc1134456688_a_a_e @ X3 @ Y3 ) )
% 0.27/0.63 = A2 )
% 0.27/0.63 => ( Y3 = A2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % snd_eqD
% 0.27/0.63 thf(fact_323_snd__conv,axiom,
% 0.27/0.63 ! [X1: set_a,X22: a > e] :
% 0.27/0.63 ( ( produc317566658_a_a_e @ ( produc1134456688_a_a_e @ X1 @ X22 ) )
% 0.27/0.63 = X22 ) ).
% 0.27/0.63
% 0.27/0.63 % snd_conv
% 0.27/0.63 thf(fact_324_eq__snd__iff,axiom,
% 0.27/0.63 ! [B2: a > e,P: produc715398134_a_a_e] :
% 0.27/0.63 ( ( B2
% 0.27/0.63 = ( produc317566658_a_a_e @ P ) )
% 0.27/0.63 = ( ? [A3: set_a] :
% 0.27/0.63 ( P
% 0.27/0.63 = ( produc1134456688_a_a_e @ A3 @ B2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_snd_iff
% 0.27/0.63 thf(fact_325_prod__eq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y2: produc715398134_a_a_e,Z: produc715398134_a_a_e] : ( Y2 = Z ) )
% 0.27/0.63 = ( ^ [S3: produc715398134_a_a_e,T: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ( produc1040928388_a_a_e @ S3 )
% 0.27/0.63 = ( produc1040928388_a_a_e @ T ) )
% 0.27/0.63 & ( ( produc317566658_a_a_e @ S3 )
% 0.27/0.63 = ( produc317566658_a_a_e @ T ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_eq_iff
% 0.27/0.63 thf(fact_326_prod_Oexpand,axiom,
% 0.27/0.63 ! [Prod: produc715398134_a_a_e,Prod2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ( ( produc1040928388_a_a_e @ Prod )
% 0.27/0.63 = ( produc1040928388_a_a_e @ Prod2 ) )
% 0.27/0.63 & ( ( produc317566658_a_a_e @ Prod )
% 0.27/0.63 = ( produc317566658_a_a_e @ Prod2 ) ) )
% 0.27/0.63 => ( Prod = Prod2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod.expand
% 0.27/0.63 thf(fact_327_prod__eqI,axiom,
% 0.27/0.63 ! [P: produc715398134_a_a_e,Q2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( ( produc1040928388_a_a_e @ P )
% 0.27/0.63 = ( produc1040928388_a_a_e @ Q2 ) )
% 0.27/0.63 => ( ( ( produc317566658_a_a_e @ P )
% 0.27/0.63 = ( produc317566658_a_a_e @ Q2 ) )
% 0.27/0.63 => ( P = Q2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_eqI
% 0.27/0.63 thf(fact_328_UNIV__eq__I,axiom,
% 0.27/0.63 ! [A: set_set_a] :
% 0.27/0.63 ( ! [X2: set_a] : ( member_set_a @ X2 @ A )
% 0.27/0.63 => ( top_top_set_set_a = A ) ) ).
% 0.27/0.63
% 0.27/0.63 % UNIV_eq_I
% 0.27/0.63 thf(fact_329_UNIV__eq__I,axiom,
% 0.27/0.63 ! [A: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ! [X2: produc715398134_a_a_e] : ( member1258382221_a_a_e @ X2 @ A )
% 0.27/0.63 => ( top_to1601855068_a_a_e = A ) ) ).
% 0.27/0.63
% 0.27/0.63 % UNIV_eq_I
% 0.27/0.63 thf(fact_330_UNIV__witness,axiom,
% 0.27/0.63 ? [X2: set_a] : ( member_set_a @ X2 @ top_top_set_set_a ) ).
% 0.27/0.63
% 0.27/0.63 % UNIV_witness
% 0.27/0.63 thf(fact_331_UNIV__witness,axiom,
% 0.27/0.63 ? [X2: produc715398134_a_a_e] : ( member1258382221_a_a_e @ X2 @ top_to1601855068_a_a_e ) ).
% 0.27/0.63
% 0.27/0.63 % UNIV_witness
% 0.27/0.63 thf(fact_332_surjective__pairing,axiom,
% 0.27/0.63 ! [T2: produc715398134_a_a_e] :
% 0.27/0.63 ( T2
% 0.27/0.63 = ( produc1134456688_a_a_e @ ( produc1040928388_a_a_e @ T2 ) @ ( produc317566658_a_a_e @ T2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % surjective_pairing
% 0.27/0.63 thf(fact_333_prod_Oexhaust__sel,axiom,
% 0.27/0.63 ! [Prod: produc715398134_a_a_e] :
% 0.27/0.63 ( Prod
% 0.27/0.63 = ( produc1134456688_a_a_e @ ( produc1040928388_a_a_e @ Prod ) @ ( produc317566658_a_a_e @ Prod ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod.exhaust_sel
% 0.27/0.63 thf(fact_334_prod__fun__imageE,axiom,
% 0.27/0.63 ! [C2: produc715398134_a_a_e,F: set_a > set_a,G: ( a > e ) > a > e,R2: set_Pr204296108_a_a_e] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ C2 @ ( image_625620211_a_a_e @ ( produc1443219402_e_a_e @ F @ G ) @ R2 ) )
% 0.27/0.63 => ~ ! [X2: set_a,Y: a > e] :
% 0.27/0.63 ( ( C2
% 0.27/0.63 = ( produc1134456688_a_a_e @ ( F @ X2 ) @ ( G @ Y ) ) )
% 0.27/0.63 => ~ ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ X2 @ Y ) @ R2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_fun_imageE
% 0.27/0.63 thf(fact_335_exI__realizer,axiom,
% 0.27/0.63 ! [P2: ( a > e ) > set_a > $o,Y3: a > e,X3: set_a] :
% 0.27/0.63 ( ( P2 @ Y3 @ X3 )
% 0.27/0.63 => ( P2 @ ( produc317566658_a_a_e @ ( produc1134456688_a_a_e @ X3 @ Y3 ) ) @ ( produc1040928388_a_a_e @ ( produc1134456688_a_a_e @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % exI_realizer
% 0.27/0.63 thf(fact_336_conjI__realizer,axiom,
% 0.27/0.63 ! [P2: set_a > $o,P: set_a,Q: ( a > e ) > $o,Q2: a > e] :
% 0.27/0.63 ( ( P2 @ P )
% 0.27/0.63 => ( ( Q @ Q2 )
% 0.27/0.63 => ( ( P2 @ ( produc1040928388_a_a_e @ ( produc1134456688_a_a_e @ P @ Q2 ) ) )
% 0.27/0.63 & ( Q @ ( produc317566658_a_a_e @ ( produc1134456688_a_a_e @ P @ Q2 ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % conjI_realizer
% 0.27/0.63 thf(fact_337_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.27/0.63 ! [P2: set_a > ( a > e ) > $o,X3: set_a,Y3: a > e,A2: produc715398134_a_a_e] :
% 0.27/0.63 ( ( P2 @ X3 @ Y3 )
% 0.27/0.63 => ( ( A2
% 0.27/0.63 = ( produc1134456688_a_a_e @ X3 @ Y3 ) )
% 0.27/0.63 => ( P2 @ ( produc1040928388_a_a_e @ A2 ) @ ( produc317566658_a_a_e @ A2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % BNF_Greatest_Fixpoint.subst_Pair
% 0.27/0.63 thf(fact_338_top__empty__eq,axiom,
% 0.27/0.63 ( top_top_set_a_o
% 0.27/0.63 = ( ^ [X4: set_a] : ( member_set_a @ X4 @ top_top_set_set_a ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % top_empty_eq
% 0.27/0.63 thf(fact_339_top__empty__eq,axiom,
% 0.27/0.63 ( top_to2000253225_a_e_o
% 0.27/0.63 = ( ^ [X4: produc715398134_a_a_e] : ( member1258382221_a_a_e @ X4 @ top_to1601855068_a_a_e ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % top_empty_eq
% 0.27/0.63 thf(fact_340_exE__realizer_H,axiom,
% 0.27/0.63 ! [P2: ( a > e ) > set_a > $o,P: produc715398134_a_a_e] :
% 0.27/0.63 ( ( P2 @ ( produc317566658_a_a_e @ P ) @ ( produc1040928388_a_a_e @ P ) )
% 0.27/0.63 => ~ ! [X2: set_a,Y: a > e] :
% 0.27/0.63 ~ ( P2 @ Y @ X2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % exE_realizer'
% 0.27/0.63 thf(fact_341_Collect__split__mono__strong,axiom,
% 0.27/0.63 ! [X6: set_set_a,A: set_Pr204296108_a_a_e,Y7: set_a_e,P2: set_a > ( a > e ) > $o,Q: set_a > ( a > e ) > $o] :
% 0.27/0.63 ( ( X6
% 0.27/0.63 = ( image_64240033_set_a @ produc1040928388_a_a_e @ A ) )
% 0.27/0.63 => ( ( Y7
% 0.27/0.63 = ( image_1149879910_e_a_e @ produc317566658_a_a_e @ A ) )
% 0.27/0.63 => ( ! [X2: set_a] :
% 0.27/0.63 ( ( member_set_a @ X2 @ X6 )
% 0.27/0.63 => ! [Xa2: a > e] :
% 0.27/0.63 ( ( member_a_e @ Xa2 @ Y7 )
% 0.27/0.63 => ( ( P2 @ X2 @ Xa2 )
% 0.27/0.63 => ( Q @ X2 @ Xa2 ) ) ) )
% 0.27/0.63 => ( ( ord_le700723212_a_a_e @ A @ ( collec1369693387_a_a_e @ ( produc1341862587_a_e_o @ P2 ) ) )
% 0.27/0.63 => ( ord_le700723212_a_a_e @ A @ ( collec1369693387_a_a_e @ ( produc1341862587_a_e_o @ Q ) ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Collect_split_mono_strong
% 0.27/0.63 thf(fact_342_sndOp__def,axiom,
% 0.27/0.63 ( bNF_sn375433437_a_a_e
% 0.27/0.63 = ( ^ [P4: set_a > set_a > $o,Q3: set_a > ( a > e ) > $o,Ac: produc715398134_a_a_e] : ( produc1134456688_a_a_e @ ( bNF_pi929741261_a_a_e @ P4 @ Q3 @ ( produc1040928388_a_a_e @ Ac ) @ ( produc317566658_a_a_e @ Ac ) ) @ ( produc317566658_a_a_e @ Ac ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sndOp_def
% 0.27/0.63 thf(fact_343_Product__Type_OCollect__case__prodD,axiom,
% 0.27/0.63 ! [X3: produc715398134_a_a_e,A: set_a > ( a > e ) > $o] :
% 0.27/0.63 ( ( member1258382221_a_a_e @ X3 @ ( collec1369693387_a_a_e @ ( produc1341862587_a_e_o @ A ) ) )
% 0.27/0.63 => ( A @ ( produc1040928388_a_a_e @ X3 ) @ ( produc317566658_a_a_e @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Product_Type.Collect_case_prodD
% 0.27/0.63 thf(fact_344_fstOp__def,axiom,
% 0.27/0.63 ( bNF_fs1024561536_e_a_e
% 0.27/0.63 = ( ^ [P4: set_a > ( a > e ) > $o,Q3: ( a > e ) > ( a > e ) > $o,Ac: produc715398134_a_a_e] : ( produc1134456688_a_a_e @ ( produc1040928388_a_a_e @ Ac ) @ ( bNF_pi1175744974_e_a_e @ P4 @ Q3 @ ( produc1040928388_a_a_e @ Ac ) @ ( produc317566658_a_a_e @ Ac ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fstOp_def
% 0.27/0.63 thf(fact_345_mem__case__prodE,axiom,
% 0.27/0.63 ! [Z2: set_a,C2: set_a > ( a > e ) > set_set_a,P: produc715398134_a_a_e] :
% 0.27/0.63 ( ( member_set_a @ Z2 @ ( produc1620938593_set_a @ C2 @ P ) )
% 0.27/0.63 => ~ ! [X2: set_a,Y: a > e] :
% 0.27/0.63 ( ( P
% 0.27/0.63 = ( produc1134456688_a_a_e @ X2 @ Y ) )
% 0.27/0.71 => ~ ( member_set_a @ Z2 @ ( C2 @ X2 @ Y ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % mem_case_prodE
% 0.27/0.71 thf(fact_346_mem__case__prodE,axiom,
% 0.27/0.71 ! [Z2: produc715398134_a_a_e,C2: set_a > ( a > e ) > set_Pr204296108_a_a_e,P: produc715398134_a_a_e] :
% 0.27/0.71 ( ( member1258382221_a_a_e @ Z2 @ ( produc1096319049_a_a_e @ C2 @ P ) )
% 0.27/0.71 => ~ ! [X2: set_a,Y: a > e] :
% 0.27/0.71 ( ( P
% 0.27/0.71 = ( produc1134456688_a_a_e @ X2 @ Y ) )
% 0.27/0.71 => ~ ( member1258382221_a_a_e @ Z2 @ ( C2 @ X2 @ Y ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % mem_case_prodE
% 0.27/0.71 thf(fact_347_in__rel__def,axiom,
% 0.27/0.71 ( fun_in_rel_set_a_a_e
% 0.27/0.71 = ( ^ [R3: set_Pr204296108_a_a_e,X4: set_a,Y4: a > e] : ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ X4 @ Y4 ) @ R3 ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % in_rel_def
% 0.27/0.71 thf(fact_348_fstOp__in,axiom,
% 0.27/0.71 ! [Ac2: produc715398134_a_a_e,P2: set_a > ( a > e ) > $o,Q: ( a > e ) > ( a > e ) > $o] :
% 0.27/0.71 ( ( member1258382221_a_a_e @ Ac2 @ ( collec1369693387_a_a_e @ ( produc1341862587_a_e_o @ ( relcom658603713_e_a_e @ P2 @ Q ) ) ) )
% 0.27/0.71 => ( member1258382221_a_a_e @ ( bNF_fs1024561536_e_a_e @ P2 @ Q @ Ac2 ) @ ( collec1369693387_a_a_e @ ( produc1341862587_a_e_o @ P2 ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % fstOp_in
% 0.27/0.71 thf(fact_349_sndOp__in,axiom,
% 0.27/0.71 ! [Ac2: produc715398134_a_a_e,P2: set_a > set_a > $o,Q: set_a > ( a > e ) > $o] :
% 0.27/0.71 ( ( member1258382221_a_a_e @ Ac2 @ ( collec1369693387_a_a_e @ ( produc1341862587_a_e_o @ ( relcom779348378_a_a_e @ P2 @ Q ) ) ) )
% 0.27/0.71 => ( member1258382221_a_a_e @ ( bNF_sn375433437_a_a_e @ P2 @ Q @ Ac2 ) @ ( collec1369693387_a_a_e @ ( produc1341862587_a_e_o @ Q ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % sndOp_in
% 0.27/0.71 thf(fact_350_image2__eqI,axiom,
% 0.27/0.71 ! [B2: set_a,F: set_a > set_a,X3: set_a,C2: a > e,G: set_a > a > e,A: set_set_a] :
% 0.27/0.71 ( ( B2
% 0.27/0.71 = ( F @ X3 ) )
% 0.27/0.71 => ( ( C2
% 0.27/0.71 = ( G @ X3 ) )
% 0.27/0.71 => ( ( member_set_a @ X3 @ A )
% 0.27/0.71 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ B2 @ C2 ) @ ( bNF_Gr1872575811_a_a_e @ A @ F @ G ) ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % image2_eqI
% 0.27/0.71 thf(fact_351_image2__eqI,axiom,
% 0.27/0.71 ! [B2: set_a,F: produc715398134_a_a_e > set_a,X3: produc715398134_a_a_e,C2: a > e,G: produc715398134_a_a_e > a > e,A: set_Pr204296108_a_a_e] :
% 0.27/0.71 ( ( B2
% 0.27/0.71 = ( F @ X3 ) )
% 0.27/0.71 => ( ( C2
% 0.27/0.71 = ( G @ X3 ) )
% 0.27/0.71 => ( ( member1258382221_a_a_e @ X3 @ A )
% 0.27/0.71 => ( member1258382221_a_a_e @ ( produc1134456688_a_a_e @ B2 @ C2 ) @ ( bNF_Gr2072183031_a_a_e @ A @ F @ G ) ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 % image2_eqI
% 0.27/0.71
% 0.27/0.71 % Conjectures (2)
% 0.27/0.71 thf(conj_0,hypothesis,
% 0.27/0.71 ! [A7: set_a] :
% 0.27/0.71 ( ( member_set_a @ A7 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
% 0.27/0.71 => ( ( ord_less_eq_set_a @ a1 @ A7 )
% 0.27/0.71 => ( ( ord_less_eq_set_a @ a2 @ A7 )
% 0.27/0.71 => ( ( ord_less_eq_set_a @ a3 @ A7 )
% 0.27/0.71 => thesis ) ) ) ) ).
% 0.27/0.71
% 0.27/0.71 thf(conj_1,conjecture,
% 0.27/0.71 thesis ).
% 0.27/0.71
% 0.27/0.71 %------------------------------------------------------------------------------
% 0.27/0.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.O6KzcByvkp/cvc5---1.0.5_13318.p...
% 0.27/0.71 (declare-sort $$unsorted 0)
% 0.27/0.71 (declare-sort tptp.set_Pr1710391469_a_a_e 0)
% 0.27/0.71 (declare-sort tptp.produc169085773_a_a_e 0)
% 0.27/0.71 (declare-sort tptp.set_se821189730_a_a_e 0)
% 0.27/0.71 (declare-sort tptp.set_Pr2045688071_set_a 0)
% 0.27/0.71 (declare-sort tptp.set_Pr204296108_a_a_e 0)
% 0.27/0.71 (declare-sort tptp.set_Pr305929312_set_a 0)
% 0.27/0.71 (declare-sort tptp.produc1691597095_set_a 0)
% 0.27/0.71 (declare-sort tptp.produc715398134_a_a_e 0)
% 0.27/0.71 (declare-sort tptp.produc1965228714_set_a 0)
% 0.27/0.71 (declare-sort tptp.set_set_set_a 0)
% 0.27/0.71 (declare-sort tptp.set_set_a 0)
% 0.27/0.71 (declare-sort tptp.set_a_e 0)
% 0.27/0.71 (declare-sort tptp.set_a 0)
% 0.27/0.71 (declare-sort tptp.e 0)
% 0.27/0.71 (declare-sort tptp.a 0)
% 0.27/0.71 (declare-fun tptp.bNF_fs1024561536_e_a_e ((-> tptp.set_a (-> tptp.a tptp.e) Bool) (-> (-> tptp.a tptp.e) (-> tptp.a tptp.e) Bool) tptp.produc715398134_a_a_e) tptp.produc715398134_a_a_e)
% 0.27/0.71 (declare-fun tptp.bNF_pi1175744974_e_a_e ((-> tptp.set_a (-> tptp.a tptp.e) Bool) (-> (-> tptp.a tptp.e) (-> tptp.a tptp.e) Bool) tptp.set_a (-> tptp.a tptp.e) tptp.a) tptp.e)
% 0.27/0.71 (declare-fun tptp.bNF_pi929741261_a_a_e ((-> tptp.set_a tptp.set_a Bool) (-> tptp.set_a (-> tptp.a tptp.e) Bool) tptp.set_a (-> tptp.a tptp.e)) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.bNF_sn375433437_a_a_e ((-> tptp.set_a tptp.set_a Bool) (-> tptp.set_a (-> tptp.a tptp.e) Bool) tptp.produc715398134_a_a_e) tptp.produc715398134_a_a_e)
% 0.27/0.71 (declare-fun tptp.bNF_Gr2072183031_a_a_e (tptp.set_Pr204296108_a_a_e (-> tptp.produc715398134_a_a_e tptp.set_a) (-> tptp.produc715398134_a_a_e tptp.a tptp.e)) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.bNF_Gr1872575811_a_a_e (tptp.set_set_a (-> tptp.set_a tptp.set_a) (-> tptp.set_a tptp.a tptp.e)) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.finite33065488_a_a_e (tptp.set_Pr204296108_a_a_e) tptp.set_se821189730_a_a_e)
% 0.27/0.71 (declare-fun tptp.finite_Fpow_set_a (tptp.set_set_a) tptp.set_set_set_a)
% 0.27/0.71 (declare-fun tptp.finite_Fpow_a (tptp.set_a) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.fun_in_rel_set_a_a_e (tptp.set_Pr204296108_a_a_e tptp.set_a (-> tptp.a tptp.e)) Bool)
% 0.27/0.71 (declare-fun tptp.ord_less_eq_o_set_a ((-> Bool tptp.set_a) (-> Bool tptp.set_a)) Bool)
% 0.27/0.71 (declare-fun tptp.ord_less_eq_set_a_e (tptp.set_a_e tptp.set_a_e) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le802356416_set_a (tptp.set_Pr305929312_set_a tptp.set_Pr305929312_set_a) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le700723212_a_a_e (tptp.set_Pr204296108_a_a_e tptp.set_Pr204296108_a_a_e) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le2103863998_set_a (tptp.set_set_set_a tptp.set_set_set_a) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le318720350_set_a (tptp.set_set_a tptp.set_set_a) Bool)
% 0.27/0.71 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.27/0.71 (declare-fun tptp.order_Greatest_set_a ((-> tptp.set_a Bool)) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.top_to2000253225_a_e_o (tptp.produc715398134_a_a_e) Bool)
% 0.27/0.71 (declare-fun tptp.top_top_set_a_o (tptp.set_a) Bool)
% 0.27/0.71 (declare-fun tptp.top_to970499581_a_a_e () tptp.set_Pr1710391469_a_a_e)
% 0.27/0.71 (declare-fun tptp.top_to1601855068_a_a_e () tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.top_to144004695_set_a () tptp.set_Pr2045688071_set_a)
% 0.27/0.71 (declare-fun tptp.top_top_set_set_a () tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.top_top_set_a () tptp.set_a)
% 0.27/0.71 (declare-fun tptp.produc479206876_set_a ((-> tptp.a tptp.e) tptp.set_a) tptp.produc1965228714_set_a)
% 0.27/0.71 (declare-fun tptp.produc1134456688_a_a_e (tptp.set_a (-> tptp.a tptp.e)) tptp.produc715398134_a_a_e)
% 0.27/0.71 (declare-fun tptp.produc952037978_a_e_o ((-> tptp.produc715398134_a_a_e Bool) tptp.set_a (-> tptp.a tptp.e)) Bool)
% 0.27/0.71 (declare-fun tptp.produc387505142_set_a ((-> tptp.produc715398134_a_a_e tptp.set_a) (-> tptp.produc715398134_a_a_e tptp.set_a) tptp.produc169085773_a_a_e) tptp.produc1691597095_set_a)
% 0.27/0.71 (declare-fun tptp.produc1443219402_e_a_e ((-> tptp.set_a tptp.set_a) (-> (-> tptp.a tptp.e) tptp.a tptp.e) tptp.produc715398134_a_a_e) tptp.produc715398134_a_a_e)
% 0.27/0.71 (declare-fun tptp.produc1341862587_a_e_o ((-> tptp.set_a (-> tptp.a tptp.e) Bool) tptp.produc715398134_a_a_e) Bool)
% 0.27/0.71 (declare-fun tptp.produc1096319049_a_a_e ((-> tptp.set_a (-> tptp.a tptp.e) tptp.set_Pr204296108_a_a_e) tptp.produc715398134_a_a_e) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.produc1620938593_set_a ((-> tptp.set_a (-> tptp.a tptp.e) tptp.set_set_a) tptp.produc715398134_a_a_e) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.produc385678576_set_a (tptp.produc1965228714_set_a tptp.a) tptp.e)
% 0.27/0.71 (declare-fun tptp.produc1040928388_a_a_e (tptp.produc715398134_a_a_e) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.produc1809800494_set_a (tptp.produc1965228714_set_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.produc317566658_a_a_e (tptp.produc715398134_a_a_e tptp.a) tptp.e)
% 0.27/0.71 (declare-fun tptp.produc100464700_set_a (tptp.produc1965228714_set_a) tptp.produc715398134_a_a_e)
% 0.27/0.71 (declare-fun tptp.produc755714512_a_a_e (tptp.produc715398134_a_a_e) tptp.produc1965228714_set_a)
% 0.27/0.71 (declare-fun tptp.domain_set_a_a_e (tptp.set_Pr204296108_a_a_e) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.range_set_a_a_e (tptp.set_Pr204296108_a_a_e) tptp.set_a_e)
% 0.27/0.71 (declare-fun tptp.converse_a_e_set_a (tptp.set_Pr305929312_set_a) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.converse_set_a_a_e (tptp.set_Pr204296108_a_a_e) tptp.set_Pr305929312_set_a)
% 0.27/0.71 (declare-fun tptp.relcom658603713_e_a_e ((-> tptp.set_a (-> tptp.a tptp.e) Bool) (-> (-> tptp.a tptp.e) (-> tptp.a tptp.e) Bool) tptp.set_a (-> tptp.a tptp.e)) Bool)
% 0.27/0.71 (declare-fun tptp.relcom779348378_a_a_e ((-> tptp.set_a tptp.set_a Bool) (-> tptp.set_a (-> tptp.a tptp.e) Bool) tptp.set_a (-> tptp.a tptp.e)) Bool)
% 0.27/0.71 (declare-fun tptp.collec1369693387_a_a_e ((-> tptp.produc715398134_a_a_e Bool)) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.collect_set_a ((-> tptp.set_a Bool)) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.pow_Pr328302361_a_a_e (tptp.set_Pr204296108_a_a_e) tptp.set_se821189730_a_a_e)
% 0.27/0.71 (declare-fun tptp.pow_set_a (tptp.set_set_a) tptp.set_set_set_a)
% 0.27/0.71 (declare-fun tptp.pow_a (tptp.set_a) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.image_a_e_a ((-> (-> tptp.a tptp.e) tptp.a) tptp.set_a_e) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.image_376979367_a_a_e ((-> tptp.produc1965228714_set_a tptp.produc715398134_a_a_e) tptp.set_Pr305929312_set_a) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.image_2101504031_set_a ((-> tptp.produc169085773_a_a_e tptp.produc1691597095_set_a) tptp.set_Pr1710391469_a_a_e) tptp.set_Pr2045688071_set_a)
% 0.27/0.71 (declare-fun tptp.image_1149879910_e_a_e ((-> tptp.produc715398134_a_a_e tptp.a tptp.e) tptp.set_Pr204296108_a_a_e) tptp.set_a_e)
% 0.27/0.71 (declare-fun tptp.image_1875450791_set_a ((-> tptp.produc715398134_a_a_e tptp.produc1965228714_set_a) tptp.set_Pr204296108_a_a_e) tptp.set_Pr305929312_set_a)
% 0.27/0.71 (declare-fun tptp.image_625620211_a_a_e ((-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e) tptp.set_Pr204296108_a_a_e) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.image_64240033_set_a ((-> tptp.produc715398134_a_a_e tptp.set_a) tptp.set_Pr204296108_a_a_e) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.image_2116492353_a_e_a ((-> tptp.produc715398134_a_a_e tptp.a) tptp.set_Pr204296108_a_a_e) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.image_1441218763_set_a ((-> tptp.set_Pr204296108_a_a_e tptp.set_set_a) tptp.set_se821189730_a_a_e) tptp.set_set_set_a)
% 0.27/0.71 (declare-fun tptp.image_1956910981_set_a ((-> tptp.set_set_a tptp.set_set_a) tptp.set_set_set_a) tptp.set_set_set_a)
% 0.27/0.71 (declare-fun tptp.image_402591269_set_a ((-> tptp.set_set_a tptp.set_a) tptp.set_set_set_a) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.image_set_set_a_a ((-> tptp.set_set_a tptp.a) tptp.set_set_set_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.image_set_a_a_e ((-> tptp.set_a tptp.a tptp.e) tptp.set_set_a) tptp.set_a_e)
% 0.27/0.71 (declare-fun tptp.image_210900495_a_a_e ((-> tptp.set_a tptp.produc715398134_a_a_e) tptp.set_set_a) tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.image_1930509541_set_a ((-> tptp.set_a tptp.set_set_a) tptp.set_set_a) tptp.set_set_set_a)
% 0.27/0.71 (declare-fun tptp.image_set_a_set_a ((-> tptp.set_a tptp.set_a) tptp.set_set_a) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.image_set_a_a ((-> tptp.set_a tptp.a) tptp.set_set_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.image_a_a_e ((-> tptp.a tptp.a tptp.e) tptp.set_a) tptp.set_a_e)
% 0.27/0.71 (declare-fun tptp.image_a_set_set_a ((-> tptp.a tptp.set_set_a) tptp.set_a) tptp.set_set_set_a)
% 0.27/0.71 (declare-fun tptp.image_a_set_a ((-> tptp.a tptp.set_a) tptp.set_a) tptp.set_set_a)
% 0.27/0.71 (declare-fun tptp.image_a_a ((-> tptp.a tptp.a) tptp.set_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.member_a_e ((-> tptp.a tptp.e) tptp.set_a_e) Bool)
% 0.27/0.71 (declare-fun tptp.member360729153_set_a (tptp.produc1965228714_set_a tptp.set_Pr305929312_set_a) Bool)
% 0.27/0.71 (declare-fun tptp.member1258382221_a_a_e (tptp.produc715398134_a_a_e tptp.set_Pr204296108_a_a_e) Bool)
% 0.27/0.71 (declare-fun tptp.member1437121347_a_a_e (tptp.set_Pr204296108_a_a_e tptp.set_se821189730_a_a_e) Bool)
% 0.27/0.71 (declare-fun tptp.member_set_set_a (tptp.set_set_a tptp.set_set_set_a) Bool)
% 0.27/0.71 (declare-fun tptp.member_set_a (tptp.set_a tptp.set_set_a) Bool)
% 0.27/0.71 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.27/0.71 (declare-fun tptp.c () tptp.set_Pr204296108_a_a_e)
% 0.27/0.71 (declare-fun tptp.a1 () tptp.set_a)
% 0.27/0.71 (declare-fun tptp.a2 () tptp.set_a)
% 0.27/0.71 (declare-fun tptp.a3 () tptp.set_a)
% 0.27/0.71 (declare-fun tptp.b1 (tptp.a) tptp.e)
% 0.27/0.71 (declare-fun tptp.b2 (tptp.a) tptp.e)
% 0.27/0.71 (declare-fun tptp.b3 (tptp.a) tptp.e)
% 0.27/0.71 (declare-fun tptp.thesis () Bool)
% 0.27/0.71 (assert (forall ((X tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X) tptp.c) (forall ((Xa tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.produc1040928388_a_a_e X))) (let ((_let_2 (@ tptp.produc1040928388_a_a_e Xa))) (=> (@ (@ tptp.member1258382221_a_a_e Xa) tptp.c) (or (@ (@ tptp.ord_less_eq_set_a _let_1) _let_2) (@ (@ tptp.ord_less_eq_set_a _let_2) _let_1)))))))))
% 0.27/0.71 (assert (exists ((X2 tptp.set_a)) (and (@ (@ tptp.member_set_a X2) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c)) (@ (@ tptp.ord_less_eq_set_a tptp.a1) X2) (@ (@ tptp.ord_less_eq_set_a tptp.a2) X2) (@ (@ tptp.ord_less_eq_set_a tptp.a3) X2))))
% 0.27/0.71 (assert (or (@ (@ tptp.ord_less_eq_set_a tptp.a1) tptp.a2) (@ (@ tptp.ord_less_eq_set_a tptp.a2) tptp.a1)))
% 0.27/0.71 (assert (or (@ (@ tptp.ord_less_eq_set_a tptp.a1) tptp.a3) (@ (@ tptp.ord_less_eq_set_a tptp.a3) tptp.a1)))
% 0.27/0.71 (assert (or (@ (@ tptp.ord_less_eq_set_a tptp.a2) tptp.a3) (@ (@ tptp.ord_less_eq_set_a tptp.a3) tptp.a2)))
% 0.27/0.71 (assert (@ (@ tptp.member_set_a tptp.a3) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c)))
% 0.27/0.71 (assert (@ (@ tptp.member_set_a tptp.a2) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c)))
% 0.27/0.71 (assert (@ (@ tptp.member_set_a tptp.a1) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c)))
% 0.27/0.71 (assert (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e tptp.a1) tptp.b1)) tptp.c))
% 0.27/0.71 (assert (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e tptp.a2) tptp.b2)) tptp.c))
% 0.27/0.71 (assert (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e tptp.a3) tptp.b3)) tptp.c))
% 0.27/0.71 (assert (forall ((A tptp.set_a_e) (B tptp.set_a_e)) (=> (forall ((X2 (-> tptp.a tptp.e))) (let ((_let_1 (@ tptp.member_a_e X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a_e A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr305929312_set_a) (B tptp.set_Pr305929312_set_a)) (=> (forall ((X2 tptp.produc1965228714_set_a)) (let ((_let_1 (@ tptp.member360729153_set_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le802356416_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a)) (=> (forall ((X2 tptp.set_set_a)) (let ((_let_1 (@ tptp.member_set_set_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le2103863998_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (forall ((X2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le318720350_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le700723212_a_a_e A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (@ (@ tptp.ord_le700723212_a_a_e B) A) (= A B)))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (@ (@ tptp.ord_le318720350_set_a B) A) (= A B)))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (=> (@ (@ tptp.ord_le2103863998_set_a B) A) (= A B)))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (= A B)))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_set_a_set_a F) A))))))
% 0.27/0.71 (assert (forall ((B2 tptp.produc715398134_a_a_e) (F (-> tptp.set_a tptp.produc715398134_a_a_e)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_210900495_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) A))))))
% 0.27/0.71 (assert (forall ((B2 tptp.produc715398134_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e)) (X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_625620211_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (X3 tptp.a) (A tptp.set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a X3) A) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A))))))
% 0.27/0.71 (assert (forall ((B2 tptp.a) (F (-> tptp.set_a tptp.a)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_a B2) (@ (@ tptp.image_set_a_a F) A))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_a) (F (-> tptp.a tptp.set_a)) (X3 tptp.a) (A tptp.set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a X3) A) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_a_set_a F) A))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.a tptp.e)) (F (-> tptp.a tptp.a tptp.e)) (X3 tptp.a) (A tptp.set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a X3) A) (@ (@ tptp.member_a_e B2) (@ (@ tptp.image_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((B2 tptp.a) (F (-> (-> tptp.a tptp.e) tptp.a)) (X3 (-> tptp.a tptp.e)) (A tptp.set_a_e)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a_e X3) A) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_e_a F) A))))))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.a tptp.e)) (F (-> tptp.set_a tptp.a tptp.e)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_a_e B2) (@ (@ tptp.image_set_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Pr204296108_a_a_e)) (@ (@ tptp.ord_le700723212_a_a_e X3) X3)))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_a)) (@ (@ tptp.ord_le318720350_set_a X3) X3)))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_set_a)) (@ (@ tptp.ord_le2103863998_set_a X3) X3)))
% 0.27/0.71 (assert (forall ((X3 (-> Bool tptp.set_a))) (@ (@ tptp.ord_less_eq_o_set_a X3) X3)))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a X3) X3)))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.a tptp.a))) (let ((_let_1 (@ tptp.image_a_a F))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.a tptp.set_a))) (let ((_let_1 (@ tptp.image_a_set_a F))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (F (-> tptp.set_a tptp.a))) (let ((_let_1 (@ tptp.image_set_a_a F))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.a tptp.set_set_a))) (let ((_let_1 (@ tptp.image_a_set_set_a F))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le2103863998_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (F (-> tptp.set_a tptp.set_a))) (let ((_let_1 (@ tptp.image_set_a_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.a))) (let ((_let_1 (@ tptp.image_set_set_a_a F))) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (F (-> tptp.set_a tptp.set_set_a))) (let ((_let_1 (@ tptp.image_1930509541_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (@ (@ tptp.ord_le2103863998_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_a))) (let ((_let_1 (@ tptp.image_402591269_set_a F))) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_set_a))) (let ((_let_1 (@ tptp.image_1956910981_set_a F))) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (@ (@ tptp.ord_le2103863998_set_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.a)) (B tptp.set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_set_a_a F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_set_a_set_a F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.a)) (B tptp.set_a)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_2116492353_a_e_a F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (@ (@ tptp.ord_le700723212_a_a_e (@ (@ tptp.image_210900495_a_a_e F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (B tptp.set_set_a)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_64240033_set_a F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (@ (@ tptp.ord_le700723212_a_a_e (@ (@ tptp.image_625620211_a_a_e F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (F (-> tptp.a tptp.a)) (B tptp.set_a)) (=> (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (F (-> tptp.a tptp.set_a)) (B tptp.set_set_a)) (=> (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_a_set_a F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (F (-> tptp.a tptp.a tptp.e)) (B tptp.set_a_e)) (=> (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A) (@ (@ tptp.member_a_e (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a_e (@ (@ tptp.image_a_a_e F) A)) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_a_e) (F (-> (-> tptp.a tptp.e) tptp.a)) (B tptp.set_a)) (=> (forall ((X2 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member_a_e X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_e_a F) A)) B))))
% 0.27/0.71 (assert (forall ((B tptp.set_a) (F (-> tptp.a tptp.a)) (A tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_a_a F) A)) (not (forall ((C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a C) A) (not (= B (@ (@ tptp.image_a_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_64240033_set_a F) A)) (not (forall ((C tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e C) A) (not (= B (@ (@ tptp.image_64240033_set_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_a) (F (-> tptp.set_a tptp.a)) (A tptp.set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_a_a F) A)) (not (forall ((C tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a C) A) (not (= B (@ (@ tptp.image_set_a_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.a tptp.set_a)) (A tptp.set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_a_set_a F) A)) (not (forall ((C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a C) A) (not (= B (@ (@ tptp.image_a_set_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_a) (F (-> tptp.set_set_a tptp.a)) (A tptp.set_set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_set_a_a F) A)) (not (forall ((C tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a C) A) (not (= B (@ (@ tptp.image_set_set_a_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (A tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_set_a_set_a F) A)) (not (forall ((C tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a C) A) (not (= B (@ (@ tptp.image_set_a_set_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_set_a) (F (-> tptp.a tptp.set_set_a)) (A tptp.set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_a_set_set_a F) A)) (not (forall ((C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a C) A) (not (= B (@ (@ tptp.image_a_set_set_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_a)) (A tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_402591269_set_a F) A)) (not (forall ((C tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a C) A) (not (= B (@ (@ tptp.image_402591269_set_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_set_a) (F (-> tptp.set_a tptp.set_set_a)) (A tptp.set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1930509541_set_a F) A)) (not (forall ((C tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a C) A) (not (= B (@ (@ tptp.image_1930509541_set_a F) C)))))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_set_a)) (A tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1956910981_set_a F) A)) (not (forall ((C tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a C) A) (not (= B (@ (@ tptp.image_1956910981_set_a F) C)))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_a tptp.a)) (A tptp.set_set_a) (B tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_set_a_a F) A)) B) (forall ((X4 tptp.set_a)) (=> (@ (@ tptp.member_set_a X4) A) (@ (@ tptp.member_a (@ F X4)) B))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.a tptp.a)) (A tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A)) B) (forall ((X4 tptp.a)) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_a (@ F X4)) B))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_a tptp.produc715398134_a_a_e)) (A tptp.set_set_a) (B tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.ord_le700723212_a_a_e (@ (@ tptp.image_210900495_a_a_e F) A)) B) (forall ((X4 tptp.set_a)) (=> (@ (@ tptp.member_set_a X4) A) (@ (@ tptp.member1258382221_a_a_e (@ F X4)) B))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_a tptp.set_a)) (A tptp.set_set_a) (B tptp.set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_set_a_set_a F) A)) B) (forall ((X4 tptp.set_a)) (=> (@ (@ tptp.member_set_a X4) A) (@ (@ tptp.member_set_a (@ F X4)) B))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_Pr204296108_a_a_e tptp.set_set_a)) (A tptp.set_se821189730_a_a_e) (B tptp.set_set_set_a)) (= (@ (@ tptp.ord_le2103863998_set_a (@ (@ tptp.image_1441218763_set_a F) A)) B) (forall ((X4 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1437121347_a_a_e X4) A) (@ (@ tptp.member_set_set_a (@ F X4)) B))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_64240033_set_a F) A)) B) (forall ((X4 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X4) A) (@ (@ tptp.member_set_a (@ F X4)) B))))))
% 0.27/0.71 (assert (forall ((B tptp.set_a) (F (-> tptp.a tptp.a)) (A tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_a_a F) A)) (exists ((AA tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a AA) A) (= B (@ (@ tptp.image_a_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_64240033_set_a F) A)) (exists ((AA tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e AA) A) (= B (@ (@ tptp.image_64240033_set_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_a) (F (-> tptp.set_a tptp.a)) (A tptp.set_set_a)) (= (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_a_a F) A)) (exists ((AA tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a AA) A) (= B (@ (@ tptp.image_set_a_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.a tptp.set_a)) (A tptp.set_a)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_a_set_a F) A)) (exists ((AA tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a AA) A) (= B (@ (@ tptp.image_a_set_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_a) (F (-> tptp.set_set_a tptp.a)) (A tptp.set_set_set_a)) (= (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_set_a_a F) A)) (exists ((AA tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a AA) A) (= B (@ (@ tptp.image_set_set_a_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (A tptp.set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_set_a_set_a F) A)) (exists ((AA tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a AA) A) (= B (@ (@ tptp.image_set_a_set_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_set_a) (F (-> tptp.a tptp.set_set_a)) (A tptp.set_a)) (= (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_a_set_set_a F) A)) (exists ((AA tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a AA) A) (= B (@ (@ tptp.image_a_set_set_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_a)) (A tptp.set_set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_402591269_set_a F) A)) (exists ((AA tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a AA) A) (= B (@ (@ tptp.image_402591269_set_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_set_a) (F (-> tptp.set_a tptp.set_set_a)) (A tptp.set_set_a)) (= (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1930509541_set_a F) A)) (exists ((AA tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a AA) A) (= B (@ (@ tptp.image_1930509541_set_a F) AA)))))))
% 0.27/0.71 (assert (forall ((B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_set_a)) (A tptp.set_set_set_a)) (= (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1956910981_set_a F) A)) (exists ((AA tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a AA) A) (= B (@ (@ tptp.image_1956910981_set_a F) AA)))))))
% 0.27/0.71 (assert (forall ((P tptp.produc1965228714_set_a)) (exists ((X2 (-> tptp.a tptp.e)) (Y tptp.set_a)) (= P (@ (@ tptp.produc479206876_set_a X2) Y)))))
% 0.27/0.71 (assert (forall ((P tptp.produc715398134_a_a_e)) (exists ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (= P (@ (@ tptp.produc1134456688_a_a_e X2) Y)))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_Pr204296108_a_a_e) (A2 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) A2) (=> (@ (@ tptp.ord_le700723212_a_a_e A2) B2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_set_a) (A2 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B2) A2) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_set_set_a) (A2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B2) A2) (=> (@ (@ tptp.ord_le2103863998_set_a A2) B2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((B2 (-> Bool tptp.set_a)) (A2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) A2) (=> (@ (@ tptp.ord_less_eq_o_set_a A2) B2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_a) (A2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (= A2 B2)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_Pr204296108_a_a_e) (Z tptp.set_Pr204296108_a_a_e)) (= Y2 Z)) (lambda ((A3 tptp.set_Pr204296108_a_a_e) (B3 tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e B3) A3) (@ (@ tptp.ord_le700723212_a_a_e A3) B3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_set_a) (Z tptp.set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_a) (B3 tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a B3) A3) (@ (@ tptp.ord_le318720350_set_a A3) B3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_set_set_a) (Z tptp.set_set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_set_a) (B3 tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a B3) A3) (@ (@ tptp.ord_le2103863998_set_a A3) B3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 (-> Bool tptp.set_a)) (Z (-> Bool tptp.set_a))) (= Y2 Z)) (lambda ((A3 (-> Bool tptp.set_a)) (B3 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_o_set_a B3) A3) (@ (@ tptp.ord_less_eq_o_set_a A3) B3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_a) (B3 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a B3) A3) (@ (@ tptp.ord_less_eq_set_a A3) B3)))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_Pr204296108_a_a_e) (A2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e C2))) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_set_a) (A2 tptp.set_set_a) (C2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a C2))) (=> (@ (@ tptp.ord_le318720350_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_set_set_a) (A2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a C2))) (=> (@ (@ tptp.ord_le2103863998_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.27/0.71 (assert (forall ((B2 (-> Bool tptp.set_a)) (A2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a C2))) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_a) (A2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_Pr204296108_a_a_e)) (@ (@ tptp.ord_le700723212_a_a_e A2) A2)))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a)) (@ (@ tptp.ord_le318720350_set_a A2) A2)))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_set_a)) (@ (@ tptp.ord_le2103863998_set_a A2) A2)))
% 0.27/0.71 (assert (forall ((A2 (-> Bool tptp.set_a))) (@ (@ tptp.ord_less_eq_o_set_a A2) A2)))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A2) A2)))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Pr204296108_a_a_e) (Y3 tptp.set_Pr204296108_a_a_e) (Z2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le700723212_a_a_e Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_a) (Y3 tptp.set_set_a) (Z2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le318720350_set_a Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_set_a) (Y3 tptp.set_set_set_a) (Z2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le2103863998_set_a Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.71 (assert (forall ((X3 (-> Bool tptp.set_a)) (Y3 (-> Bool tptp.set_a)) (Z2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_o_set_a Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (Y3 tptp.set_a) (Z2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_set_a Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e A2) B2) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) A2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (@ (@ tptp.ord_le318720350_set_a B2) A2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a A2) B2) (=> (@ (@ tptp.ord_le2103863998_set_a B2) A2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) A2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (= A2 B2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (C2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) C2) (@ (@ tptp.ord_le700723212_a_a_e A2) C2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (C2 tptp.set_set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le318720350_set_a B2) C2) (@ (@ tptp.ord_le318720350_set_a A2) C2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le2103863998_set_a B2) C2) (@ (@ tptp.ord_le2103863998_set_a A2) C2)))))
% 0.27/0.71 (assert (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (@ (@ tptp.ord_less_eq_o_set_a A2) C2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (@ (@ tptp.ord_less_eq_set_a A2) C2)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_Pr204296108_a_a_e) (Z tptp.set_Pr204296108_a_a_e)) (= Y2 Z)) (lambda ((A3 tptp.set_Pr204296108_a_a_e) (B3 tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e A3) B3) (@ (@ tptp.ord_le700723212_a_a_e B3) A3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_set_a) (Z tptp.set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_a) (B3 tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a A3) B3) (@ (@ tptp.ord_le318720350_set_a B3) A3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_set_set_a) (Z tptp.set_set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_set_a) (B3 tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a A3) B3) (@ (@ tptp.ord_le2103863998_set_a B3) A3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 (-> Bool tptp.set_a)) (Z (-> Bool tptp.set_a))) (= Y2 Z)) (lambda ((A3 (-> Bool tptp.set_a)) (B3 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_o_set_a A3) B3) (@ (@ tptp.ord_less_eq_o_set_a B3) A3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_a) (B3 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A3) B3) (@ (@ tptp.ord_less_eq_set_a B3) A3)))))
% 0.27/0.71 (assert (forall ((Y3 tptp.set_Pr204296108_a_a_e) (X3 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e Y3) X3) (= (@ (@ tptp.ord_le700723212_a_a_e X3) Y3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((Y3 tptp.set_set_a) (X3 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a Y3) X3) (= (@ (@ tptp.ord_le318720350_set_a X3) Y3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((Y3 tptp.set_set_set_a) (X3 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a Y3) X3) (= (@ (@ tptp.ord_le2103863998_set_a X3) Y3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((Y3 (-> Bool tptp.set_a)) (X3 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a Y3) X3) (= (@ (@ tptp.ord_less_eq_o_set_a X3) Y3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((Y3 tptp.set_a) (X3 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a Y3) X3) (= (@ (@ tptp.ord_less_eq_set_a X3) Y3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (C2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le318720350_set_a B2) C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2103863998_set_a B2) C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (@ _let_1 C2))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Pr204296108_a_a_e) (Y3 tptp.set_Pr204296108_a_a_e)) (=> (= X3 Y3) (@ (@ tptp.ord_le700723212_a_a_e X3) Y3))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_a) (Y3 tptp.set_set_a)) (=> (= X3 Y3) (@ (@ tptp.ord_le318720350_set_a X3) Y3))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_set_a) (Y3 tptp.set_set_set_a)) (=> (= X3 Y3) (@ (@ tptp.ord_le2103863998_set_a X3) Y3))))
% 0.27/0.71 (assert (forall ((X3 (-> Bool tptp.set_a)) (Y3 (-> Bool tptp.set_a))) (=> (= X3 Y3) (@ (@ tptp.ord_less_eq_o_set_a X3) Y3))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (Y3 tptp.set_a)) (=> (= X3 Y3) (@ (@ tptp.ord_less_eq_set_a X3) Y3))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_Pr204296108_a_a_e) (Y3 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e X3) Y3) (=> (@ (@ tptp.ord_le700723212_a_a_e Y3) X3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_a) (Y3 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X3) Y3) (=> (@ (@ tptp.ord_le318720350_set_a Y3) X3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_set_set_a) (Y3 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a X3) Y3) (=> (@ (@ tptp.ord_le2103863998_set_a Y3) X3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((X3 (-> Bool tptp.set_a)) (Y3 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X3) Y3) (=> (@ (@ tptp.ord_less_eq_o_set_a Y3) X3) (= X3 Y3)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (Y3 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y3) (=> (@ (@ tptp.ord_less_eq_set_a Y3) X3) (= X3 Y3)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_Pr204296108_a_a_e) (Z tptp.set_Pr204296108_a_a_e)) (= Y2 Z)) (lambda ((X4 tptp.set_Pr204296108_a_a_e) (Y4 tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e X4) Y4) (@ (@ tptp.ord_le700723212_a_a_e Y4) X4)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_set_a) (Z tptp.set_set_a)) (= Y2 Z)) (lambda ((X4 tptp.set_set_a) (Y4 tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a X4) Y4) (@ (@ tptp.ord_le318720350_set_a Y4) X4)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_set_set_a) (Z tptp.set_set_set_a)) (= Y2 Z)) (lambda ((X4 tptp.set_set_set_a) (Y4 tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a X4) Y4) (@ (@ tptp.ord_le2103863998_set_a Y4) X4)))))
% 0.27/0.71 (assert (= (lambda ((Y2 (-> Bool tptp.set_a)) (Z (-> Bool tptp.set_a))) (= Y2 Z)) (lambda ((X4 (-> Bool tptp.set_a)) (Y4 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_o_set_a X4) Y4) (@ (@ tptp.ord_less_eq_o_set_a Y4) X4)))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((X4 tptp.set_a) (Y4 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a X4) Y4) (@ (@ tptp.ord_less_eq_set_a Y4) X4)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_set_a)) (C2 tptp.set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_le318720350_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le318720350_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_set_set_a)) (C2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_le2103863998_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le2103863998_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_o_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_o_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_set_a)) (C2 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_le318720350_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le318720350_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (F (-> tptp.set_set_set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_set_a) (Y tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (F (-> (-> Bool tptp.set_a) tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_o_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_set_set_a)) (C2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_le2103863998_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le2103863998_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_less_eq_o_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_o_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_Pr204296108_a_a_e) (F (-> (-> Bool tptp.set_a) tptp.set_Pr204296108_a_a_e)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_le700723212_a_a_e (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le700723212_a_a_e A2) (@ F C2)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_a) (F (-> (-> Bool tptp.set_a) tptp.set_set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_le318720350_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le318720350_set_a A2) (@ F C2)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_set_set_a) (F (-> (-> Bool tptp.set_a) tptp.set_set_set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_le2103863998_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le2103863998_set_a A2) (@ F C2)))))))
% 0.27/0.71 (assert (forall ((A2 (-> Bool tptp.set_a)) (F (-> (-> Bool tptp.set_a) Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_less_eq_o_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_o_set_a A2) (@ F C2)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B2 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a A2) (@ F C2)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_set_a (@ F B2)) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ _let_1 (@ F C2))))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (P2 (-> tptp.set_a Bool))) (= (@ (@ tptp.member_set_a A2) (@ tptp.collect_set_a P2)) (@ P2 A2))))
% 0.27/0.71 (assert (forall ((A2 tptp.produc715398134_a_a_e) (P2 (-> tptp.produc715398134_a_a_e Bool))) (= (@ (@ tptp.member1258382221_a_a_e A2) (@ tptp.collec1369693387_a_a_e P2)) (@ P2 A2))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a)) (= (@ tptp.collect_set_a (lambda ((X4 tptp.set_a)) (@ (@ tptp.member_set_a X4) A))) A)))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e)) (= (@ tptp.collec1369693387_a_a_e (lambda ((X4 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X4) A))) A)))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (A tptp.set_set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a))) (=> (@ (@ tptp.member_set_a X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_set_a_set_a F) A))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (A tptp.set_set_a) (B2 tptp.produc715398134_a_a_e) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member_set_a X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_210900495_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) A))))))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (B2 tptp.produc715398134_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_625620211_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_a Bool))) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) (@ (@ tptp.image_64240033_set_a F) A)) (@ P2 X2))) (forall ((X tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X) A) (@ P2 (@ F X)))))))
% 0.27/0.71 (assert (forall ((M tptp.set_Pr204296108_a_a_e) (N tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (G (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (= M N) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) N) (= (@ F X2) (@ G X2)))) (= (@ (@ tptp.image_64240033_set_a F) M) (@ (@ tptp.image_64240033_set_a G) N))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_a Bool))) (=> (exists ((X tptp.set_a)) (and (@ (@ tptp.member_set_a X) (@ (@ tptp.image_64240033_set_a F) A)) (@ P2 X))) (exists ((X2 tptp.produc715398134_a_a_e)) (and (@ (@ tptp.member1258382221_a_a_e X2) A) (@ P2 (@ F X2)))))))
% 0.27/0.71 (assert (forall ((Z2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_set_a Z2) (@ (@ tptp.image_64240033_set_a F) A)) (exists ((X4 tptp.produc715398134_a_a_e)) (and (@ (@ tptp.member1258382221_a_a_e X4) A) (= Z2 (@ F X4)))))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a))) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_set_a (@ F X3)) (@ (@ tptp.image_set_a_set_a F) A)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member1258382221_a_a_e (@ F X3)) (@ (@ tptp.image_210900495_a_a_e F) A)))))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member_set_a (@ F X3)) (@ (@ tptp.image_64240033_set_a F) A)))))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member1258382221_a_a_e (@ F X3)) (@ (@ tptp.image_625620211_a_a_e F) A)))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P2)) (@ tptp.collect_a Q)) (forall ((X4 tptp.a)) (=> (@ P2 X4) (@ Q X4))))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A4) B4) (@ (@ tptp.ord_less_eq_set_a B4) A4)))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C3 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_a B) C3) (@ _let_1 C3))))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X2 tptp.a)) (=> (@ P2 X2) (@ Q X2))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P2)) (@ tptp.collect_a Q)))))
% 0.27/0.71 (assert (= tptp.ord_le318720350_set_a (lambda ((A4 tptp.set_set_a) (B4 tptp.set_set_a)) (forall ((T tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (= tptp.ord_le700723212_a_a_e (lambda ((A4 tptp.set_Pr204296108_a_a_e) (B4 tptp.set_Pr204296108_a_a_e)) (forall ((T tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_a B) A))))
% 0.27/0.71 (assert (= tptp.ord_le318720350_set_a (lambda ((A4 tptp.set_set_a) (B4 tptp.set_set_a)) (forall ((X4 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (= tptp.ord_le700723212_a_a_e (lambda ((A4 tptp.set_Pr204296108_a_a_e) (B4 tptp.set_Pr204296108_a_a_e)) (forall ((X4 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_a A) B) (not (@ (@ tptp.ord_less_eq_set_a B) A)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a C2))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (C2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e C2))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C2 tptp.a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X3))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X3))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.27/0.71 (assert (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e)) (Y1 tptp.set_a) (Y22 (-> tptp.a tptp.e))) (= (= (@ (@ tptp.produc1134456688_a_a_e X1) X22) (@ (@ tptp.produc1134456688_a_a_e Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (A5 tptp.set_a) (B5 (-> tptp.a tptp.e))) (= (= (@ (@ tptp.produc1134456688_a_a_e A2) B2) (@ (@ tptp.produc1134456688_a_a_e A5) B5)) (and (= A2 A5) (= B2 B5)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (P tptp.produc715398134_a_a_e)) (= (= A2 (@ tptp.produc1040928388_a_a_e P)) (exists ((B3 (-> tptp.a tptp.e))) (= P (@ (@ tptp.produc1134456688_a_a_e A2) B3))))))
% 0.27/0.71 (assert (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e))) (= (@ tptp.produc1040928388_a_a_e (@ (@ tptp.produc1134456688_a_a_e X1) X22)) X1)))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (Y3 (-> tptp.a tptp.e)) (A2 tptp.set_a)) (=> (= (@ tptp.produc1040928388_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) A2) (= X3 A2))))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e) (Y3 tptp.set_a) (Z2 (-> tptp.a tptp.e))) (=> (= X3 (@ (@ tptp.produc1134456688_a_a_e Y3) Z2)) (= (@ tptp.produc1040928388_a_a_e X3) Y3))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_set_a Bool))) (= (forall ((B4 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B4) (@ (@ tptp.image_64240033_set_a F) A)) (@ P2 B4))) (forall ((B4 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e B4) A) (@ P2 (@ (@ tptp.image_64240033_set_a F) B4)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.a tptp.a)) (A tptp.set_a) (P2 (-> tptp.set_a Bool))) (= (forall ((B4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B4) (@ (@ tptp.image_a_a F) A)) (@ P2 B4))) (forall ((B4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B4) A) (@ P2 (@ (@ tptp.image_a_a F) B4)))))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.set_a Bool)) (X3 tptp.set_a)) (=> (@ P2 X3) (=> (forall ((Y tptp.set_a)) (=> (@ P2 Y) (@ (@ tptp.ord_less_eq_set_a Y) X3))) (= (@ tptp.order_Greatest_set_a P2) X3)))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.set_a Bool)) (X3 tptp.set_a) (Q (-> tptp.set_a Bool))) (=> (@ P2 X3) (=> (forall ((Y tptp.set_a)) (=> (@ P2 Y) (@ (@ tptp.ord_less_eq_set_a Y) X3))) (=> (forall ((X2 tptp.set_a)) (=> (@ P2 X2) (=> (forall ((Y5 tptp.set_a)) (=> (@ P2 Y5) (@ (@ tptp.ord_less_eq_set_a Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_Greatest_set_a P2)))))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.produc715398134_a_a_e Bool)) (Prod tptp.produc715398134_a_a_e)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (@ P2 (@ (@ tptp.produc1134456688_a_a_e A6) B6))) (@ P2 Prod))))
% 0.27/0.71 (assert (forall ((Y3 tptp.produc715398134_a_a_e)) (not (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (not (= Y3 (@ (@ tptp.produc1134456688_a_a_e A6) B6)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (A5 tptp.set_a) (B5 (-> tptp.a tptp.e))) (=> (= (@ (@ tptp.produc1134456688_a_a_e A2) B2) (@ (@ tptp.produc1134456688_a_a_e A5) B5)) (not (=> (= A2 A5) (not (= B2 B5)))))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.produc715398134_a_a_e Bool)) (P tptp.produc715398134_a_a_e)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (@ P2 (@ (@ tptp.produc1134456688_a_a_e A6) B6))) (@ P2 P))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) B) (@ (@ tptp.ord_le2103863998_set_a (@ (@ tptp.image_1441218763_set_a _let_1) (@ tptp.finite33065488_a_a_e A))) (@ tptp.finite_Fpow_set_a B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (not (@ (@ tptp.ord_le318720350_set_a A) B)) (exists ((A6 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a A6))) (and (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (not (@ (@ tptp.ord_le700723212_a_a_e A) B)) (exists ((A6 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e A6))) (and (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (not (@ (@ tptp.ord_less_eq_set_a A) B)) (exists ((A6 tptp.a)) (let ((_let_1 (@ tptp.member_a A6))) (and (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.ord_le318720350_set_a B) A))) (let ((_let_2 (@ tptp.member_set_a X3))) (=> (or (@ (@ tptp.ord_le318720350_set_a A) B) _let_1) (=> (@ _let_2 A) (=> (not (@ _let_2 B)) _let_1)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ (@ tptp.ord_le700723212_a_a_e B) A))) (let ((_let_2 (@ tptp.member1258382221_a_a_e X3))) (=> (or (@ (@ tptp.ord_le700723212_a_a_e A) B) _let_1) (=> (@ _let_2 A) (=> (not (@ _let_2 B)) _let_1)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ (@ tptp.ord_less_eq_set_a B) A))) (let ((_let_2 (@ tptp.member_a X3))) (=> (or (@ (@ tptp.ord_less_eq_set_a A) B) _let_1) (=> (@ _let_2 A) (=> (not (@ _let_2 B)) _let_1)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ tptp.finite_Fpow_a A)) (@ tptp.finite_Fpow_a B)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) C2)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C2))) (=> (= A2 B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) A)) (exists ((X2 tptp.produc715398134_a_a_e)) (and (@ (@ tptp.member1258382221_a_a_e X2) A) (= B2 (@ F X2)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_set_a_set_a F) A)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_210900495_a_a_e F) A)))))
% 0.27/0.71 (assert (forall ((A2 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_64240033_set_a F) A)))))
% 0.27/0.71 (assert (forall ((A2 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_625620211_a_a_e F) A)))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_set_a) (A2 tptp.set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_set_a_set_a F) A))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (B tptp.set_set_a) (A2 tptp.produc715398134_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_64240033_set_a F) A))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e) (A2 tptp.set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_210900495_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e) (A2 tptp.produc715398134_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_625620211_a_a_e F) A))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X3))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (not (= A B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X3))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (not (= A B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (not (= A B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (not (@ (@ tptp.ord_le318720350_set_a A) B)) (exists ((X2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X2))) (and (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (not (@ (@ tptp.ord_le700723212_a_a_e A) B)) (exists ((X2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X2))) (and (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (not (@ (@ tptp.ord_less_eq_set_a A) B)) (exists ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (and (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A) A)))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (not (= A B)) (=> (@ (@ tptp.ord_le318720350_set_a B) A) (exists ((X2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X2))) (and (@ _let_1 A) (not (@ _let_1 B)))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (not (= A B)) (=> (@ (@ tptp.ord_le700723212_a_a_e B) A) (exists ((X2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X2))) (and (@ _let_1 A) (not (@ _let_1 B)))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (exists ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (and (@ _let_1 A) (not (@ _let_1 B)))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.ord_le318720350_set_a A) B))) (let ((_let_2 (@ tptp.member_set_a X3))) (=> (or _let_1 (@ (@ tptp.ord_le318720350_set_a B) A)) (=> (not (@ _let_2 A)) (=> (@ _let_2 B) _let_1)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ (@ tptp.ord_le700723212_a_a_e A) B))) (let ((_let_2 (@ tptp.member1258382221_a_a_e X3))) (=> (or _let_1 (@ (@ tptp.ord_le700723212_a_a_e B) A)) (=> (not (@ _let_2 A)) (=> (@ _let_2 B) _let_1)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ (@ tptp.ord_less_eq_set_a A) B))) (let ((_let_2 (@ tptp.member_a X3))) (=> (or _let_1 (@ (@ tptp.ord_less_eq_set_a B) A)) (=> (not (@ _let_2 A)) (=> (@ _let_2 B) _let_1)))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) B) (@ (@ tptp.ord_le2103863998_set_a (@ (@ tptp.image_1441218763_set_a _let_1) (@ tptp.pow_Pr328302361_a_a_e A))) (@ tptp.pow_set_a B))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (C3 (-> tptp.produc715398134_a_a_e tptp.set_a)) (D (-> tptp.produc715398134_a_a_e tptp.set_a)) (Sup (-> tptp.set_set_a tptp.set_a))) (=> (= A B) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) B) (= (@ C3 X2) (@ D X2)))) (= (@ Sup (@ (@ tptp.image_64240033_set_a C3) A)) (@ Sup (@ (@ tptp.image_64240033_set_a D) B)))))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (C3 (-> tptp.produc715398134_a_a_e tptp.set_a)) (D (-> tptp.produc715398134_a_a_e tptp.set_a)) (Inf (-> tptp.set_set_a tptp.set_a))) (=> (= A B) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) B) (= (@ C3 X2) (@ D X2)))) (= (@ Inf (@ (@ tptp.image_64240033_set_a C3) A)) (@ Inf (@ (@ tptp.image_64240033_set_a D) B)))))))
% 0.27/0.71 (assert (forall ((R tptp.set_Pr204296108_a_a_e) (S tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (let ((_let_1 (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X2) Y)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le700723212_a_a_e R) S))))
% 0.27/0.71 (assert (forall ((R tptp.set_a) (S (-> tptp.a tptp.e)) (R2 tptp.set_Pr204296108_a_a_e) (S2 (-> tptp.a tptp.e))) (let ((_let_1 (@ tptp.produc1134456688_a_a_e R))) (=> (@ (@ tptp.member1258382221_a_a_e (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1258382221_a_a_e (@ _let_1 S2)) R2))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.member_set_a A) (@ tptp.pow_a B)))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.member_set_a A) (@ tptp.pow_a B)) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_a)) (@ (@ tptp.member_set_a A) (@ tptp.pow_a A))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.member_set_a A) (@ tptp.pow_a B)) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ tptp.pow_a A)) (@ tptp.pow_a B)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (= (@ _let_1 A) B) (= (@ (@ tptp.image_1441218763_set_a _let_1) (@ tptp.pow_Pr328302361_a_a_e A)) (@ tptp.pow_set_a B))))))
% 0.27/0.71 (assert (= tptp.ord_less_eq_o_set_a (lambda ((X5 (-> Bool tptp.set_a)) (Y6 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_set_a (@ X5 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_set_a (@ X5 true)) (@ Y6 true))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e Bool)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (=> (@ F (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ (@ (@ tptp.produc952037978_a_e_o F) A2) B2))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e Bool)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (=> (@ (@ (@ tptp.produc952037978_a_e_o F) A2) B2) (@ F (@ (@ tptp.produc1134456688_a_a_e A2) B2)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e Bool)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (=> (@ (@ (@ tptp.produc952037978_a_e_o F) A2) B2) (@ F (@ (@ tptp.produc1134456688_a_a_e A2) B2)))))
% 0.27/0.71 (assert (forall ((R2 tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) R2) (@ tptp.domain_set_a_a_e R2))))
% 0.27/0.71 (assert (= tptp.domain_set_a_a_e (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e)))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_a_e B2) (@ tptp.range_set_a_a_e R)) (not (forall ((A6 tptp.set_a)) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B2)) R)))))))
% 0.27/0.71 (assert (forall ((A2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_a_e A2) (@ tptp.range_set_a_a_e R)) (exists ((Y4 tptp.set_a)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e Y4) A2)) R)))))
% 0.27/0.71 (assert (forall ((A2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_a_e A2) (@ tptp.range_set_a_a_e R)) (not (forall ((A6 tptp.set_a)) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) A2)) R)))))))
% 0.27/0.71 (assert (forall ((A2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_a_e A2) (@ tptp.range_set_a_a_e R)) (exists ((A3 tptp.set_a) (B3 (-> tptp.a tptp.e))) (and (= A2 B3) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A3) B3)) R))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R) (@ (@ tptp.member_a_e B2) (@ tptp.range_set_a_a_e R)))))
% 0.27/0.71 (assert (forall ((X3 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e) (P2 (-> (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member_a_e X3) (@ tptp.range_set_a_a_e R)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B6)) R) (@ P2 B6))) (@ P2 X3)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (not (forall ((B6 (-> tptp.a tptp.e))) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B6)) R)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (exists ((Y4 (-> tptp.a tptp.e))) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) Y4)) R)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (not (forall ((B6 (-> tptp.a tptp.e))) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B6)) R)))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (exists ((A3 tptp.set_a) (B3 (-> tptp.a tptp.e))) (and (= A2 A3) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A3) B3)) R))))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R) (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (R tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_a Bool))) (=> (@ (@ tptp.member_set_a X3) (@ tptp.domain_set_a_a_e R)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B6)) R) (@ P2 A6))) (@ P2 X3)))))
% 0.27/0.71 (assert (forall ((Y3 (-> tptp.a tptp.e)) (X3 tptp.set_a) (A tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a Y3) X3)) (@ (@ tptp.image_1875450791_set_a tptp.produc755714512_a_a_e) A)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) A))))
% 0.27/0.71 (assert (forall ((Y3 tptp.set_a) (X3 (-> tptp.a tptp.e)) (A tptp.set_Pr305929312_set_a)) (= (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e Y3) X3)) (@ (@ tptp.image_376979367_a_a_e tptp.produc100464700_set_a) A)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a X3) Y3)) A))))
% 0.27/0.71 (assert (forall ((X3 (-> tptp.a tptp.e)) (Y3 tptp.set_a)) (= (@ tptp.produc100464700_set_a (@ (@ tptp.produc479206876_set_a X3) Y3)) (@ (@ tptp.produc1134456688_a_a_e Y3) X3))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (Y3 (-> tptp.a tptp.e))) (= (@ tptp.produc755714512_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) (@ (@ tptp.produc479206876_set_a Y3) X3))))
% 0.27/0.71 (assert (forall ((A2 (-> tptp.a tptp.e)) (B2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A2) B2)) (@ tptp.converse_set_a_a_e R)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) A2)) R))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (= (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ tptp.converse_a_e_set_a R)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a B2) A2)) R))))
% 0.27/0.71 (assert (forall ((X1 (-> tptp.a tptp.e)) (X22 tptp.set_a) (R tptp.set_Pr204296108_a_a_e) (P2 (-> (-> tptp.a tptp.e) tptp.set_a Bool))) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a X1) X22)) (@ tptp.converse_set_a_a_e R)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B6)) R) (@ (@ P2 B6) A6))) (@ (@ P2 X1) X22)))))
% 0.27/0.71 (assert (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a) (P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X1) X22)) (@ tptp.converse_a_e_set_a R)) (=> (forall ((A6 (-> tptp.a tptp.e)) (B6 tptp.set_a)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A6) B6)) R) (@ (@ P2 B6) A6))) (@ (@ P2 X1) X22)))))
% 0.27/0.71 (assert (forall ((A2 (-> tptp.a tptp.e)) (B2 tptp.set_a) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A2) B2)) R) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) A2)) (@ tptp.converse_a_e_set_a R)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a B2) A2)) (@ tptp.converse_set_a_a_e R)))))
% 0.27/0.71 (assert (forall ((A1 (-> tptp.a tptp.e)) (A22 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A1) A22)) (@ tptp.converse_set_a_a_e R)) (exists ((A3 tptp.set_a) (B3 (-> tptp.a tptp.e))) (and (= A1 B3) (= A22 A3) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A3) B3)) R))))))
% 0.27/0.71 (assert (forall ((A1 tptp.set_a) (A22 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (= (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A1) A22)) (@ tptp.converse_a_e_set_a R)) (exists ((A3 (-> tptp.a tptp.e)) (B3 tptp.set_a)) (and (= A1 B3) (= A22 A3) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A3) B3)) R))))))
% 0.27/0.71 (assert (forall ((A1 (-> tptp.a tptp.e)) (A22 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A1) A22)) (@ tptp.converse_set_a_a_e R)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A22) A1)) R))))
% 0.27/0.71 (assert (forall ((A1 tptp.set_a) (A22 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A1) A22)) (@ tptp.converse_a_e_set_a R)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A22) A1)) R))))
% 0.27/0.71 (assert (forall ((Yx tptp.produc1965228714_set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member360729153_set_a Yx) (@ tptp.converse_set_a_a_e R)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= Yx (@ (@ tptp.produc479206876_set_a Y) X2)) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X2) Y)) R))))))))
% 0.27/0.71 (assert (forall ((Yx tptp.produc715398134_a_a_e) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member1258382221_a_a_e Yx) (@ tptp.converse_a_e_set_a R)) (not (forall ((X2 (-> tptp.a tptp.e)) (Y tptp.set_a)) (=> (= Yx (@ (@ tptp.produc1134456688_a_a_e Y) X2)) (not (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a X2) Y)) R))))))))
% 0.27/0.71 (assert (forall ((A2 (-> tptp.a tptp.e)) (B2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A2) B2)) (@ tptp.converse_set_a_a_e R)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) A2)) R))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ tptp.converse_a_e_set_a R)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a B2) A2)) R))))
% 0.27/0.71 (assert (= tptp.produc100464700_set_a (lambda ((P3 tptp.produc1965228714_set_a)) (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1809800494_set_a P3)) (@ tptp.produc385678576_set_a P3)))))
% 0.27/0.71 (assert (= tptp.produc755714512_a_a_e (lambda ((P3 tptp.produc715398134_a_a_e)) (@ (@ tptp.produc479206876_set_a (@ tptp.produc317566658_a_a_e P3)) (@ tptp.produc1040928388_a_a_e P3)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R2 tptp.set_Pr204296108_a_a_e) (F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R2) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e (@ F A2)) (@ G B2))) (@ (@ tptp.image_625620211_a_a_e (@ (@ tptp.produc1443219402_e_a_e F) G)) R2)))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a)) (@ (@ tptp.member_set_a X3) tptp.top_top_set_set_a)))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X3) tptp.top_to1601855068_a_a_e)))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (= (@ (@ (@ tptp.produc1443219402_e_a_e F) G) (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ (@ tptp.produc1134456688_a_a_e (@ F A2)) (@ G B2)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e)) (X3 tptp.produc715398134_a_a_e)) (= (@ tptp.produc1040928388_a_a_e (@ (@ (@ tptp.produc1443219402_e_a_e F) G) X3)) (@ F (@ tptp.produc1040928388_a_a_e X3)))))
% 0.27/0.71 (assert (forall ((Prod tptp.produc715398134_a_a_e)) (= (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1040928388_a_a_e Prod)) (@ tptp.produc317566658_a_a_e Prod)) Prod)))
% 0.27/0.71 (assert (forall ((X3 tptp.produc1965228714_set_a)) (= (@ tptp.produc1040928388_a_a_e (@ tptp.produc100464700_set_a X3)) (@ tptp.produc1809800494_set_a X3))))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e)) (= (@ tptp.produc1809800494_set_a (@ tptp.produc755714512_a_a_e X3)) (@ tptp.produc1040928388_a_a_e X3))))
% 0.27/0.71 (assert (= (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e)) (@ (@ tptp.member_set_a (@ F X3)) (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e))))
% 0.27/0.71 (assert (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e)) (=> (= B2 (@ F X3)) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e)))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a))) (= (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (forall ((Y4 tptp.set_a)) (exists ((X4 tptp.produc715398134_a_a_e)) (= Y4 (@ F X4)))))))
% 0.27/0.71 (assert (forall ((G (-> tptp.produc715398134_a_a_e tptp.set_a)) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (forall ((X2 tptp.set_a)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_64240033_set_a G) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (Y3 tptp.set_a)) (=> (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (not (forall ((X2 tptp.produc715398134_a_a_e)) (not (= Y3 (@ F X2))))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (Y3 tptp.set_a)) (=> (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (exists ((X2 tptp.produc715398134_a_a_e)) (= Y3 (@ F X2))))))
% 0.27/0.71 (assert (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (G (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (=> (= (@ (@ tptp.image_64240033_set_a G) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (= (@ (@ tptp.image_2101504031_set_a (@ (@ tptp.produc387505142_set_a F) G)) tptp.top_to970499581_a_a_e) tptp.top_to144004695_set_a)))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a tptp.top_top_set_a) A2) (= A2 tptp.top_top_set_a))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a tptp.top_top_set_a) A2) (= A2 tptp.top_top_set_a))))
% 0.27/0.71 (assert (forall ((A2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A2) tptp.top_top_set_a)))
% 0.27/0.71 (assert (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A) tptp.top_top_set_a)))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e) (Y3 tptp.set_a) (Z2 (-> tptp.a tptp.e))) (=> (= X3 (@ (@ tptp.produc1134456688_a_a_e Y3) Z2)) (= (@ tptp.produc317566658_a_a_e X3) Z2))))
% 0.27/0.71 (assert (forall ((X3 tptp.set_a) (Y3 (-> tptp.a tptp.e)) (A2 (-> tptp.a tptp.e))) (=> (= (@ tptp.produc317566658_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) A2) (= Y3 A2))))
% 0.27/0.71 (assert (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e))) (= (@ tptp.produc317566658_a_a_e (@ (@ tptp.produc1134456688_a_a_e X1) X22)) X22)))
% 0.27/0.71 (assert (forall ((B2 (-> tptp.a tptp.e)) (P tptp.produc715398134_a_a_e)) (= (= B2 (@ tptp.produc317566658_a_a_e P)) (exists ((A3 tptp.set_a)) (= P (@ (@ tptp.produc1134456688_a_a_e A3) B2))))))
% 0.27/0.71 (assert (= (lambda ((Y2 tptp.produc715398134_a_a_e) (Z tptp.produc715398134_a_a_e)) (= Y2 Z)) (lambda ((S3 tptp.produc715398134_a_a_e) (T tptp.produc715398134_a_a_e)) (and (= (@ tptp.produc1040928388_a_a_e S3) (@ tptp.produc1040928388_a_a_e T)) (= (@ tptp.produc317566658_a_a_e S3) (@ tptp.produc317566658_a_a_e T))))))
% 0.27/0.71 (assert (forall ((Prod tptp.produc715398134_a_a_e) (Prod2 tptp.produc715398134_a_a_e)) (=> (and (= (@ tptp.produc1040928388_a_a_e Prod) (@ tptp.produc1040928388_a_a_e Prod2)) (= (@ tptp.produc317566658_a_a_e Prod) (@ tptp.produc317566658_a_a_e Prod2))) (= Prod Prod2))))
% 0.27/0.71 (assert (forall ((P tptp.produc715398134_a_a_e) (Q2 tptp.produc715398134_a_a_e)) (=> (= (@ tptp.produc1040928388_a_a_e P) (@ tptp.produc1040928388_a_a_e Q2)) (=> (= (@ tptp.produc317566658_a_a_e P) (@ tptp.produc317566658_a_a_e Q2)) (= P Q2)))))
% 0.27/0.71 (assert (forall ((A tptp.set_set_a)) (=> (forall ((X2 tptp.set_a)) (@ (@ tptp.member_set_a X2) A)) (= tptp.top_top_set_set_a A))))
% 0.27/0.71 (assert (forall ((A tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X2) A)) (= tptp.top_to1601855068_a_a_e A))))
% 0.27/0.71 (assert (exists ((X2 tptp.set_a)) (@ (@ tptp.member_set_a X2) tptp.top_top_set_set_a)))
% 0.27/0.71 (assert (exists ((X2 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X2) tptp.top_to1601855068_a_a_e)))
% 0.27/0.71 (assert (forall ((T2 tptp.produc715398134_a_a_e)) (= T2 (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1040928388_a_a_e T2)) (@ tptp.produc317566658_a_a_e T2)))))
% 0.27/0.71 (assert (forall ((Prod tptp.produc715398134_a_a_e)) (= Prod (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1040928388_a_a_e Prod)) (@ tptp.produc317566658_a_a_e Prod)))))
% 0.27/0.71 (assert (forall ((C2 tptp.produc715398134_a_a_e) (F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e)) (R2 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e C2) (@ (@ tptp.image_625620211_a_a_e (@ (@ tptp.produc1443219402_e_a_e F) G)) R2)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= C2 (@ (@ tptp.produc1134456688_a_a_e (@ F X2)) (@ G Y))) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X2) Y)) R2))))))))
% 0.27/0.71 (assert (forall ((P2 (-> (-> tptp.a tptp.e) tptp.set_a Bool)) (Y3 (-> tptp.a tptp.e)) (X3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.produc1134456688_a_a_e X3) Y3))) (=> (@ (@ P2 Y3) X3) (@ (@ P2 (@ tptp.produc317566658_a_a_e _let_1)) (@ tptp.produc1040928388_a_a_e _let_1))))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.set_a Bool)) (P tptp.set_a) (Q (-> (-> tptp.a tptp.e) Bool)) (Q2 (-> tptp.a tptp.e))) (let ((_let_1 (@ (@ tptp.produc1134456688_a_a_e P) Q2))) (=> (@ P2 P) (=> (@ Q Q2) (and (@ P2 (@ tptp.produc1040928388_a_a_e _let_1)) (@ Q (@ tptp.produc317566658_a_a_e _let_1))))))))
% 0.27/0.71 (assert (forall ((P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (X3 tptp.set_a) (Y3 (-> tptp.a tptp.e)) (A2 tptp.produc715398134_a_a_e)) (=> (@ (@ P2 X3) Y3) (=> (= A2 (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) (@ (@ P2 (@ tptp.produc1040928388_a_a_e A2)) (@ tptp.produc317566658_a_a_e A2))))))
% 0.27/0.71 (assert (= tptp.top_top_set_a_o (lambda ((X4 tptp.set_a)) (@ (@ tptp.member_set_a X4) tptp.top_top_set_set_a))))
% 0.27/0.71 (assert (= tptp.top_to2000253225_a_e_o (lambda ((X4 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X4) tptp.top_to1601855068_a_a_e))))
% 0.27/0.71 (assert (forall ((P2 (-> (-> tptp.a tptp.e) tptp.set_a Bool)) (P tptp.produc715398134_a_a_e)) (=> (@ (@ P2 (@ tptp.produc317566658_a_a_e P)) (@ tptp.produc1040928388_a_a_e P)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (not (@ (@ P2 Y) X2)))))))
% 0.27/0.71 (assert (forall ((X6 tptp.set_set_a) (A tptp.set_Pr204296108_a_a_e) (Y7 tptp.set_a_e) (P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Q (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e A))) (=> (= X6 (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) A)) (=> (= Y7 (@ (@ tptp.image_1149879910_e_a_e tptp.produc317566658_a_a_e) A)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) X6) (forall ((Xa2 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member_a_e Xa2) Y7) (=> (@ (@ P2 X2) Xa2) (@ (@ Q X2) Xa2)))))) (=> (@ _let_1 (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o P2))) (@ _let_1 (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o Q))))))))))
% 0.27/0.71 (assert (= tptp.bNF_sn375433437_a_a_e (lambda ((P4 (-> tptp.set_a tptp.set_a Bool)) (Q3 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Ac tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.produc317566658_a_a_e Ac))) (@ (@ tptp.produc1134456688_a_a_e (@ (@ (@ (@ tptp.bNF_pi929741261_a_a_e P4) Q3) (@ tptp.produc1040928388_a_a_e Ac)) _let_1)) _let_1)))))
% 0.27/0.71 (assert (forall ((X3 tptp.produc715398134_a_a_e) (A (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e X3) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o A))) (@ (@ A (@ tptp.produc1040928388_a_a_e X3)) (@ tptp.produc317566658_a_a_e X3)))))
% 0.27/0.71 (assert (= tptp.bNF_fs1024561536_e_a_e (lambda ((P4 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Q3 (-> (-> tptp.a tptp.e) (-> tptp.a tptp.e) Bool)) (Ac tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.produc1040928388_a_a_e Ac))) (@ (@ tptp.produc1134456688_a_a_e _let_1) (@ (@ (@ (@ tptp.bNF_pi1175744974_e_a_e P4) Q3) _let_1) (@ tptp.produc317566658_a_a_e Ac)))))))
% 0.27/0.71 (assert (forall ((Z2 tptp.set_a) (C2 (-> tptp.set_a (-> tptp.a tptp.e) tptp.set_set_a)) (P tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member_set_a Z2) (@ (@ tptp.produc1620938593_set_a C2) P)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= P (@ (@ tptp.produc1134456688_a_a_e X2) Y)) (not (@ (@ tptp.member_set_a Z2) (@ (@ C2 X2) Y)))))))))
% 0.27/0.71 (assert (forall ((Z2 tptp.produc715398134_a_a_e) (C2 (-> tptp.set_a (-> tptp.a tptp.e) tptp.set_Pr204296108_a_a_e)) (P tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e Z2) (@ (@ tptp.produc1096319049_a_a_e C2) P)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= P (@ (@ tptp.produc1134456688_a_a_e X2) Y)) (not (@ (@ tptp.member1258382221_a_a_e Z2) (@ (@ C2 X2) Y)))))))))
% 0.27/0.71 (assert (= tptp.fun_in_rel_set_a_a_e (lambda ((R3 tptp.set_Pr204296108_a_a_e) (X4 tptp.set_a) (Y4 (-> tptp.a tptp.e))) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X4) Y4)) R3))))
% 0.27/0.71 (assert (forall ((Ac2 tptp.produc715398134_a_a_e) (P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Q (-> (-> tptp.a tptp.e) (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e Ac2) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o (@ (@ tptp.relcom658603713_e_a_e P2) Q)))) (@ (@ tptp.member1258382221_a_a_e (@ (@ (@ tptp.bNF_fs1024561536_e_a_e P2) Q) Ac2)) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o P2))))))
% 0.27/0.71 (assert (forall ((Ac2 tptp.produc715398134_a_a_e) (P2 (-> tptp.set_a tptp.set_a Bool)) (Q (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e Ac2) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o (@ (@ tptp.relcom779348378_a_a_e P2) Q)))) (@ (@ tptp.member1258382221_a_a_e (@ (@ (@ tptp.bNF_sn375433437_a_a_e P2) Q) Ac2)) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o Q))))))
% 0.81/1.06 (assert (forall ((B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (X3 tptp.set_a) (C2 (-> tptp.a tptp.e)) (G (-> tptp.set_a tptp.a tptp.e)) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (= C2 (@ G X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) C2)) (@ (@ (@ tptp.bNF_Gr1872575811_a_a_e A) F) G)))))))
% 0.81/1.06 (assert (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e) (C2 (-> tptp.a tptp.e)) (G (-> tptp.produc715398134_a_a_e tptp.a tptp.e)) (A tptp.set_Pr204296108_a_a_e)) (=> (= B2 (@ F X3)) (=> (= C2 (@ G X3)) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) C2)) (@ (@ (@ tptp.bNF_Gr2072183031_a_a_e A) F) G)))))))
% 0.81/1.06 (assert (forall ((A7 tptp.set_a)) (=> (@ (@ tptp.member_set_a A7) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c)) (=> (@ (@ tptp.ord_less_eq_set_a tptp.a1) A7) (=> (@ (@ tptp.ord_less_eq_set_a tptp.a2) A7) (=> (@ (@ tptp.ord_less_eq_set_a tptp.a3) A7) tptp.thesis))))))
% 0.81/1.06 (assert (not tptp.thesis))
% 0.81/1.06 (set-info :filename cvc5---1.0.5_13318)
% 0.81/1.06 (check-sat-assuming ( true ))
% 0.81/1.06 ------- get file name : TPTP file name is ITP028^1
% 0.81/1.06 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13318.smt2...
% 0.81/1.06 --- Run --ho-elim --full-saturate-quant at 10...
% 0.81/1.06 % SZS status Theorem for ITP028^1
% 0.81/1.06 % SZS output start Proof for ITP028^1
% 0.81/1.06 (
% 0.81/1.06 (let ((_let_1 (not tptp.thesis))) (let ((_let_2 (forall ((A7 tptp.set_a)) (=> (@ (@ tptp.member_set_a A7) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c)) (=> (@ (@ tptp.ord_less_eq_set_a tptp.a1) A7) (=> (@ (@ tptp.ord_less_eq_set_a tptp.a2) A7) (=> (@ (@ tptp.ord_less_eq_set_a tptp.a3) A7) tptp.thesis))))))) (let ((_let_3 (= tptp.fun_in_rel_set_a_a_e (lambda ((R3 tptp.set_Pr204296108_a_a_e) (X4 tptp.set_a) (Y4 (-> tptp.a tptp.e))) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X4) Y4)) R3))))) (let ((_let_4 (= tptp.bNF_fs1024561536_e_a_e (lambda ((P4 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Q3 (-> (-> tptp.a tptp.e) (-> tptp.a tptp.e) Bool)) (Ac tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.produc1040928388_a_a_e Ac))) (@ (@ tptp.produc1134456688_a_a_e _let_1) (@ (@ (@ (@ tptp.bNF_pi1175744974_e_a_e P4) Q3) _let_1) (@ tptp.produc317566658_a_a_e Ac)))))))) (let ((_let_5 (= tptp.bNF_sn375433437_a_a_e (lambda ((P4 (-> tptp.set_a tptp.set_a Bool)) (Q3 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Ac tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.produc317566658_a_a_e Ac))) (@ (@ tptp.produc1134456688_a_a_e (@ (@ (@ (@ tptp.bNF_pi929741261_a_a_e P4) Q3) (@ tptp.produc1040928388_a_a_e Ac)) _let_1)) _let_1)))))) (let ((_let_6 (= tptp.top_to2000253225_a_e_o (lambda ((X4 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X4) tptp.top_to1601855068_a_a_e))))) (let ((_let_7 (= tptp.top_top_set_a_o (lambda ((X4 tptp.set_a)) (@ (@ tptp.member_set_a X4) tptp.top_top_set_set_a))))) (let ((_let_8 (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e))) (let ((_let_9 (= (@ _let_8 tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a))) (let ((_let_10 (= tptp.produc755714512_a_a_e (lambda ((P3 tptp.produc715398134_a_a_e)) (@ (@ tptp.produc479206876_set_a (@ tptp.produc317566658_a_a_e P3)) (@ tptp.produc1040928388_a_a_e P3)))))) (let ((_let_11 (= tptp.produc100464700_set_a (lambda ((P3 tptp.produc1965228714_set_a)) (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1809800494_set_a P3)) (@ tptp.produc385678576_set_a P3)))))) (let ((_let_12 (= tptp.domain_set_a_a_e _let_8))) (let ((_let_13 (= tptp.ord_less_eq_o_set_a (lambda ((X5 (-> Bool tptp.set_a)) (Y6 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_set_a (@ X5 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_set_a (@ X5 true)) (@ Y6 true))))))) (let ((_let_14 (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))) (let ((_let_15 (= tptp.ord_le700723212_a_a_e (lambda ((A4 tptp.set_Pr204296108_a_a_e) (B4 tptp.set_Pr204296108_a_a_e)) (forall ((T tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))) (let ((_let_16 (= tptp.ord_le318720350_set_a (lambda ((A4 tptp.set_set_a) (B4 tptp.set_set_a)) (forall ((T tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))) (let ((_let_17 (@ _let_8 tptp.c))) (let ((_let_18 (@ tptp.ord_less_eq_set_a tptp.a3))) (let ((_let_19 (@ tptp.ord_less_eq_set_a tptp.a2))) (let ((_let_20 (@ tptp.ord_less_eq_set_a tptp.a1))) (let ((_let_21 (exists ((X2 tptp.set_a)) (and (@ (@ tptp.member_set_a X2) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c)) (@ (@ tptp.ord_less_eq_set_a tptp.a1) X2) (@ (@ tptp.ord_less_eq_set_a tptp.a2) X2) (@ (@ tptp.ord_less_eq_set_a tptp.a3) X2))))) (let ((_let_22 (forall ((A7 tptp.set_a)) (or (not (ho_82 (ho_84 k_83 A7) (ho_130 (ho_129 k_128 k_52) tptp.c))) (not (forall ((T tptp.a)) (let ((_let_1 (ho_72 k_71 T))) (or (not (ho_70 _let_1 tptp.a1)) (ho_70 _let_1 A7))))) (not (forall ((T tptp.a)) (let ((_let_1 (ho_72 k_71 T))) (or (not (ho_70 _let_1 tptp.a2)) (ho_70 _let_1 A7))))) (not (forall ((T tptp.a)) (let ((_let_1 (ho_72 k_71 T))) (or (not (ho_70 _let_1 tptp.a3)) (ho_70 _let_1 A7))))))))) (let ((_let_23 (forall ((X2 tptp.set_a)) (or (not (ho_82 (ho_84 k_83 X2) (ho_130 (ho_129 k_128 k_52) tptp.c))) (not (forall ((T tptp.a)) (let ((_let_1 (ho_72 k_71 T))) (or (not (ho_70 _let_1 tptp.a1)) (ho_70 _let_1 X2))))) (not (forall ((T tptp.a)) (let ((_let_1 (ho_72 k_71 T))) (or (not (ho_70 _let_1 tptp.a2)) (ho_70 _let_1 X2))))) (not (forall ((T tptp.a)) (let ((_let_1 (ho_72 k_71 T))) (or (not (ho_70 _let_1 tptp.a3)) (ho_70 _let_1 X2))))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_26 _let_25 _let_24) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (ASSUME :args (_let_12)))) (let ((_let_29 (ASSUME :args (_let_11)))) (let ((_let_30 (ASSUME :args (_let_10)))) (let ((_let_31 (SYMM (ASSUME :args (_let_9))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (ASSUME :args (_let_6)))) (let ((_let_34 (ASSUME :args (_let_5)))) (let ((_let_35 (ASSUME :args (_let_4)))) (let ((_let_36 (ASSUME :args (_let_3)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_1)) :args ((= tptp.thesis false))) _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24) :args ((or tptp.thesis (forall ((A7 tptp.set_a)) (or (not (@ (@ tptp.member_set_a A7) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c))) (not (@ (@ tptp.ord_less_eq_set_a tptp.a1) A7)) (not (@ (@ tptp.ord_less_eq_set_a tptp.a2) A7)) (not (@ (@ tptp.ord_less_eq_set_a tptp.a3) A7))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A7 tptp.set_a)) (or (not (@ (@ tptp.member_set_a A7) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c))) (not (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (or (not (@ _let_1 tptp.a1)) (@ _let_1 A7))))) (not (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (or (not (@ _let_1 tptp.a2)) (@ _let_1 A7))))) (not (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (or (not (@ _let_1 tptp.a3)) (@ _let_1 A7))))))) _let_22))))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_23 (= T T) (= X2 A7)))) (EQ_RESOLVE (ASSUME :args (_let_21)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24) :args ((not (forall ((X2 tptp.set_a)) (or (not (@ (@ tptp.member_set_a X2) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c))) (not (@ (@ tptp.ord_less_eq_set_a tptp.a1) X2)) (not (@ (@ tptp.ord_less_eq_set_a tptp.a2) X2)) (not (@ (@ tptp.ord_less_eq_set_a tptp.a3) X2))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X2 tptp.set_a)) (or (not (@ (@ tptp.member_set_a X2) (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) tptp.c))) (not (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (or (not (@ _let_1 tptp.a1)) (@ _let_1 X2))))) (not (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (or (not (@ _let_1 tptp.a2)) (@ _let_1 X2))))) (not (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (or (not (@ _let_1 tptp.a3)) (@ _let_1 X2)))))))) (not _let_23)))))) :args ((not _let_22) true _let_23)) :args (false true _let_22)) :args ((forall ((X tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X) tptp.c) (forall ((Xa tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.produc1040928388_a_a_e X))) (let ((_let_2 (@ tptp.produc1040928388_a_a_e Xa))) (=> (@ (@ tptp.member1258382221_a_a_e Xa) tptp.c) (or (@ (@ tptp.ord_less_eq_set_a _let_1) _let_2) (@ (@ tptp.ord_less_eq_set_a _let_2) _let_1)))))))) _let_21 (or (@ _let_20 tptp.a2) (@ _let_19 tptp.a1)) (or (@ _let_20 tptp.a3) (@ _let_18 tptp.a1)) (or (@ _let_19 tptp.a3) (@ _let_18 tptp.a2)) (@ (@ tptp.member_set_a tptp.a3) _let_17) (@ (@ tptp.member_set_a tptp.a2) _let_17) (@ (@ tptp.member_set_a tptp.a1) _let_17) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e tptp.a1) tptp.b1)) tptp.c) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e tptp.a2) tptp.b2)) tptp.c) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e tptp.a3) tptp.b3)) tptp.c) (forall ((A tptp.set_a_e) (B tptp.set_a_e)) (=> (forall ((X2 (-> tptp.a tptp.e))) (let ((_let_1 (@ tptp.member_a_e X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a_e A) B))) (forall ((A tptp.set_Pr305929312_set_a) (B tptp.set_Pr305929312_set_a)) (=> (forall ((X2 tptp.produc1965228714_set_a)) (let ((_let_1 (@ tptp.member360729153_set_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le802356416_set_a A) B))) (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a)) (=> (forall ((X2 tptp.set_set_a)) (let ((_let_1 (@ tptp.member_set_set_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le2103863998_set_a A) B))) (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (forall ((X2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le318720350_set_a A) B))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le700723212_a_a_e A) B))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a A) B))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (@ (@ tptp.ord_le700723212_a_a_e B) A) (= A B)))) (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (@ (@ tptp.ord_le318720350_set_a B) A) (= A B)))) (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (=> (@ (@ tptp.ord_le2103863998_set_a B) A) (= A B)))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (= A B)))) (forall ((B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_set_a_set_a F) A))))) (forall ((B2 tptp.produc715398134_a_a_e) (F (-> tptp.set_a tptp.produc715398134_a_a_e)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_210900495_a_a_e F) A))))) (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) A))))) (forall ((B2 tptp.produc715398134_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e)) (X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_625620211_a_a_e F) A))))) (forall ((B2 tptp.a) (F (-> tptp.a tptp.a)) (X3 tptp.a) (A tptp.set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a X3) A) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_a F) A))))) (forall ((B2 tptp.a) (F (-> tptp.set_a tptp.a)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_a B2) (@ (@ tptp.image_set_a_a F) A))))) (forall ((B2 tptp.set_a) (F (-> tptp.a tptp.set_a)) (X3 tptp.a) (A tptp.set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a X3) A) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_a_set_a F) A))))) (forall ((B2 (-> tptp.a tptp.e)) (F (-> tptp.a tptp.a tptp.e)) (X3 tptp.a) (A tptp.set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a X3) A) (@ (@ tptp.member_a_e B2) (@ (@ tptp.image_a_a_e F) A))))) (forall ((B2 tptp.a) (F (-> (-> tptp.a tptp.e) tptp.a)) (X3 (-> tptp.a tptp.e)) (A tptp.set_a_e)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_a_e X3) A) (@ (@ tptp.member_a B2) (@ (@ tptp.image_a_e_a F) A))))) (forall ((B2 (-> tptp.a tptp.e)) (F (-> tptp.set_a tptp.a tptp.e)) (X3 tptp.set_a) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_a_e B2) (@ (@ tptp.image_set_a_a_e F) A))))) (forall ((X3 tptp.set_Pr204296108_a_a_e)) (@ (@ tptp.ord_le700723212_a_a_e X3) X3)) (forall ((X3 tptp.set_set_a)) (@ (@ tptp.ord_le318720350_set_a X3) X3)) (forall ((X3 tptp.set_set_set_a)) (@ (@ tptp.ord_le2103863998_set_a X3) X3)) (forall ((X3 (-> Bool tptp.set_a))) (@ (@ tptp.ord_less_eq_o_set_a X3) X3)) (forall ((X3 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a X3) X3)) (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.a tptp.a))) (let ((_let_1 (@ tptp.image_a_a F))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.a tptp.set_a))) (let ((_let_1 (@ tptp.image_a_set_a F))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (F (-> tptp.set_a tptp.a))) (let ((_let_1 (@ tptp.image_set_a_a F))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.a tptp.set_set_a))) (let ((_let_1 (@ tptp.image_a_set_set_a F))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le2103863998_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (F (-> tptp.set_a tptp.set_a))) (let ((_let_1 (@ tptp.image_set_a_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.a))) (let ((_let_1 (@ tptp.image_set_set_a_a F))) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (F (-> tptp.set_a tptp.set_set_a))) (let ((_let_1 (@ tptp.image_1930509541_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (@ (@ tptp.ord_le2103863998_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_a))) (let ((_let_1 (@ tptp.image_402591269_set_a F))) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_set_set_a) (B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_set_a))) (let ((_let_1 (@ tptp.image_1956910981_set_a F))) (=> (@ (@ tptp.ord_le2103863998_set_a A) B) (@ (@ tptp.ord_le2103863998_set_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.a)) (B tptp.set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_set_a_a F) A)) B))) (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_set_a_set_a F) A)) B))) (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.a)) (B tptp.set_a)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_2116492353_a_e_a F) A)) B))) (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (@ (@ tptp.ord_le700723212_a_a_e (@ (@ tptp.image_210900495_a_a_e F) A)) B))) (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (B tptp.set_set_a)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_64240033_set_a F) A)) B))) (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (@ (@ tptp.ord_le700723212_a_a_e (@ (@ tptp.image_625620211_a_a_e F) A)) B))) (forall ((A tptp.set_a) (F (-> tptp.a tptp.a)) (B tptp.set_a)) (=> (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A)) B))) (forall ((A tptp.set_a) (F (-> tptp.a tptp.set_a)) (B tptp.set_set_a)) (=> (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_a_set_a F) A)) B))) (forall ((A tptp.set_a) (F (-> tptp.a tptp.a tptp.e)) (B tptp.set_a_e)) (=> (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A) (@ (@ tptp.member_a_e (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a_e (@ (@ tptp.image_a_a_e F) A)) B))) (forall ((A tptp.set_a_e) (F (-> (-> tptp.a tptp.e) tptp.a)) (B tptp.set_a)) (=> (forall ((X2 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member_a_e X2) A) (@ (@ tptp.member_a (@ F X2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_e_a F) A)) B))) (forall ((B tptp.set_a) (F (-> tptp.a tptp.a)) (A tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_a_a F) A)) (not (forall ((C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a C) A) (not (= B (@ (@ tptp.image_a_a F) C)))))))) (forall ((B tptp.set_set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_64240033_set_a F) A)) (not (forall ((C tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e C) A) (not (= B (@ (@ tptp.image_64240033_set_a F) C)))))))) (forall ((B tptp.set_a) (F (-> tptp.set_a tptp.a)) (A tptp.set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_a_a F) A)) (not (forall ((C tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a C) A) (not (= B (@ (@ tptp.image_set_a_a F) C)))))))) (forall ((B tptp.set_set_a) (F (-> tptp.a tptp.set_a)) (A tptp.set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_a_set_a F) A)) (not (forall ((C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a C) A) (not (= B (@ (@ tptp.image_a_set_a F) C)))))))) (forall ((B tptp.set_a) (F (-> tptp.set_set_a tptp.a)) (A tptp.set_set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_set_a_a F) A)) (not (forall ((C tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a C) A) (not (= B (@ (@ tptp.image_set_set_a_a F) C)))))))) (forall ((B tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (A tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_set_a_set_a F) A)) (not (forall ((C tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a C) A) (not (= B (@ (@ tptp.image_set_a_set_a F) C)))))))) (forall ((B tptp.set_set_set_a) (F (-> tptp.a tptp.set_set_a)) (A tptp.set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_a_set_set_a F) A)) (not (forall ((C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a C) A) (not (= B (@ (@ tptp.image_a_set_set_a F) C)))))))) (forall ((B tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_a)) (A tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_402591269_set_a F) A)) (not (forall ((C tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a C) A) (not (= B (@ (@ tptp.image_402591269_set_a F) C)))))))) (forall ((B tptp.set_set_set_a) (F (-> tptp.set_a tptp.set_set_a)) (A tptp.set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1930509541_set_a F) A)) (not (forall ((C tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a C) A) (not (= B (@ (@ tptp.image_1930509541_set_a F) C)))))))) (forall ((B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_set_a)) (A tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1956910981_set_a F) A)) (not (forall ((C tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a C) A) (not (= B (@ (@ tptp.image_1956910981_set_a F) C)))))))) (forall ((F (-> tptp.set_a tptp.a)) (A tptp.set_set_a) (B tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_set_a_a F) A)) B) (forall ((X4 tptp.set_a)) (=> (@ (@ tptp.member_set_a X4) A) (@ (@ tptp.member_a (@ F X4)) B))))) (forall ((F (-> tptp.a tptp.a)) (A tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A)) B) (forall ((X4 tptp.a)) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_a (@ F X4)) B))))) (forall ((F (-> tptp.set_a tptp.produc715398134_a_a_e)) (A tptp.set_set_a) (B tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.ord_le700723212_a_a_e (@ (@ tptp.image_210900495_a_a_e F) A)) B) (forall ((X4 tptp.set_a)) (=> (@ (@ tptp.member_set_a X4) A) (@ (@ tptp.member1258382221_a_a_e (@ F X4)) B))))) (forall ((F (-> tptp.set_a tptp.set_a)) (A tptp.set_set_a) (B tptp.set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_set_a_set_a F) A)) B) (forall ((X4 tptp.set_a)) (=> (@ (@ tptp.member_set_a X4) A) (@ (@ tptp.member_set_a (@ F X4)) B))))) (forall ((F (-> tptp.set_Pr204296108_a_a_e tptp.set_set_a)) (A tptp.set_se821189730_a_a_e) (B tptp.set_set_set_a)) (= (@ (@ tptp.ord_le2103863998_set_a (@ (@ tptp.image_1441218763_set_a F) A)) B) (forall ((X4 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1437121347_a_a_e X4) A) (@ (@ tptp.member_set_set_a (@ F X4)) B))))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a (@ (@ tptp.image_64240033_set_a F) A)) B) (forall ((X4 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X4) A) (@ (@ tptp.member_set_a (@ F X4)) B))))) (forall ((B tptp.set_a) (F (-> tptp.a tptp.a)) (A tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_a_a F) A)) (exists ((AA tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a AA) A) (= B (@ (@ tptp.image_a_a F) AA)))))) (forall ((B tptp.set_set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_64240033_set_a F) A)) (exists ((AA tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e AA) A) (= B (@ (@ tptp.image_64240033_set_a F) AA)))))) (forall ((B tptp.set_a) (F (-> tptp.set_a tptp.a)) (A tptp.set_set_a)) (= (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_a_a F) A)) (exists ((AA tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a AA) A) (= B (@ (@ tptp.image_set_a_a F) AA)))))) (forall ((B tptp.set_set_a) (F (-> tptp.a tptp.set_a)) (A tptp.set_a)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_a_set_a F) A)) (exists ((AA tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a AA) A) (= B (@ (@ tptp.image_a_set_a F) AA)))))) (forall ((B tptp.set_a) (F (-> tptp.set_set_a tptp.a)) (A tptp.set_set_set_a)) (= (@ (@ tptp.ord_less_eq_set_a B) (@ (@ tptp.image_set_set_a_a F) A)) (exists ((AA tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a AA) A) (= B (@ (@ tptp.image_set_set_a_a F) AA)))))) (forall ((B tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (A tptp.set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_set_a_set_a F) A)) (exists ((AA tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a AA) A) (= B (@ (@ tptp.image_set_a_set_a F) AA)))))) (forall ((B tptp.set_set_set_a) (F (-> tptp.a tptp.set_set_a)) (A tptp.set_a)) (= (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_a_set_set_a F) A)) (exists ((AA tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a AA) A) (= B (@ (@ tptp.image_a_set_set_a F) AA)))))) (forall ((B tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_a)) (A tptp.set_set_set_a)) (= (@ (@ tptp.ord_le318720350_set_a B) (@ (@ tptp.image_402591269_set_a F) A)) (exists ((AA tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a AA) A) (= B (@ (@ tptp.image_402591269_set_a F) AA)))))) (forall ((B tptp.set_set_set_a) (F (-> tptp.set_a tptp.set_set_a)) (A tptp.set_set_a)) (= (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1930509541_set_a F) A)) (exists ((AA tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a AA) A) (= B (@ (@ tptp.image_1930509541_set_a F) AA)))))) (forall ((B tptp.set_set_set_a) (F (-> tptp.set_set_a tptp.set_set_a)) (A tptp.set_set_set_a)) (= (@ (@ tptp.ord_le2103863998_set_a B) (@ (@ tptp.image_1956910981_set_a F) A)) (exists ((AA tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a AA) A) (= B (@ (@ tptp.image_1956910981_set_a F) AA)))))) (forall ((P tptp.produc1965228714_set_a)) (exists ((X2 (-> tptp.a tptp.e)) (Y tptp.set_a)) (= P (@ (@ tptp.produc479206876_set_a X2) Y)))) (forall ((P tptp.produc715398134_a_a_e)) (exists ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (= P (@ (@ tptp.produc1134456688_a_a_e X2) Y)))) (forall ((B2 tptp.set_Pr204296108_a_a_e) (A2 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) A2) (=> (@ (@ tptp.ord_le700723212_a_a_e A2) B2) (= A2 B2)))) (forall ((B2 tptp.set_set_a) (A2 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B2) A2) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (= A2 B2)))) (forall ((B2 tptp.set_set_set_a) (A2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a B2) A2) (=> (@ (@ tptp.ord_le2103863998_set_a A2) B2) (= A2 B2)))) (forall ((B2 (-> Bool tptp.set_a)) (A2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) A2) (=> (@ (@ tptp.ord_less_eq_o_set_a A2) B2) (= A2 B2)))) (forall ((B2 tptp.set_a) (A2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (= A2 B2)))) (= (lambda ((Y2 tptp.set_Pr204296108_a_a_e) (Z tptp.set_Pr204296108_a_a_e)) (= Y2 Z)) (lambda ((A3 tptp.set_Pr204296108_a_a_e) (B3 tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e B3) A3) (@ (@ tptp.ord_le700723212_a_a_e A3) B3)))) (= (lambda ((Y2 tptp.set_set_a) (Z tptp.set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_a) (B3 tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a B3) A3) (@ (@ tptp.ord_le318720350_set_a A3) B3)))) (= (lambda ((Y2 tptp.set_set_set_a) (Z tptp.set_set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_set_a) (B3 tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a B3) A3) (@ (@ tptp.ord_le2103863998_set_a A3) B3)))) (= (lambda ((Y2 (-> Bool tptp.set_a)) (Z (-> Bool tptp.set_a))) (= Y2 Z)) (lambda ((A3 (-> Bool tptp.set_a)) (B3 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_o_set_a B3) A3) (@ (@ tptp.ord_less_eq_o_set_a A3) B3)))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_a) (B3 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a B3) A3) (@ (@ tptp.ord_less_eq_set_a A3) B3)))) (forall ((B2 tptp.set_Pr204296108_a_a_e) (A2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e C2))) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.set_set_a) (A2 tptp.set_set_a) (C2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a C2))) (=> (@ (@ tptp.ord_le318720350_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.set_set_set_a) (A2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a C2))) (=> (@ (@ tptp.ord_le2103863998_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 (-> Bool tptp.set_a)) (A2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a C2))) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.set_a) (A2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((A2 tptp.set_Pr204296108_a_a_e)) (@ (@ tptp.ord_le700723212_a_a_e A2) A2)) (forall ((A2 tptp.set_set_a)) (@ (@ tptp.ord_le318720350_set_a A2) A2)) (forall ((A2 tptp.set_set_set_a)) (@ (@ tptp.ord_le2103863998_set_a A2) A2)) (forall ((A2 (-> Bool tptp.set_a))) (@ (@ tptp.ord_less_eq_o_set_a A2) A2)) (forall ((A2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A2) A2)) (forall ((X3 tptp.set_Pr204296108_a_a_e) (Y3 tptp.set_Pr204296108_a_a_e) (Z2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le700723212_a_a_e Y3) Z2) (@ _let_1 Z2))))) (forall ((X3 tptp.set_set_a) (Y3 tptp.set_set_a) (Z2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le318720350_set_a Y3) Z2) (@ _let_1 Z2))))) (forall ((X3 tptp.set_set_set_a) (Y3 tptp.set_set_set_a) (Z2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le2103863998_set_a Y3) Z2) (@ _let_1 Z2))))) (forall ((X3 (-> Bool tptp.set_a)) (Y3 (-> Bool tptp.set_a)) (Z2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_o_set_a Y3) Z2) (@ _let_1 Z2))))) (forall ((X3 tptp.set_a) (Y3 tptp.set_a) (Z2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_set_a Y3) Z2) (@ _let_1 Z2))))) (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e A2) B2) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (@ (@ tptp.ord_le318720350_set_a B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a A2) B2) (=> (@ (@ tptp.ord_le2103863998_set_a B2) A2) (= A2 B2)))) (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (C2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))) (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) C2) (@ (@ tptp.ord_le700723212_a_a_e A2) C2)))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (C2 tptp.set_set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le318720350_set_a B2) C2) (@ (@ tptp.ord_le318720350_set_a A2) C2)))) (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le2103863998_set_a B2) C2) (@ (@ tptp.ord_le2103863998_set_a A2) C2)))) (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (@ (@ tptp.ord_less_eq_o_set_a A2) C2)))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (@ (@ tptp.ord_less_eq_set_a A2) C2)))) (= (lambda ((Y2 tptp.set_Pr204296108_a_a_e) (Z tptp.set_Pr204296108_a_a_e)) (= Y2 Z)) (lambda ((A3 tptp.set_Pr204296108_a_a_e) (B3 tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e A3) B3) (@ (@ tptp.ord_le700723212_a_a_e B3) A3)))) (= (lambda ((Y2 tptp.set_set_a) (Z tptp.set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_a) (B3 tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a A3) B3) (@ (@ tptp.ord_le318720350_set_a B3) A3)))) (= (lambda ((Y2 tptp.set_set_set_a) (Z tptp.set_set_set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_set_set_a) (B3 tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a A3) B3) (@ (@ tptp.ord_le2103863998_set_a B3) A3)))) (= (lambda ((Y2 (-> Bool tptp.set_a)) (Z (-> Bool tptp.set_a))) (= Y2 Z)) (lambda ((A3 (-> Bool tptp.set_a)) (B3 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_o_set_a A3) B3) (@ (@ tptp.ord_less_eq_o_set_a B3) A3)))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A3 tptp.set_a) (B3 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A3) B3) (@ (@ tptp.ord_less_eq_set_a B3) A3)))) (forall ((Y3 tptp.set_Pr204296108_a_a_e) (X3 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e Y3) X3) (= (@ (@ tptp.ord_le700723212_a_a_e X3) Y3) (= X3 Y3)))) (forall ((Y3 tptp.set_set_a) (X3 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a Y3) X3) (= (@ (@ tptp.ord_le318720350_set_a X3) Y3) (= X3 Y3)))) (forall ((Y3 tptp.set_set_set_a) (X3 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a Y3) X3) (= (@ (@ tptp.ord_le2103863998_set_a X3) Y3) (= X3 Y3)))) (forall ((Y3 (-> Bool tptp.set_a)) (X3 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a Y3) X3) (= (@ (@ tptp.ord_less_eq_o_set_a X3) Y3) (= X3 Y3)))) (forall ((Y3 tptp.set_a) (X3 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a Y3) X3) (= (@ (@ tptp.ord_less_eq_set_a X3) Y3) (= X3 Y3)))) (forall ((A2 tptp.set_Pr204296108_a_a_e) (B2 tptp.set_Pr204296108_a_a_e) (C2 tptp.set_Pr204296108_a_a_e)) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le700723212_a_a_e B2) C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (C2 tptp.set_set_a)) (let ((_let_1 (@ tptp.ord_le318720350_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le318720350_set_a B2) C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (C2 tptp.set_set_set_a)) (let ((_let_1 (@ tptp.ord_le2103863998_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2103863998_set_a B2) C2) (@ _let_1 C2))))) (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (let ((_let_1 (@ tptp.ord_less_eq_o_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (@ _let_1 C2))))) (forall ((X3 tptp.set_Pr204296108_a_a_e) (Y3 tptp.set_Pr204296108_a_a_e)) (=> (= X3 Y3) (@ (@ tptp.ord_le700723212_a_a_e X3) Y3))) (forall ((X3 tptp.set_set_a) (Y3 tptp.set_set_a)) (=> (= X3 Y3) (@ (@ tptp.ord_le318720350_set_a X3) Y3))) (forall ((X3 tptp.set_set_set_a) (Y3 tptp.set_set_set_a)) (=> (= X3 Y3) (@ (@ tptp.ord_le2103863998_set_a X3) Y3))) (forall ((X3 (-> Bool tptp.set_a)) (Y3 (-> Bool tptp.set_a))) (=> (= X3 Y3) (@ (@ tptp.ord_less_eq_o_set_a X3) Y3))) (forall ((X3 tptp.set_a) (Y3 tptp.set_a)) (=> (= X3 Y3) (@ (@ tptp.ord_less_eq_set_a X3) Y3))) (forall ((X3 tptp.set_Pr204296108_a_a_e) (Y3 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e X3) Y3) (=> (@ (@ tptp.ord_le700723212_a_a_e Y3) X3) (= X3 Y3)))) (forall ((X3 tptp.set_set_a) (Y3 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X3) Y3) (=> (@ (@ tptp.ord_le318720350_set_a Y3) X3) (= X3 Y3)))) (forall ((X3 tptp.set_set_set_a) (Y3 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a X3) Y3) (=> (@ (@ tptp.ord_le2103863998_set_a Y3) X3) (= X3 Y3)))) (forall ((X3 (-> Bool tptp.set_a)) (Y3 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X3) Y3) (=> (@ (@ tptp.ord_less_eq_o_set_a Y3) X3) (= X3 Y3)))) (forall ((X3 tptp.set_a) (Y3 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y3) (=> (@ (@ tptp.ord_less_eq_set_a Y3) X3) (= X3 Y3)))) (= (lambda ((Y2 tptp.set_Pr204296108_a_a_e) (Z tptp.set_Pr204296108_a_a_e)) (= Y2 Z)) (lambda ((X4 tptp.set_Pr204296108_a_a_e) (Y4 tptp.set_Pr204296108_a_a_e)) (and (@ (@ tptp.ord_le700723212_a_a_e X4) Y4) (@ (@ tptp.ord_le700723212_a_a_e Y4) X4)))) (= (lambda ((Y2 tptp.set_set_a) (Z tptp.set_set_a)) (= Y2 Z)) (lambda ((X4 tptp.set_set_a) (Y4 tptp.set_set_a)) (and (@ (@ tptp.ord_le318720350_set_a X4) Y4) (@ (@ tptp.ord_le318720350_set_a Y4) X4)))) (= (lambda ((Y2 tptp.set_set_set_a) (Z tptp.set_set_set_a)) (= Y2 Z)) (lambda ((X4 tptp.set_set_set_a) (Y4 tptp.set_set_set_a)) (and (@ (@ tptp.ord_le2103863998_set_a X4) Y4) (@ (@ tptp.ord_le2103863998_set_a Y4) X4)))) (= (lambda ((Y2 (-> Bool tptp.set_a)) (Z (-> Bool tptp.set_a))) (= Y2 Z)) (lambda ((X4 (-> Bool tptp.set_a)) (Y4 (-> Bool tptp.set_a))) (and (@ (@ tptp.ord_less_eq_o_set_a X4) Y4) (@ (@ tptp.ord_less_eq_o_set_a Y4) X4)))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((X4 tptp.set_a) (Y4 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a X4) Y4) (@ (@ tptp.ord_less_eq_set_a Y4) X4)))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_set_a)) (C2 tptp.set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_le318720350_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le318720350_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_set_set_a)) (C2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_le2103863998_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le2103863998_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_o_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_o_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_set_a)) (C2 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_le318720350_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le318720350_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_set_set_a) (B2 tptp.set_set_set_a) (F (-> tptp.set_set_set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_set_a) (Y tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le2103863998_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))) (forall ((A2 (-> Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (F (-> (-> Bool tptp.set_a) tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_o_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a tptp.set_set_set_a)) (C2 tptp.set_set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_le2103863998_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le2103863998_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_set_a) (B2 tptp.set_set_a) (F (-> tptp.set_set_a Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_le318720350_set_a A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X2 tptp.set_set_a) (Y tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a X2) Y) (@ (@ tptp.ord_less_eq_o_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_o_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_Pr204296108_a_a_e) (F (-> (-> Bool tptp.set_a) tptp.set_Pr204296108_a_a_e)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_le700723212_a_a_e (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le700723212_a_a_e A2) (@ F C2)))))) (forall ((A2 tptp.set_set_a) (F (-> (-> Bool tptp.set_a) tptp.set_set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_le318720350_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le318720350_set_a A2) (@ F C2)))))) (forall ((A2 tptp.set_set_set_a) (F (-> (-> Bool tptp.set_a) tptp.set_set_set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_le2103863998_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_le2103863998_set_a A2) (@ F C2)))))) (forall ((A2 (-> Bool tptp.set_a)) (F (-> (-> Bool tptp.set_a) Bool tptp.set_a)) (B2 (-> Bool tptp.set_a)) (C2 (-> Bool tptp.set_a))) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_o_set_a B2) C2) (=> (forall ((X2 (-> Bool tptp.set_a)) (Y (-> Bool tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_o_set_a X2) Y) (@ (@ tptp.ord_less_eq_o_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_o_set_a A2) (@ F C2)))))) (forall ((A2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B2 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a A2) (@ F C2)))))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_set_a (@ F B2)) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))) (forall ((A2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_set_a B2) C2) (=> (forall ((X2 tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X2) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y)))) (@ _let_1 (@ F C2))))))) (forall ((A2 tptp.set_a) (P2 (-> tptp.set_a Bool))) (= (@ (@ tptp.member_set_a A2) (@ tptp.collect_set_a P2)) (@ P2 A2))) (forall ((A2 tptp.produc715398134_a_a_e) (P2 (-> tptp.produc715398134_a_a_e Bool))) (= (@ (@ tptp.member1258382221_a_a_e A2) (@ tptp.collec1369693387_a_a_e P2)) (@ P2 A2))) (forall ((A tptp.set_set_a)) (= (@ tptp.collect_set_a (lambda ((X4 tptp.set_a)) (@ (@ tptp.member_set_a X4) A))) A)) (forall ((A tptp.set_Pr204296108_a_a_e)) (= (@ tptp.collec1369693387_a_a_e (lambda ((X4 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X4) A))) A)) (forall ((X3 tptp.set_a) (A tptp.set_set_a) (B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a))) (=> (@ (@ tptp.member_set_a X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_set_a_set_a F) A))))) (forall ((X3 tptp.set_a) (A tptp.set_set_a) (B2 tptp.produc715398134_a_a_e) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member_set_a X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_210900495_a_a_e F) A))))) (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) A))))) (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (B2 tptp.produc715398134_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (=> (= B2 (@ F X3)) (@ (@ tptp.member1258382221_a_a_e B2) (@ (@ tptp.image_625620211_a_a_e F) A))))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_a Bool))) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) (@ (@ tptp.image_64240033_set_a F) A)) (@ P2 X2))) (forall ((X tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X) A) (@ P2 (@ F X)))))) (forall ((M tptp.set_Pr204296108_a_a_e) (N tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (G (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (= M N) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) N) (= (@ F X2) (@ G X2)))) (= (@ (@ tptp.image_64240033_set_a F) M) (@ (@ tptp.image_64240033_set_a G) N))))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_a Bool))) (=> (exists ((X tptp.set_a)) (and (@ (@ tptp.member_set_a X) (@ (@ tptp.image_64240033_set_a F) A)) (@ P2 X))) (exists ((X2 tptp.produc715398134_a_a_e)) (and (@ (@ tptp.member1258382221_a_a_e X2) A) (@ P2 (@ F X2)))))) (forall ((Z2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_set_a Z2) (@ (@ tptp.image_64240033_set_a F) A)) (exists ((X4 tptp.produc715398134_a_a_e)) (and (@ (@ tptp.member1258382221_a_a_e X4) A) (= Z2 (@ F X4)))))) (forall ((X3 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a))) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member_set_a (@ F X3)) (@ (@ tptp.image_set_a_set_a F) A)))) (forall ((X3 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member1258382221_a_a_e (@ F X3)) (@ (@ tptp.image_210900495_a_a_e F) A)))) (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member_set_a (@ F X3)) (@ (@ tptp.image_64240033_set_a F) A)))) (forall ((X3 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member1258382221_a_a_e (@ F X3)) (@ (@ tptp.image_625620211_a_a_e F) A)))) (forall ((P2 (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P2)) (@ tptp.collect_a Q)) (forall ((X4 tptp.a)) (=> (@ P2 X4) (@ Q X4))))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A4) B4) (@ (@ tptp.ord_less_eq_set_a B4) A4)))) (forall ((A tptp.set_a) (B tptp.set_a) (C3 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_a B) C3) (@ _let_1 C3))))) (forall ((P2 (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X2 tptp.a)) (=> (@ P2 X2) (@ Q X2))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P2)) (@ tptp.collect_a Q)))) _let_16 _let_15 _let_14 (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_a B) A))) (= tptp.ord_le318720350_set_a (lambda ((A4 tptp.set_set_a) (B4 tptp.set_set_a)) (forall ((X4 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (= tptp.ord_le700723212_a_a_e (lambda ((A4 tptp.set_Pr204296108_a_a_e) (B4 tptp.set_Pr204296108_a_a_e)) (forall ((X4 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_a A) B) (not (@ (@ tptp.ord_less_eq_set_a B) A)))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a C2))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (C2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e C2))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_a) (B tptp.set_a) (C2 tptp.a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X3))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X3))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e)) (Y1 tptp.set_a) (Y22 (-> tptp.a tptp.e))) (= (= (@ (@ tptp.produc1134456688_a_a_e X1) X22) (@ (@ tptp.produc1134456688_a_a_e Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (A5 tptp.set_a) (B5 (-> tptp.a tptp.e))) (= (= (@ (@ tptp.produc1134456688_a_a_e A2) B2) (@ (@ tptp.produc1134456688_a_a_e A5) B5)) (and (= A2 A5) (= B2 B5)))) (forall ((A2 tptp.set_a) (P tptp.produc715398134_a_a_e)) (= (= A2 (@ tptp.produc1040928388_a_a_e P)) (exists ((B3 (-> tptp.a tptp.e))) (= P (@ (@ tptp.produc1134456688_a_a_e A2) B3))))) (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e))) (= (@ tptp.produc1040928388_a_a_e (@ (@ tptp.produc1134456688_a_a_e X1) X22)) X1)) (forall ((X3 tptp.set_a) (Y3 (-> tptp.a tptp.e)) (A2 tptp.set_a)) (=> (= (@ tptp.produc1040928388_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) A2) (= X3 A2))) (forall ((X3 tptp.produc715398134_a_a_e) (Y3 tptp.set_a) (Z2 (-> tptp.a tptp.e))) (=> (= X3 (@ (@ tptp.produc1134456688_a_a_e Y3) Z2)) (= (@ tptp.produc1040928388_a_a_e X3) Y3))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_set_a Bool))) (= (forall ((B4 tptp.set_set_a)) (=> (@ (@ tptp.ord_le318720350_set_a B4) (@ (@ tptp.image_64240033_set_a F) A)) (@ P2 B4))) (forall ((B4 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.ord_le700723212_a_a_e B4) A) (@ P2 (@ (@ tptp.image_64240033_set_a F) B4)))))) (forall ((F (-> tptp.a tptp.a)) (A tptp.set_a) (P2 (-> tptp.set_a Bool))) (= (forall ((B4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B4) (@ (@ tptp.image_a_a F) A)) (@ P2 B4))) (forall ((B4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B4) A) (@ P2 (@ (@ tptp.image_a_a F) B4)))))) (forall ((P2 (-> tptp.set_a Bool)) (X3 tptp.set_a)) (=> (@ P2 X3) (=> (forall ((Y tptp.set_a)) (=> (@ P2 Y) (@ (@ tptp.ord_less_eq_set_a Y) X3))) (= (@ tptp.order_Greatest_set_a P2) X3)))) (forall ((P2 (-> tptp.set_a Bool)) (X3 tptp.set_a) (Q (-> tptp.set_a Bool))) (=> (@ P2 X3) (=> (forall ((Y tptp.set_a)) (=> (@ P2 Y) (@ (@ tptp.ord_less_eq_set_a Y) X3))) (=> (forall ((X2 tptp.set_a)) (=> (@ P2 X2) (=> (forall ((Y5 tptp.set_a)) (=> (@ P2 Y5) (@ (@ tptp.ord_less_eq_set_a Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_Greatest_set_a P2)))))) (forall ((P2 (-> tptp.produc715398134_a_a_e Bool)) (Prod tptp.produc715398134_a_a_e)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (@ P2 (@ (@ tptp.produc1134456688_a_a_e A6) B6))) (@ P2 Prod))) (forall ((Y3 tptp.produc715398134_a_a_e)) (not (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (not (= Y3 (@ (@ tptp.produc1134456688_a_a_e A6) B6)))))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (A5 tptp.set_a) (B5 (-> tptp.a tptp.e))) (=> (= (@ (@ tptp.produc1134456688_a_a_e A2) B2) (@ (@ tptp.produc1134456688_a_a_e A5) B5)) (not (=> (= A2 A5) (not (= B2 B5)))))) (forall ((P2 (-> tptp.produc715398134_a_a_e Bool)) (P tptp.produc715398134_a_a_e)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (@ P2 (@ (@ tptp.produc1134456688_a_a_e A6) B6))) (@ P2 P))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) B) (@ (@ tptp.ord_le2103863998_set_a (@ (@ tptp.image_1441218763_set_a _let_1) (@ tptp.finite33065488_a_a_e A))) (@ tptp.finite_Fpow_set_a B))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (not (@ (@ tptp.ord_le318720350_set_a A) B)) (exists ((A6 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a A6))) (and (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (not (@ (@ tptp.ord_le700723212_a_a_e A) B)) (exists ((A6 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e A6))) (and (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (not (@ (@ tptp.ord_less_eq_set_a A) B)) (exists ((A6 tptp.a)) (let ((_let_1 (@ tptp.member_a A6))) (and (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_a A) B))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.ord_le318720350_set_a B) A))) (let ((_let_2 (@ tptp.member_set_a X3))) (=> (or (@ (@ tptp.ord_le318720350_set_a A) B) _let_1) (=> (@ _let_2 A) (=> (not (@ _let_2 B)) _let_1)))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ (@ tptp.ord_le700723212_a_a_e B) A))) (let ((_let_2 (@ tptp.member1258382221_a_a_e X3))) (=> (or (@ (@ tptp.ord_le700723212_a_a_e A) B) _let_1) (=> (@ _let_2 A) (=> (not (@ _let_2 B)) _let_1)))))) (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ (@ tptp.ord_less_eq_set_a B) A))) (let ((_let_2 (@ tptp.member_a X3))) (=> (or (@ (@ tptp.ord_less_eq_set_a A) B) _let_1) (=> (@ _let_2 A) (=> (not (@ _let_2 B)) _let_1)))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ tptp.finite_Fpow_a A)) (@ tptp.finite_Fpow_a B)))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_a A2) C2) (@ (@ tptp.ord_less_eq_set_a B2) C2)))) (forall ((A2 tptp.set_a) (B2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C2))) (=> (= A2 B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) A)) (exists ((X2 tptp.produc715398134_a_a_e)) (and (@ (@ tptp.member1258382221_a_a_e X2) A) (= B2 (@ F X2)))))) (forall ((A2 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_set_a_set_a F) A)))) (forall ((A2 tptp.set_a) (A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_210900495_a_a_e F) A)))) (forall ((A2 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_64240033_set_a F) A)))) (forall ((A2 tptp.produc715398134_a_a_e) (A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_625620211_a_a_e F) A)))) (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_set_a) (A2 tptp.set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_set_a_set_a F) A))))) (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (B tptp.set_set_a) (A2 tptp.produc715398134_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member_set_a (@ F X2)) B))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member_set_a (@ F A2)) (@ (@ tptp.image_64240033_set_a F) A))))) (forall ((A tptp.set_set_a) (F (-> tptp.set_a tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e) (A2 tptp.set_a)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (=> (@ (@ tptp.member_set_a A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_210900495_a_a_e F) A))))) (forall ((A tptp.set_Pr204296108_a_a_e) (F (-> tptp.produc715398134_a_a_e tptp.produc715398134_a_a_e)) (B tptp.set_Pr204296108_a_a_e) (A2 tptp.produc715398134_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) A) (@ (@ tptp.member1258382221_a_a_e (@ F X2)) B))) (=> (@ (@ tptp.member1258382221_a_a_e A2) A) (@ (@ tptp.member1258382221_a_a_e (@ F A2)) (@ (@ tptp.image_625620211_a_a_e F) A))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X3))) (=> (@ (@ tptp.ord_le318720350_set_a A) B) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (not (= A B))))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X3))) (=> (@ (@ tptp.ord_le700723212_a_a_e A) B) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (not (= A B))))))) (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (not (= A B))))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (not (@ (@ tptp.ord_le318720350_set_a A) B)) (exists ((X2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X2))) (and (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (not (@ (@ tptp.ord_le700723212_a_a_e A) B)) (exists ((X2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X2))) (and (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (not (@ (@ tptp.ord_less_eq_set_a A) B)) (exists ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (and (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A) A)) (forall ((A tptp.set_set_a) (B tptp.set_set_a)) (=> (not (= A B)) (=> (@ (@ tptp.ord_le318720350_set_a B) A) (exists ((X2 tptp.set_a)) (let ((_let_1 (@ tptp.member_set_a X2))) (and (@ _let_1 A) (not (@ _let_1 B)))))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e)) (=> (not (= A B)) (=> (@ (@ tptp.ord_le700723212_a_a_e B) A) (exists ((X2 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ tptp.member1258382221_a_a_e X2))) (and (@ _let_1 A) (not (@ _let_1 B)))))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (exists ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (and (@ _let_1 A) (not (@ _let_1 B)))))))) (forall ((A tptp.set_set_a) (B tptp.set_set_a) (X3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.ord_le318720350_set_a A) B))) (let ((_let_2 (@ tptp.member_set_a X3))) (=> (or _let_1 (@ (@ tptp.ord_le318720350_set_a B) A)) (=> (not (@ _let_2 A)) (=> (@ _let_2 B) _let_1)))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (X3 tptp.produc715398134_a_a_e)) (let ((_let_1 (@ (@ tptp.ord_le700723212_a_a_e A) B))) (let ((_let_2 (@ tptp.member1258382221_a_a_e X3))) (=> (or _let_1 (@ (@ tptp.ord_le700723212_a_a_e B) A)) (=> (not (@ _let_2 A)) (=> (@ _let_2 B) _let_1)))))) (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ (@ tptp.ord_less_eq_set_a A) B))) (let ((_let_2 (@ tptp.member_a X3))) (=> (or _let_1 (@ (@ tptp.ord_less_eq_set_a B) A)) (=> (not (@ _let_2 A)) (=> (@ _let_2 B) _let_1)))))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (@ (@ tptp.ord_le318720350_set_a (@ _let_1 A)) B) (@ (@ tptp.ord_le2103863998_set_a (@ (@ tptp.image_1441218763_set_a _let_1) (@ tptp.pow_Pr328302361_a_a_e A))) (@ tptp.pow_set_a B))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (C3 (-> tptp.produc715398134_a_a_e tptp.set_a)) (D (-> tptp.produc715398134_a_a_e tptp.set_a)) (Sup (-> tptp.set_set_a tptp.set_a))) (=> (= A B) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) B) (= (@ C3 X2) (@ D X2)))) (= (@ Sup (@ (@ tptp.image_64240033_set_a C3) A)) (@ Sup (@ (@ tptp.image_64240033_set_a D) B)))))) (forall ((A tptp.set_Pr204296108_a_a_e) (B tptp.set_Pr204296108_a_a_e) (C3 (-> tptp.produc715398134_a_a_e tptp.set_a)) (D (-> tptp.produc715398134_a_a_e tptp.set_a)) (Inf (-> tptp.set_set_a tptp.set_a))) (=> (= A B) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e X2) B) (= (@ C3 X2) (@ D X2)))) (= (@ Inf (@ (@ tptp.image_64240033_set_a C3) A)) (@ Inf (@ (@ tptp.image_64240033_set_a D) B)))))) (forall ((R tptp.set_Pr204296108_a_a_e) (S tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (let ((_let_1 (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X2) Y)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le700723212_a_a_e R) S))) (forall ((R tptp.set_a) (S (-> tptp.a tptp.e)) (R2 tptp.set_Pr204296108_a_a_e) (S2 (-> tptp.a tptp.e))) (let ((_let_1 (@ tptp.produc1134456688_a_a_e R))) (=> (@ (@ tptp.member1258382221_a_a_e (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1258382221_a_a_e (@ _let_1 S2)) R2))))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.member_set_a A) (@ tptp.pow_a B)))) (forall ((A tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.member_set_a A) (@ tptp.pow_a B)) (@ (@ tptp.ord_less_eq_set_a A) B))) (forall ((A tptp.set_a)) (@ (@ tptp.member_set_a A) (@ tptp.pow_a A))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.member_set_a A) (@ tptp.pow_a B)) (@ (@ tptp.ord_less_eq_set_a A) B))) (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ (@ tptp.ord_le318720350_set_a (@ tptp.pow_a A)) (@ tptp.pow_a B)))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (A tptp.set_Pr204296108_a_a_e) (B tptp.set_set_a)) (let ((_let_1 (@ tptp.image_64240033_set_a F))) (=> (= (@ _let_1 A) B) (= (@ (@ tptp.image_1441218763_set_a _let_1) (@ tptp.pow_Pr328302361_a_a_e A)) (@ tptp.pow_set_a B))))) _let_13 (forall ((F (-> tptp.produc715398134_a_a_e Bool)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (=> (@ F (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ (@ (@ tptp.produc952037978_a_e_o F) A2) B2))) (forall ((F (-> tptp.produc715398134_a_a_e Bool)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (=> (@ (@ (@ tptp.produc952037978_a_e_o F) A2) B2) (@ F (@ (@ tptp.produc1134456688_a_a_e A2) B2)))) (forall ((F (-> tptp.produc715398134_a_a_e Bool)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (=> (@ (@ (@ tptp.produc952037978_a_e_o F) A2) B2) (@ F (@ (@ tptp.produc1134456688_a_a_e A2) B2)))) (forall ((R2 tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) R2) (@ tptp.domain_set_a_a_e R2))) _let_12 (forall ((B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_a_e B2) (@ tptp.range_set_a_a_e R)) (not (forall ((A6 tptp.set_a)) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B2)) R)))))) (forall ((A2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_a_e A2) (@ tptp.range_set_a_a_e R)) (exists ((Y4 tptp.set_a)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e Y4) A2)) R)))) (forall ((A2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_a_e A2) (@ tptp.range_set_a_a_e R)) (not (forall ((A6 tptp.set_a)) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) A2)) R)))))) (forall ((A2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_a_e A2) (@ tptp.range_set_a_a_e R)) (exists ((A3 tptp.set_a) (B3 (-> tptp.a tptp.e))) (and (= A2 B3) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A3) B3)) R))))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R) (@ (@ tptp.member_a_e B2) (@ tptp.range_set_a_a_e R)))) (forall ((X3 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e) (P2 (-> (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member_a_e X3) (@ tptp.range_set_a_a_e R)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B6)) R) (@ P2 B6))) (@ P2 X3)))) (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (not (forall ((B6 (-> tptp.a tptp.e))) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B6)) R)))))) (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (exists ((Y4 (-> tptp.a tptp.e))) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) Y4)) R)))) (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (not (forall ((B6 (-> tptp.a tptp.e))) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B6)) R)))))) (forall ((A2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)) (exists ((A3 tptp.set_a) (B3 (-> tptp.a tptp.e))) (and (= A2 A3) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A3) B3)) R))))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R) (@ (@ tptp.member_set_a A2) (@ tptp.domain_set_a_a_e R)))) (forall ((X3 tptp.set_a) (R tptp.set_Pr204296108_a_a_e) (P2 (-> tptp.set_a Bool))) (=> (@ (@ tptp.member_set_a X3) (@ tptp.domain_set_a_a_e R)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B6)) R) (@ P2 A6))) (@ P2 X3)))) (forall ((Y3 (-> tptp.a tptp.e)) (X3 tptp.set_a) (A tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a Y3) X3)) (@ (@ tptp.image_1875450791_set_a tptp.produc755714512_a_a_e) A)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) A))) (forall ((Y3 tptp.set_a) (X3 (-> tptp.a tptp.e)) (A tptp.set_Pr305929312_set_a)) (= (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e Y3) X3)) (@ (@ tptp.image_376979367_a_a_e tptp.produc100464700_set_a) A)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a X3) Y3)) A))) (forall ((X3 (-> tptp.a tptp.e)) (Y3 tptp.set_a)) (= (@ tptp.produc100464700_set_a (@ (@ tptp.produc479206876_set_a X3) Y3)) (@ (@ tptp.produc1134456688_a_a_e Y3) X3))) (forall ((X3 tptp.set_a) (Y3 (-> tptp.a tptp.e))) (= (@ tptp.produc755714512_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) (@ (@ tptp.produc479206876_set_a Y3) X3))) (forall ((A2 (-> tptp.a tptp.e)) (B2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A2) B2)) (@ tptp.converse_set_a_a_e R)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) A2)) R))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (= (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ tptp.converse_a_e_set_a R)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a B2) A2)) R))) (forall ((X1 (-> tptp.a tptp.e)) (X22 tptp.set_a) (R tptp.set_Pr204296108_a_a_e) (P2 (-> (-> tptp.a tptp.e) tptp.set_a Bool))) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a X1) X22)) (@ tptp.converse_set_a_a_e R)) (=> (forall ((A6 tptp.set_a) (B6 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A6) B6)) R) (@ (@ P2 B6) A6))) (@ (@ P2 X1) X22)))) (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a) (P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X1) X22)) (@ tptp.converse_a_e_set_a R)) (=> (forall ((A6 (-> tptp.a tptp.e)) (B6 tptp.set_a)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A6) B6)) R) (@ (@ P2 B6) A6))) (@ (@ P2 X1) X22)))) (forall ((A2 (-> tptp.a tptp.e)) (B2 tptp.set_a) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A2) B2)) R) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) A2)) (@ tptp.converse_a_e_set_a R)))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a B2) A2)) (@ tptp.converse_set_a_a_e R)))) (forall ((A1 (-> tptp.a tptp.e)) (A22 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (= (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A1) A22)) (@ tptp.converse_set_a_a_e R)) (exists ((A3 tptp.set_a) (B3 (-> tptp.a tptp.e))) (and (= A1 B3) (= A22 A3) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A3) B3)) R))))) (forall ((A1 tptp.set_a) (A22 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (= (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A1) A22)) (@ tptp.converse_a_e_set_a R)) (exists ((A3 (-> tptp.a tptp.e)) (B3 tptp.set_a)) (and (= A1 B3) (= A22 A3) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A3) B3)) R))))) (forall ((A1 (-> tptp.a tptp.e)) (A22 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A1) A22)) (@ tptp.converse_set_a_a_e R)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A22) A1)) R))) (forall ((A1 tptp.set_a) (A22 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A1) A22)) (@ tptp.converse_a_e_set_a R)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A22) A1)) R))) (forall ((Yx tptp.produc1965228714_set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member360729153_set_a Yx) (@ tptp.converse_set_a_a_e R)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= Yx (@ (@ tptp.produc479206876_set_a Y) X2)) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X2) Y)) R))))))) (forall ((Yx tptp.produc715398134_a_a_e) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member1258382221_a_a_e Yx) (@ tptp.converse_a_e_set_a R)) (not (forall ((X2 (-> tptp.a tptp.e)) (Y tptp.set_a)) (=> (= Yx (@ (@ tptp.produc1134456688_a_a_e Y) X2)) (not (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a X2) Y)) R))))))) (forall ((A2 (-> tptp.a tptp.e)) (B2 tptp.set_a) (R tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a A2) B2)) (@ tptp.converse_set_a_a_e R)) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) A2)) R))) (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R tptp.set_Pr305929312_set_a)) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ tptp.converse_a_e_set_a R)) (@ (@ tptp.member360729153_set_a (@ (@ tptp.produc479206876_set_a B2) A2)) R))) _let_11 _let_10 (forall ((A2 tptp.set_a) (B2 (-> tptp.a tptp.e)) (R2 tptp.set_Pr204296108_a_a_e) (F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e))) (=> (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e A2) B2)) R2) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e (@ F A2)) (@ G B2))) (@ (@ tptp.image_625620211_a_a_e (@ (@ tptp.produc1443219402_e_a_e F) G)) R2)))) (forall ((X3 tptp.set_a)) (@ (@ tptp.member_set_a X3) tptp.top_top_set_set_a)) (forall ((X3 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X3) tptp.top_to1601855068_a_a_e)) (forall ((F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e)) (A2 tptp.set_a) (B2 (-> tptp.a tptp.e))) (= (@ (@ (@ tptp.produc1443219402_e_a_e F) G) (@ (@ tptp.produc1134456688_a_a_e A2) B2)) (@ (@ tptp.produc1134456688_a_a_e (@ F A2)) (@ G B2)))) (forall ((F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e)) (X3 tptp.produc715398134_a_a_e)) (= (@ tptp.produc1040928388_a_a_e (@ (@ (@ tptp.produc1443219402_e_a_e F) G) X3)) (@ F (@ tptp.produc1040928388_a_a_e X3)))) (forall ((Prod tptp.produc715398134_a_a_e)) (= (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1040928388_a_a_e Prod)) (@ tptp.produc317566658_a_a_e Prod)) Prod)) (forall ((X3 tptp.produc1965228714_set_a)) (= (@ tptp.produc1040928388_a_a_e (@ tptp.produc100464700_set_a X3)) (@ tptp.produc1809800494_set_a X3))) (forall ((X3 tptp.produc715398134_a_a_e)) (= (@ tptp.produc1809800494_set_a (@ tptp.produc755714512_a_a_e X3)) (@ tptp.produc1040928388_a_a_e X3))) _let_9 (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e)) (@ (@ tptp.member_set_a (@ F X3)) (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e))) (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e)) (=> (= B2 (@ F X3)) (@ (@ tptp.member_set_a B2) (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e)))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a))) (= (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (forall ((Y4 tptp.set_a)) (exists ((X4 tptp.produc715398134_a_a_e)) (= Y4 (@ F X4)))))) (forall ((G (-> tptp.produc715398134_a_a_e tptp.set_a)) (F (-> tptp.set_a tptp.produc715398134_a_a_e))) (=> (forall ((X2 tptp.set_a)) (= (@ G (@ F X2)) X2)) (= (@ (@ tptp.image_64240033_set_a G) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (Y3 tptp.set_a)) (=> (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (not (forall ((X2 tptp.produc715398134_a_a_e)) (not (= Y3 (@ F X2))))))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (Y3 tptp.set_a)) (=> (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (exists ((X2 tptp.produc715398134_a_a_e)) (= Y3 (@ F X2))))) (forall ((F (-> tptp.produc715398134_a_a_e tptp.set_a)) (G (-> tptp.produc715398134_a_a_e tptp.set_a))) (=> (= (@ (@ tptp.image_64240033_set_a F) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (=> (= (@ (@ tptp.image_64240033_set_a G) tptp.top_to1601855068_a_a_e) tptp.top_top_set_set_a) (= (@ (@ tptp.image_2101504031_set_a (@ (@ tptp.produc387505142_set_a F) G)) tptp.top_to970499581_a_a_e) tptp.top_to144004695_set_a)))) (forall ((A2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a tptp.top_top_set_a) A2) (= A2 tptp.top_top_set_a))) (forall ((A2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a tptp.top_top_set_a) A2) (= A2 tptp.top_top_set_a))) (forall ((A2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A2) tptp.top_top_set_a)) (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A) tptp.top_top_set_a)) (forall ((X3 tptp.produc715398134_a_a_e) (Y3 tptp.set_a) (Z2 (-> tptp.a tptp.e))) (=> (= X3 (@ (@ tptp.produc1134456688_a_a_e Y3) Z2)) (= (@ tptp.produc317566658_a_a_e X3) Z2))) (forall ((X3 tptp.set_a) (Y3 (-> tptp.a tptp.e)) (A2 (-> tptp.a tptp.e))) (=> (= (@ tptp.produc317566658_a_a_e (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) A2) (= Y3 A2))) (forall ((X1 tptp.set_a) (X22 (-> tptp.a tptp.e))) (= (@ tptp.produc317566658_a_a_e (@ (@ tptp.produc1134456688_a_a_e X1) X22)) X22)) (forall ((B2 (-> tptp.a tptp.e)) (P tptp.produc715398134_a_a_e)) (= (= B2 (@ tptp.produc317566658_a_a_e P)) (exists ((A3 tptp.set_a)) (= P (@ (@ tptp.produc1134456688_a_a_e A3) B2))))) (= (lambda ((Y2 tptp.produc715398134_a_a_e) (Z tptp.produc715398134_a_a_e)) (= Y2 Z)) (lambda ((S3 tptp.produc715398134_a_a_e) (T tptp.produc715398134_a_a_e)) (and (= (@ tptp.produc1040928388_a_a_e S3) (@ tptp.produc1040928388_a_a_e T)) (= (@ tptp.produc317566658_a_a_e S3) (@ tptp.produc317566658_a_a_e T))))) (forall ((Prod tptp.produc715398134_a_a_e) (Prod2 tptp.produc715398134_a_a_e)) (=> (and (= (@ tptp.produc1040928388_a_a_e Prod) (@ tptp.produc1040928388_a_a_e Prod2)) (= (@ tptp.produc317566658_a_a_e Prod) (@ tptp.produc317566658_a_a_e Prod2))) (= Prod Prod2))) (forall ((P tptp.produc715398134_a_a_e) (Q2 tptp.produc715398134_a_a_e)) (=> (= (@ tptp.produc1040928388_a_a_e P) (@ tptp.produc1040928388_a_a_e Q2)) (=> (= (@ tptp.produc317566658_a_a_e P) (@ tptp.produc317566658_a_a_e Q2)) (= P Q2)))) (forall ((A tptp.set_set_a)) (=> (forall ((X2 tptp.set_a)) (@ (@ tptp.member_set_a X2) A)) (= tptp.top_top_set_set_a A))) (forall ((A tptp.set_Pr204296108_a_a_e)) (=> (forall ((X2 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X2) A)) (= tptp.top_to1601855068_a_a_e A))) (exists ((X2 tptp.set_a)) (@ (@ tptp.member_set_a X2) tptp.top_top_set_set_a)) (exists ((X2 tptp.produc715398134_a_a_e)) (@ (@ tptp.member1258382221_a_a_e X2) tptp.top_to1601855068_a_a_e)) (forall ((T2 tptp.produc715398134_a_a_e)) (= T2 (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1040928388_a_a_e T2)) (@ tptp.produc317566658_a_a_e T2)))) (forall ((Prod tptp.produc715398134_a_a_e)) (= Prod (@ (@ tptp.produc1134456688_a_a_e (@ tptp.produc1040928388_a_a_e Prod)) (@ tptp.produc317566658_a_a_e Prod)))) (forall ((C2 tptp.produc715398134_a_a_e) (F (-> tptp.set_a tptp.set_a)) (G (-> (-> tptp.a tptp.e) tptp.a tptp.e)) (R2 tptp.set_Pr204296108_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e C2) (@ (@ tptp.image_625620211_a_a_e (@ (@ tptp.produc1443219402_e_a_e F) G)) R2)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= C2 (@ (@ tptp.produc1134456688_a_a_e (@ F X2)) (@ G Y))) (not (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e X2) Y)) R2))))))) (forall ((P2 (-> (-> tptp.a tptp.e) tptp.set_a Bool)) (Y3 (-> tptp.a tptp.e)) (X3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.produc1134456688_a_a_e X3) Y3))) (=> (@ (@ P2 Y3) X3) (@ (@ P2 (@ tptp.produc317566658_a_a_e _let_1)) (@ tptp.produc1040928388_a_a_e _let_1))))) (forall ((P2 (-> tptp.set_a Bool)) (P tptp.set_a) (Q (-> (-> tptp.a tptp.e) Bool)) (Q2 (-> tptp.a tptp.e))) (let ((_let_1 (@ (@ tptp.produc1134456688_a_a_e P) Q2))) (=> (@ P2 P) (=> (@ Q Q2) (and (@ P2 (@ tptp.produc1040928388_a_a_e _let_1)) (@ Q (@ tptp.produc317566658_a_a_e _let_1))))))) (forall ((P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (X3 tptp.set_a) (Y3 (-> tptp.a tptp.e)) (A2 tptp.produc715398134_a_a_e)) (=> (@ (@ P2 X3) Y3) (=> (= A2 (@ (@ tptp.produc1134456688_a_a_e X3) Y3)) (@ (@ P2 (@ tptp.produc1040928388_a_a_e A2)) (@ tptp.produc317566658_a_a_e A2))))) _let_7 _let_6 (forall ((P2 (-> (-> tptp.a tptp.e) tptp.set_a Bool)) (P tptp.produc715398134_a_a_e)) (=> (@ (@ P2 (@ tptp.produc317566658_a_a_e P)) (@ tptp.produc1040928388_a_a_e P)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (not (@ (@ P2 Y) X2)))))) (forall ((X6 tptp.set_set_a) (A tptp.set_Pr204296108_a_a_e) (Y7 tptp.set_a_e) (P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Q (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (let ((_let_1 (@ tptp.ord_le700723212_a_a_e A))) (=> (= X6 (@ (@ tptp.image_64240033_set_a tptp.produc1040928388_a_a_e) A)) (=> (= Y7 (@ (@ tptp.image_1149879910_e_a_e tptp.produc317566658_a_a_e) A)) (=> (forall ((X2 tptp.set_a)) (=> (@ (@ tptp.member_set_a X2) X6) (forall ((Xa2 (-> tptp.a tptp.e))) (=> (@ (@ tptp.member_a_e Xa2) Y7) (=> (@ (@ P2 X2) Xa2) (@ (@ Q X2) Xa2)))))) (=> (@ _let_1 (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o P2))) (@ _let_1 (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o Q))))))))) _let_5 (forall ((X3 tptp.produc715398134_a_a_e) (A (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e X3) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o A))) (@ (@ A (@ tptp.produc1040928388_a_a_e X3)) (@ tptp.produc317566658_a_a_e X3)))) _let_4 (forall ((Z2 tptp.set_a) (C2 (-> tptp.set_a (-> tptp.a tptp.e) tptp.set_set_a)) (P tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member_set_a Z2) (@ (@ tptp.produc1620938593_set_a C2) P)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= P (@ (@ tptp.produc1134456688_a_a_e X2) Y)) (not (@ (@ tptp.member_set_a Z2) (@ (@ C2 X2) Y)))))))) (forall ((Z2 tptp.produc715398134_a_a_e) (C2 (-> tptp.set_a (-> tptp.a tptp.e) tptp.set_Pr204296108_a_a_e)) (P tptp.produc715398134_a_a_e)) (=> (@ (@ tptp.member1258382221_a_a_e Z2) (@ (@ tptp.produc1096319049_a_a_e C2) P)) (not (forall ((X2 tptp.set_a) (Y (-> tptp.a tptp.e))) (=> (= P (@ (@ tptp.produc1134456688_a_a_e X2) Y)) (not (@ (@ tptp.member1258382221_a_a_e Z2) (@ (@ C2 X2) Y)))))))) _let_3 (forall ((Ac2 tptp.produc715398134_a_a_e) (P2 (-> tptp.set_a (-> tptp.a tptp.e) Bool)) (Q (-> (-> tptp.a tptp.e) (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e Ac2) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o (@ (@ tptp.relcom658603713_e_a_e P2) Q)))) (@ (@ tptp.member1258382221_a_a_e (@ (@ (@ tptp.bNF_fs1024561536_e_a_e P2) Q) Ac2)) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o P2))))) (forall ((Ac2 tptp.produc715398134_a_a_e) (P2 (-> tptp.set_a tptp.set_a Bool)) (Q (-> tptp.set_a (-> tptp.a tptp.e) Bool))) (=> (@ (@ tptp.member1258382221_a_a_e Ac2) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o (@ (@ tptp.relcom779348378_a_a_e P2) Q)))) (@ (@ tptp.member1258382221_a_a_e (@ (@ (@ tptp.bNF_sn375433437_a_a_e P2) Q) Ac2)) (@ tptp.collec1369693387_a_a_e (@ tptp.produc1341862587_a_e_o Q))))) (forall ((B2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (X3 tptp.set_a) (C2 (-> tptp.a tptp.e)) (G (-> tptp.set_a tptp.a tptp.e)) (A tptp.set_set_a)) (=> (= B2 (@ F X3)) (=> (= C2 (@ G X3)) (=> (@ (@ tptp.member_set_a X3) A) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) C2)) (@ (@ (@ tptp.bNF_Gr1872575811_a_a_e A) F) G)))))) (forall ((B2 tptp.set_a) (F (-> tptp.produc715398134_a_a_e tptp.set_a)) (X3 tptp.produc715398134_a_a_e) (C2 (-> tptp.a tptp.e)) (G (-> tptp.produc715398134_a_a_e tptp.a tptp.e)) (A tptp.set_Pr204296108_a_a_e)) (=> (= B2 (@ F X3)) (=> (= C2 (@ G X3)) (=> (@ (@ tptp.member1258382221_a_a_e X3) A) (@ (@ tptp.member1258382221_a_a_e (@ (@ tptp.produc1134456688_a_a_e B2) C2)) (@ (@ (@ tptp.bNF_Gr2072183031_a_a_e A) F) G)))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))
% 0.89/1.10 )
% 0.89/1.10 % SZS output end Proof for ITP028^1
% 0.89/1.10 % cvc5---1.0.5 exiting
% 0.89/1.11 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------