TPTP Problem File: SLH0965^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : Safe_Range_RC/0021_Relational_Calculus/prob_01013_037527__17012008_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1298 ( 481 unt; 370 typ; 0 def)
% Number of atoms : 3772 (1563 equ; 0 cnn)
% Maximal formula atoms : 45 ( 4 avg)
% Number of connectives : 14137 ( 684 ~; 75 |; 188 &;11087 @)
% ( 0 <=>;2103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Number of types : 51 ( 50 usr)
% Number of type conns : 2431 (2431 >; 0 *; 0 +; 0 <<)
% Number of symbols : 323 ( 320 usr; 18 con; 0-8 aty)
% Number of variables : 4404 ( 358 ^;3906 !; 140 ?;4404 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 14:26:00.920
%------------------------------------------------------------------------------
% Could-be-implicit typings (50)
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% Explicit typings (320)
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relational_nocp_a_b: relational_fmla_a_b > $o ).
thf(sy_c_Relational__Calculus_Onocp__rel_001tf__a_001tf__b,type,
relati3149960101488570543el_a_b: relational_fmla_a_b > relational_fmla_a_b > $o ).
thf(sy_c_Relational__Calculus_Opartial__comparator__fmla_001tf__a_001tf__b,type,
relati8601483800347945207la_a_b: relati9178656908610317781_order > relational_fmla_a_b > order ).
thf(sy_c_Relational__Calculus_Oqp_001tf__a_001tf__b,type,
relational_qp_a_b: relational_fmla_a_b > $o ).
thf(sy_c_Relational__Calculus_Oqp__impl_001tf__a_001tf__b,type,
relati3725921752842749053pl_a_b: relational_fmla_a_b > $o ).
thf(sy_c_Relational__Calculus_Oqp__impl__rel_001tf__a_001tf__b,type,
relati7364465619720499582el_a_b: relational_fmla_a_b > relational_fmla_a_b > $o ).
thf(sy_c_Relational__Calculus_Orrb_001tf__a_001tf__b,type,
relational_rrb_a_b: relational_fmla_a_b > $o ).
thf(sy_c_Relational__Calculus_Osat_001tf__a_001t__Nat__Onat,type,
relational_sat_a_nat: relati9047081815478866374_a_nat > ( product_prod_nat_nat > set_list_a ) > ( nat > a ) > $o ).
thf(sy_c_Relational__Calculus_Osat_001tf__a_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati5954879512608767636la_a_b: relati7206184916280974613la_a_b > ( produc7366699395886430672_b_nat > set_list_a ) > ( nat > a ) > $o ).
thf(sy_c_Relational__Calculus_Osat_001tf__a_001tf__b,type,
relational_sat_a_b: relational_fmla_a_b > ( product_prod_b_nat > set_list_a ) > ( nat > a ) > $o ).
thf(sy_c_Relational__Calculus_Osat__rel_001tf__a_001t__Nat__Onat,type,
relati9040413291598363742_a_nat: produc3037992005704992583_nat_a > produc3037992005704992583_nat_a > $o ).
thf(sy_c_Relational__Calculus_Osat__rel_001tf__a_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati3587375677737501741la_a_b: produc565089920435310565_nat_a > produc565089920435310565_nat_a > $o ).
thf(sy_c_Relational__Calculus_Osat__rel_001tf__a_001tf__b,type,
relati4321809963887231473el_a_b: produc1132964494702330949_nat_a > produc1132964494702330949_nat_a > $o ).
thf(sy_c_Relational__Calculus_Osub_001tf__a_001tf__b,type,
relational_sub_a_b: relational_fmla_a_b > set_Re381260168593705685la_a_b ).
thf(sy_c_Relational__Calculus_Osub__rel_001tf__a_001tf__b,type,
relati7309537865537208983el_a_b: relational_fmla_a_b > relational_fmla_a_b > $o ).
thf(sy_c_Relational__Calculus_Osubst_001tf__a_001tf__b,type,
relational_subst_a_b: relational_fmla_a_b > nat > nat > relational_fmla_a_b ).
thf(sy_c_Relational__Calculus_Osubst__rel_001tf__a_001tf__b,type,
relati8369873211719781654el_a_b: produc8867654947514737559at_nat > produc8867654947514737559at_nat > $o ).
thf(sy_c_Relational__Calculus_Osubst__term_001tf__a,type,
relati7175845559408349773term_a: relational_term_a > nat > nat > relational_term_a ).
thf(sy_c_Relational__Calculus_Osubst__term__rel_001tf__a,type,
relati1089594453538404916_rel_a: produc6058688428250151583at_nat > produc6058688428250151583at_nat > $o ).
thf(sy_c_Relational__Calculus_Osubsts__bd_001tf__a_001tf__b,type,
relati3061153751618241490bd_a_b: nat > list_nat > list_nat > relational_fmla_a_b > nat ).
thf(sy_c_Relational__Calculus_Oterm_OConst_001t__List__Olist_Itf__a_J,type,
relati8210483018086767673list_a: list_a > relati383187284260386255list_a ).
thf(sy_c_Relational__Calculus_Oterm_OConst_001t__Nat__Onat,type,
relational_Const_nat: nat > relational_term_nat ).
thf(sy_c_Relational__Calculus_Oterm_OConst_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati3340789340644911146la_a_b: relational_fmla_a_b > relati112041753218324778la_a_b ).
thf(sy_c_Relational__Calculus_Oterm_OConst_001tf__a,type,
relational_Const_a: a > relational_term_a ).
thf(sy_c_Relational__Calculus_Oterm_OConst_001tf__b,type,
relational_Const_b: b > relational_term_b ).
thf(sy_c_Relational__Calculus_Oterm_OVar_001t__Nat__Onat,type,
relational_Var_nat: nat > relational_term_nat ).
thf(sy_c_Relational__Calculus_Oterm_OVar_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati2528351936964124430la_a_b: nat > relati112041753218324778la_a_b ).
thf(sy_c_Relational__Calculus_Oterm_OVar_001tf__a,type,
relational_Var_a: nat > relational_term_a ).
thf(sy_c_Relational__Calculus_Oterm_OVar_001tf__b,type,
relational_Var_b: nat > relational_term_b ).
thf(sy_c_Relational__Calculus_Oterm_Ocase__term_001tf__a_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati582353067970734056la_a_b: ( a > relational_fmla_a_b ) > ( nat > relational_fmla_a_b ) > relational_term_a > relational_fmla_a_b ).
thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
relati6186803337415672399list_a: ( list_a > list_a ) > relati383187284260386255list_a > relati383187284260386255list_a ).
thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__Nat__Onat_001t__Nat__Onat,type,
relati2575597170284168561at_nat: ( nat > nat ) > relational_term_nat > relational_term_nat ).
thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati8623550108501193999la_a_b: ( relational_fmla_a_b > relational_fmla_a_b ) > relati112041753218324778la_a_b > relati112041753218324778la_a_b ).
thf(sy_c_Relational__Calculus_Oterm_Omap__term_001tf__a_001tf__a,type,
relati3585320759856631375rm_a_a: ( a > a ) > relational_term_a > relational_term_a ).
thf(sy_c_Relational__Calculus_Oterm_Omap__term_001tf__b_001tf__b,type,
relati797865177883955343rm_b_b: ( b > b ) > relational_term_b > relational_term_b ).
thf(sy_c_Relational__Calculus_Oterm_Opred__term_001t__List__Olist_Itf__a_J,type,
relati4353722553127530653list_a: ( list_a > $o ) > relati383187284260386255list_a > $o ).
thf(sy_c_Relational__Calculus_Oterm_Opred__term_001t__Nat__Onat,type,
relati2679609588974042615rm_nat: ( nat > $o ) > relational_term_nat > $o ).
thf(sy_c_Relational__Calculus_Oterm_Opred__term_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati9173353072008103110la_a_b: ( relational_fmla_a_b > $o ) > relati112041753218324778la_a_b > $o ).
thf(sy_c_Relational__Calculus_Oterm_Opred__term_001tf__a,type,
relati6920953664156333207term_a: ( a > $o ) > relational_term_a > $o ).
thf(sy_c_Relational__Calculus_Oterm_Opred__term_001tf__b,type,
relati6920953664156333208term_b: ( b > $o ) > relational_term_b > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
relati8847882339280608716list_a: ( list_a > list_a > $o ) > relati383187284260386255list_a > relati383187284260386255list_a > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Nat__Onat_001t__List__Olist_Itf__a_J,type,
relati4525196732223128934list_a: ( nat > list_a > $o ) > relational_term_nat > relati383187284260386255list_a > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Nat__Onat_001t__Nat__Onat,type,
relati2881564729679077486at_nat: ( nat > nat > $o ) > relational_term_nat > relational_term_nat > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Nat__Onat_001tf__a,type,
relati6955175908526440928_nat_a: ( nat > a > $o ) > relational_term_nat > relational_term_a > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Nat__Onat_001tf__b,type,
relati6955175908526440929_nat_b: ( nat > b > $o ) > relational_term_nat > relational_term_b > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati4738647720883422732la_a_b: ( relational_fmla_a_b > relational_fmla_a_b > $o ) > relati112041753218324778la_a_b > relati112041753218324778la_a_b > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__a_001t__Nat__Onat,type,
relati2923244407348154498_a_nat: ( a > nat > $o ) > relational_term_a > relational_term_nat > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__a_001tf__a,type,
relati3163788165526728396rm_a_a: ( a > a > $o ) > relational_term_a > relational_term_a > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__a_001tf__b,type,
relati3163788165526728397rm_a_b: ( a > b > $o ) > relational_term_a > relational_term_b > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__b_001t__Nat__Onat,type,
relati4158688736304548995_b_nat: ( b > nat > $o ) > relational_term_b > relational_term_nat > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__b_001tf__a,type,
relati376332583554052363rm_b_a: ( b > a > $o ) > relational_term_b > relational_term_a > $o ).
thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__b_001tf__b,type,
relati376332583554052364rm_b_b: ( b > b > $o ) > relational_term_b > relational_term_b > $o ).
thf(sy_c_Relational__Calculus_Oterm_Oset__term_001t__List__Olist_Itf__a_J,type,
relati1115505217504806350list_a: relati383187284260386255list_a > set_list_a ).
thf(sy_c_Relational__Calculus_Oterm_Oset__term_001t__Nat__Onat,type,
relati7416457470477713926rm_nat: relational_term_nat > set_nat ).
thf(sy_c_Relational__Calculus_Oterm_Oset__term_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
relati7240241301533008341la_a_b: relati112041753218324778la_a_b > set_Re381260168593705685la_a_b ).
thf(sy_c_Relational__Calculus_Oterm_Oset__term_001tf__a,type,
relati2096729434547099208term_a: relational_term_a > set_a ).
thf(sy_c_Relational__Calculus_Oterm_Oset__term_001tf__b,type,
relati2096729434547099209term_b: relational_term_b > set_b ).
thf(sy_c_Set_OCollect_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
collec8200894614646537018term_a: ( list_R6823256787227418703term_a > $o ) > set_li7681422004278482351term_a ).
thf(sy_c_Set_OCollect_001t__List__Olist_Itf__a_J,type,
collect_list_a: ( list_a > $o ) > set_list_a ).
thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(sy_c_Set_OCollect_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
collec3419995626248312948la_a_b: ( relational_fmla_a_b > $o ) > set_Re381260168593705685la_a_b ).
thf(sy_c_Set_OCollect_001t__Relational____Calculus__Oterm_Itf__a_J,type,
collec7376311432011962548term_a: ( relational_term_a > $o ) > set_Re5178783185447174953term_a ).
thf(sy_c_Set_OCollect_001tf__a,type,
collect_a: ( a > $o ) > set_a ).
thf(sy_c_Set_OCollect_001tf__b,type,
collect_b: ( b > $o ) > set_b ).
thf(sy_c_Set_Oimage_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
image_6790371041703824709la_a_b: ( relational_fmla_a_b > relational_fmla_a_b ) > set_Re381260168593705685la_a_b > set_Re381260168593705685la_a_b ).
thf(sy_c_Set_Oimage_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_001t__Set__Oset_It__Nat__Onat_J,type,
image_8719518604786020652et_nat: ( relational_fmla_a_b > set_nat ) > set_Re381260168593705685la_a_b > set_set_nat ).
thf(sy_c_Set_Oimage_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
image_1080223610614215258_set_a: ( relational_term_a > set_a ) > set_Re5178783185447174953term_a > set_set_a ).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_J_001t__Set__Oset_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_J,type,
image_7051608999182166449la_a_b: ( set_Re381260168593705685la_a_b > set_Re381260168593705685la_a_b ) > set_se6865892389300016395la_a_b > set_se6865892389300016395la_a_b ).
thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
image_a_a: ( a > a ) > set_a > set_a ).
thf(sy_c_Set_Oimage_001tf__b_001tf__b,type,
image_b_b: ( b > b ) > set_b > set_b ).
thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
insert_nat: nat > set_nat > set_nat ).
thf(sy_c_Set_Oinsert_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
insert7010464514620295119la_a_b: relational_fmla_a_b > set_Re381260168593705685la_a_b > set_Re381260168593705685la_a_b ).
thf(sy_c_Set_Oinsert_001tf__a,type,
insert_a: a > set_a > set_a ).
thf(sy_c_Set_Oinsert_001tf__b,type,
insert_b: b > set_b > set_b ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
accp_P3115975753873020414_nat_a: ( produc3037992005704992583_nat_a > produc3037992005704992583_nat_a > $o ) > produc3037992005704992583_nat_a > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mt__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
accp_P932837839904948380_nat_a: ( produc565089920435310565_nat_a > produc565089920435310565_nat_a > $o ) > produc565089920435310565_nat_a > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Nat__Onat_J,type,
accp_P4351966040938400857_b_nat: ( produc7366699395886430672_b_nat > produc7366699395886430672_b_nat > $o ) > produc7366699395886430672_b_nat > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
accp_P6721201822162371452_nat_a: ( produc1132964494702330949_nat_a > produc1132964494702330949_nat_a > $o ) > produc1132964494702330949_nat_a > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
accp_P2470304046166516174at_nat: ( produc8867654947514737559at_nat > produc8867654947514737559at_nat > $o ) > produc8867654947514737559at_nat > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
accp_P7512640865500879912at_nat: ( produc6058688428250151583at_nat > produc6058688428250151583at_nat > $o ) > produc6058688428250151583at_nat > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
accp_R989495437599811158la_a_b: ( relational_fmla_a_b > relational_fmla_a_b > $o ) > relational_fmla_a_b > $o ).
thf(sy_c_Wellfounded_Oaccp_001t__Relational____Calculus__Oterm_Itf__a_J,type,
accp_R1925461290012245842term_a: ( relational_term_a > relational_term_a > $o ) > relational_term_a > $o ).
thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
member_list_a: list_a > set_list_a > $o ).
thf(sy_c_member_001t__Nat__Onat,type,
member_nat: nat > set_nat > $o ).
thf(sy_c_member_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
member4680049679412964150la_a_b: relational_fmla_a_b > set_Re381260168593705685la_a_b > $o ).
thf(sy_c_member_001t__Relational____Calculus__Oterm_Itf__a_J,type,
member5466445112152945266term_a: relational_term_a > set_Re5178783185447174953term_a > $o ).
thf(sy_c_member_001tf__a,type,
member_a: a > set_a > $o ).
thf(sy_c_member_001tf__b,type,
member_b: b > set_b > $o ).
thf(sy_v_b,type,
b2: $o ).
% Relevant facts (922)
thf(fact_0_fmla_Oinject_I2_J,axiom,
! [X2: $o,Y2: $o] :
( ( ( relational_Bool_a_b @ X2 )
= ( relational_Bool_a_b @ Y2 ) )
= ( X2 = Y2 ) ) ).
% fmla.inject(2)
thf(fact_1_cpropagated__simps_I1_J,axiom,
! [B: $o] : ( relati1591879772219623554ed_a_b @ ( relational_Bool_a_b @ B ) ) ).
% cpropagated_simps(1)
thf(fact_2_qp__impl_Osimps_I4_J,axiom,
! [V: $o] :
~ ( relati3725921752842749053pl_a_b @ ( relational_Bool_a_b @ V ) ) ).
% qp_impl.simps(4)
thf(fact_3_fmla_Osimps_I51_J,axiom,
! [F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,X2: $o] :
( ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Bool_a_b @ X2 ) )
= ( F2 @ X2 ) ) ).
% fmla.simps(51)
thf(fact_4_fmla_Osel_I3_J,axiom,
! [X2: $o] :
( ( relati2638701775882563405ol_a_b @ ( relational_Bool_a_b @ X2 ) )
= X2 ) ).
% fmla.sel(3)
thf(fact_5_erase_Osimps_I1_J,axiom,
! [T: $o,X: nat] :
( ( relational_erase_a_b @ ( relational_Bool_a_b @ T ) @ X )
= ( relational_Bool_a_b @ T ) ) ).
% erase.simps(1)
thf(fact_6_fmla_Odisc_I44_J,axiom,
! [X2: $o] :
~ ( relati5212983245281121968ts_a_b @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.disc(44)
thf(fact_7_fmla_Odisc_I23_J,axiom,
! [X2: $o] :
~ ( relati4321004860440572638eg_a_b @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.disc(23)
thf(fact_8_fmla_Odisc_I16_J,axiom,
! [X2: $o] :
~ ( relational_is_Eq_a_b @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.disc(16)
thf(fact_9_fmla_Odisc_I2_J,axiom,
! [X2: $o] :
~ ( relati3644702733014758741ed_a_b @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.disc(2)
thf(fact_10_fmla_Odisc_I37_J,axiom,
! [X2: $o] :
~ ( relati5350680195807439568sj_a_b @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.disc(37)
thf(fact_11_fmla_Odisc_I30_J,axiom,
! [X2: $o] :
~ ( relati8168519172193746908nj_a_b @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.disc(30)
thf(fact_12_fmla_Odistinct__disc_I42_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ Fmla )
=> ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(42)
thf(fact_13_fmla_Odistinct__disc_I41_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ Fmla )
=> ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).
% fmla.distinct_disc(41)
thf(fact_14_fmla_Odistinct__disc_I40_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ Fmla )
=> ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(40)
thf(fact_15_fmla_Odistinct__disc_I39_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ Fmla )
=> ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).
% fmla.distinct_disc(39)
thf(fact_16_fmla_Odistinct__disc_I38_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ Fmla )
=> ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(38)
thf(fact_17_fmla_Odistinct__disc_I37_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ Fmla )
=> ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(37)
thf(fact_18_fmla_Odistinct__disc_I36_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ Fmla )
=> ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).
% fmla.distinct_disc(36)
thf(fact_19_fmla_Odistinct__disc_I35_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ Fmla )
=> ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).
% fmla.distinct_disc(35)
thf(fact_20_fmla_Odistinct__disc_I34_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ Fmla )
=> ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).
% fmla.distinct_disc(34)
thf(fact_21_fmla_Odistinct__disc_I33_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ Fmla )
=> ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(33)
thf(fact_22_fmla_Odistinct__disc_I32_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ Fmla )
=> ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).
% fmla.distinct_disc(32)
thf(fact_23_fmla_Odistinct__disc_I31_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ Fmla )
=> ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(31)
thf(fact_24_fmla_Odistinct__disc_I30_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ Fmla )
=> ~ ( relational_is_Eq_a_b @ Fmla ) ) ).
% fmla.distinct_disc(30)
thf(fact_25_fmla_Odistinct__disc_I29_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ Fmla )
=> ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).
% fmla.distinct_disc(29)
thf(fact_26_fmla_Odistinct__disc_I28_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ Fmla )
=> ~ ( relational_is_Eq_a_b @ Fmla ) ) ).
% fmla.distinct_disc(28)
thf(fact_27_fmla_Odistinct__disc_I27_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ Fmla )
=> ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(27)
thf(fact_28_fmla_Odistinct__disc_I26_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ Fmla )
=> ~ ( relational_is_Eq_a_b @ Fmla ) ) ).
% fmla.distinct_disc(26)
thf(fact_29_fmla_Odistinct__disc_I25_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ Fmla )
=> ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(25)
thf(fact_30_fmla_Odistinct__disc_I24_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ Fmla )
=> ~ ( relational_is_Eq_a_b @ Fmla ) ) ).
% fmla.distinct_disc(24)
thf(fact_31_fmla_Odistinct__disc_I23_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ Fmla )
=> ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).
% fmla.distinct_disc(23)
thf(fact_32_fmla_Odistinct__disc_I12_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ Fmla )
=> ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).
% fmla.distinct_disc(12)
thf(fact_33_fmla_Odistinct__disc_I11_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ Fmla )
=> ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).
% fmla.distinct_disc(11)
thf(fact_34_fmla_Odistinct__disc_I10_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ Fmla )
=> ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).
% fmla.distinct_disc(10)
thf(fact_35_fmla_Odistinct__disc_I9_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ Fmla )
=> ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(9)
thf(fact_36_fmla_Odistinct__disc_I8_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ Fmla )
=> ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).
% fmla.distinct_disc(8)
thf(fact_37_fmla_Odistinct__disc_I7_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ Fmla )
=> ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(7)
thf(fact_38_fmla_Odistinct__disc_I6_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ Fmla )
=> ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).
% fmla.distinct_disc(6)
thf(fact_39_fmla_Odistinct__disc_I5_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ Fmla )
=> ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).
% fmla.distinct_disc(5)
thf(fact_40_fmla_Odistinct__disc_I4_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ Fmla )
=> ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).
% fmla.distinct_disc(4)
thf(fact_41_fmla_Odistinct__disc_I3_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ Fmla )
=> ~ ( relational_is_Eq_a_b @ Fmla ) ) ).
% fmla.distinct_disc(3)
thf(fact_42_fmla_Oexhaust__disc,axiom,
! [Fmla: relational_fmla_a_b] :
( ~ ( relati3644702733014758741ed_a_b @ Fmla )
=> ( ~ ( relati6551038146797045342ol_a_b @ Fmla )
=> ( ~ ( relational_is_Eq_a_b @ Fmla )
=> ( ~ ( relati4321004860440572638eg_a_b @ Fmla )
=> ( ~ ( relati8168519172193746908nj_a_b @ Fmla )
=> ( ~ ( relati5350680195807439568sj_a_b @ Fmla )
=> ( relati5212983245281121968ts_a_b @ Fmla ) ) ) ) ) ) ) ).
% fmla.exhaust_disc
thf(fact_43_fmla_Ocollapse_I2_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Fmla )
=> ( ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) )
= Fmla ) ) ).
% fmla.collapse(2)
thf(fact_44_mem__Collect__eq,axiom,
! [A: relational_fmla_a_b,P: relational_fmla_a_b > $o] :
( ( member4680049679412964150la_a_b @ A @ ( collec3419995626248312948la_a_b @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_45_mem__Collect__eq,axiom,
! [A: nat,P: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_46_mem__Collect__eq,axiom,
! [A: b,P: b > $o] :
( ( member_b @ A @ ( collect_b @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_47_mem__Collect__eq,axiom,
! [A: list_a,P: list_a > $o] :
( ( member_list_a @ A @ ( collect_list_a @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_48_mem__Collect__eq,axiom,
! [A: a,P: a > $o] :
( ( member_a @ A @ ( collect_a @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_49_Collect__mem__eq,axiom,
! [A2: set_Re381260168593705685la_a_b] :
( ( collec3419995626248312948la_a_b
@ ^ [X3: relational_fmla_a_b] : ( member4680049679412964150la_a_b @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_50_Collect__mem__eq,axiom,
! [A2: set_nat] :
( ( collect_nat
@ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_51_Collect__mem__eq,axiom,
! [A2: set_b] :
( ( collect_b
@ ^ [X3: b] : ( member_b @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_52_Collect__mem__eq,axiom,
! [A2: set_list_a] :
( ( collect_list_a
@ ^ [X3: list_a] : ( member_list_a @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_53_Collect__mem__eq,axiom,
! [A2: set_a] :
( ( collect_a
@ ^ [X3: a] : ( member_a @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_54_cpropagated__simps_I2_J,axiom,
! [P2: b,Ts: list_R6823256787227418703term_a] : ( relati1591879772219623554ed_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) ) ).
% cpropagated_simps(2)
thf(fact_55_cpropagated__sub,axiom,
! [Q: relational_fmla_a_b,Q2: relational_fmla_a_b] :
( ( relati1591879772219623554ed_a_b @ Q )
=> ( ( member4680049679412964150la_a_b @ Q2 @ ( relational_sub_a_b @ Q ) )
=> ( relati1591879772219623554ed_a_b @ Q2 ) ) ) ).
% cpropagated_sub
thf(fact_56_qp__code,axiom,
relational_qp_a_b = relati3725921752842749053pl_a_b ).
% qp_code
thf(fact_57_qp__imp__qp__impl,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_qp_a_b @ Q )
=> ( relati3725921752842749053pl_a_b @ Q ) ) ).
% qp_imp_qp_impl
thf(fact_58_qp__impl__imp__qp,axiom,
! [Q: relational_fmla_a_b] :
( ( relati3725921752842749053pl_a_b @ Q )
=> ( relational_qp_a_b @ Q ) ) ).
% qp_impl_imp_qp
thf(fact_59_fmla_Omap__disc__iff_I7_J,axiom,
! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati5212983245281121968ts_a_b @ A ) ) ).
% fmla.map_disc_iff(7)
thf(fact_60_fmla_Omap__disc__iff_I4_J,axiom,
! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati4321004860440572638eg_a_b @ A ) ) ).
% fmla.map_disc_iff(4)
thf(fact_61_fmla_Omap__disc__iff_I3_J,axiom,
! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relational_is_Eq_a_b @ A ) ) ).
% fmla.map_disc_iff(3)
thf(fact_62_fmla_Omap__disc__iff_I1_J,axiom,
! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati3644702733014758741ed_a_b @ A ) ) ).
% fmla.map_disc_iff(1)
thf(fact_63_fmla_Omap__disc__iff_I6_J,axiom,
! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati5350680195807439568sj_a_b @ A ) ) ).
% fmla.map_disc_iff(6)
thf(fact_64_fmla_Oinject_I1_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a,Y11: b,Y12: list_R6823256787227418703term_a] :
( ( ( relational_Pred_b_a @ X11 @ X12 )
= ( relational_Pred_b_a @ Y11 @ Y12 ) )
= ( ( X11 = Y11 )
& ( X12 = Y12 ) ) ) ).
% fmla.inject(1)
thf(fact_65_fmla_Omap__disc__iff_I2_J,axiom,
! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati6551038146797045342ol_a_b @ A ) ) ).
% fmla.map_disc_iff(2)
thf(fact_66_fmla_Omap__disc__iff_I5_J,axiom,
! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati8168519172193746908nj_a_b @ A ) ) ).
% fmla.map_disc_iff(5)
thf(fact_67_fmla_Odisc_I8_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati6551038146797045342ol_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.disc(8)
thf(fact_68_fmla_Omap__sel_I3_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati6551038146797045342ol_a_b @ A )
=> ( ( relati2638701775882563405ol_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati2638701775882563405ol_a_b @ A ) ) ) ).
% fmla.map_sel(3)
thf(fact_69_fmla_Osimps_I65_J,axiom,
! [F1: a > a,F2: b > b,X2: $o] :
( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Bool_a_b @ X2 ) )
= ( relational_Bool_a_b @ X2 ) ) ).
% fmla.simps(65)
thf(fact_70_fmla_Odistinct_I1_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a,X2: $o] :
( ( relational_Pred_b_a @ X11 @ X12 )
!= ( relational_Bool_a_b @ X2 ) ) ).
% fmla.distinct(1)
thf(fact_71_fmla_Odisc_I29_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati8168519172193746908nj_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.disc(29)
thf(fact_72_fmla_Odisc_I36_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati5350680195807439568sj_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.disc(36)
thf(fact_73_is__Pred__def,axiom,
( relati3644702733014758741ed_a_b
= ( ^ [Fmla2: relational_fmla_a_b] :
? [X112: b,X122: list_R6823256787227418703term_a] :
( Fmla2
= ( relational_Pred_b_a @ X112 @ X122 ) ) ) ) ).
% is_Pred_def
thf(fact_74_fmla_OdiscI_I1_J,axiom,
! [Fmla: relational_fmla_a_b,X11: b,X12: list_R6823256787227418703term_a] :
( ( Fmla
= ( relational_Pred_b_a @ X11 @ X12 ) )
=> ( relati3644702733014758741ed_a_b @ Fmla ) ) ).
% fmla.discI(1)
thf(fact_75_fmla_Odisc_I1_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] : ( relati3644702733014758741ed_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.disc(1)
thf(fact_76_fmla_Osimps_I50_J,axiom,
! [F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,X11: b,X12: list_R6823256787227418703term_a] :
( ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Pred_b_a @ X11 @ X12 ) )
= ( F1 @ X11 @ X12 ) ) ).
% fmla.simps(50)
thf(fact_77_fmla_Odisc_I15_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
~ ( relational_is_Eq_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.disc(15)
thf(fact_78_fmla_Odisc_I22_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati4321004860440572638eg_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.disc(22)
thf(fact_79_fmla_Odisc_I43_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati5212983245281121968ts_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.disc(43)
thf(fact_80_fmla_Odisc_I9_J,axiom,
! [X2: $o] : ( relati6551038146797045342ol_a_b @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.disc(9)
thf(fact_81_fmla_OdiscI_I2_J,axiom,
! [Fmla: relational_fmla_a_b,X2: $o] :
( ( Fmla
= ( relational_Bool_a_b @ X2 ) )
=> ( relati6551038146797045342ol_a_b @ Fmla ) ) ).
% fmla.discI(2)
thf(fact_82_is__Bool__def,axiom,
( relati6551038146797045342ol_a_b
= ( ^ [Fmla2: relational_fmla_a_b] :
? [X22: $o] :
( Fmla2
= ( relational_Bool_a_b @ X22 ) ) ) ) ).
% is_Bool_def
thf(fact_83_qp__impl_Osimps_I2_J,axiom,
! [X: b,Ts: list_R6823256787227418703term_a] : ( relati3725921752842749053pl_a_b @ ( relational_Pred_b_a @ X @ Ts ) ) ).
% qp_impl.simps(2)
thf(fact_84_fmla_Odistinct__disc_I17_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Fmla )
=> ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(17)
thf(fact_85_fmla_Odistinct__disc_I18_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ Fmla )
=> ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).
% fmla.distinct_disc(18)
thf(fact_86_fmla_Odistinct__disc_I19_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Fmla )
=> ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).
% fmla.distinct_disc(19)
thf(fact_87_fmla_Odistinct__disc_I20_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ Fmla )
=> ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).
% fmla.distinct_disc(20)
thf(fact_88_fmla_Odistinct__disc_I1_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ Fmla )
=> ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).
% fmla.distinct_disc(1)
thf(fact_89_fmla_Odistinct__disc_I2_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Fmla )
=> ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).
% fmla.distinct_disc(2)
thf(fact_90_fmla_Odistinct__disc_I13_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Fmla )
=> ~ ( relational_is_Eq_a_b @ Fmla ) ) ).
% fmla.distinct_disc(13)
thf(fact_91_fmla_Odistinct__disc_I14_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ Fmla )
=> ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).
% fmla.distinct_disc(14)
thf(fact_92_fmla_Odistinct__disc_I15_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Fmla )
=> ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).
% fmla.distinct_disc(15)
thf(fact_93_fmla_Odistinct__disc_I16_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ Fmla )
=> ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).
% fmla.distinct_disc(16)
thf(fact_94_fmla_Odistinct__disc_I21_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Fmla )
=> ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).
% fmla.distinct_disc(21)
thf(fact_95_fmla_Odistinct__disc_I22_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ Fmla )
=> ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).
% fmla.distinct_disc(22)
thf(fact_96_erase_Osimps_I2_J,axiom,
! [X: nat,Ts: list_R6823256787227418703term_a,P2: b] :
( ( ( member_nat @ X @ ( relati4569515538964159125_set_a @ Ts ) )
=> ( ( relational_erase_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) @ X )
= ( relational_Bool_a_b @ $false ) ) )
& ( ~ ( member_nat @ X @ ( relati4569515538964159125_set_a @ Ts ) )
=> ( ( relational_erase_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) @ X )
= ( relational_Pred_b_a @ P2 @ Ts ) ) ) ) ).
% erase.simps(2)
thf(fact_97_fmla_Omap__sel_I11_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati5212983245281121968ts_a_b @ A )
=> ( ( relati9218598872894977428s1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati9218598872894977428s1_a_b @ A ) ) ) ).
% fmla.map_sel(11)
thf(fact_98_fmla_Omap__sel_I4_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relational_is_Eq_a_b @ A )
=> ( ( relati5459635069493737188q1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati5459635069493737188q1_a_b @ A ) ) ) ).
% fmla.map_sel(4)
thf(fact_99_fmla_Omap__sel_I1_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati3644702733014758741ed_a_b @ A )
=> ( ( relati91604085239814319d1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( F2 @ ( relati91604085239814319d1_a_b @ A ) ) ) ) ).
% fmla.map_sel(1)
thf(fact_100_fmla_Omap__sel_I12_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati5212983245281121968ts_a_b @ A )
=> ( ( relati5591445451228332309s2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati5591445451228332309s2_a_b @ A ) ) ) ) ).
% fmla.map_sel(12)
thf(fact_101_fmla_Omap__sel_I6_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati4321004860440572638eg_a_b @ A )
=> ( ( relati5982302313924697647eg_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati5982302313924697647eg_a_b @ A ) ) ) ) ).
% fmla.map_sel(6)
thf(fact_102_fmla_Omap__sel_I7_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati8168519172193746908nj_a_b @ A )
=> ( ( relati5154284022127734760j1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati5154284022127734760j1_a_b @ A ) ) ) ) ).
% fmla.map_sel(7)
thf(fact_103_fmla_Omap__sel_I8_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati8168519172193746908nj_a_b @ A )
=> ( ( relati1527130600461089641j2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati1527130600461089641j2_a_b @ A ) ) ) ) ).
% fmla.map_sel(8)
thf(fact_104_fmla_Omap__sel_I9_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati5350680195807439568sj_a_b @ A )
=> ( ( relati3334262663314506228j1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati3334262663314506228j1_a_b @ A ) ) ) ) ).
% fmla.map_sel(9)
thf(fact_105_fmla_Omap__sel_I10_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati5350680195807439568sj_a_b @ A )
=> ( ( relati8930481278502636917j2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati8930481278502636917j2_a_b @ A ) ) ) ) ).
% fmla.map_sel(10)
thf(fact_106_cpropagated__def,axiom,
( relati1591879772219623554ed_a_b
= ( ^ [Q3: relational_fmla_a_b] :
( ( relational_nocp_a_b @ Q3 )
| ( relati6551038146797045342ol_a_b @ Q3 ) ) ) ) ).
% cpropagated_def
thf(fact_107_nocp_Osimps_I1_J,axiom,
! [B: $o] :
~ ( relational_nocp_a_b @ ( relational_Bool_a_b @ B ) ) ).
% nocp.simps(1)
thf(fact_108_nocp_Osimps_I2_J,axiom,
! [P2: b,Ts: list_R6823256787227418703term_a] : ( relational_nocp_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) ) ).
% nocp.simps(2)
thf(fact_109_nocp__cpropagated,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_nocp_a_b @ Q )
=> ( relati1591879772219623554ed_a_b @ Q ) ) ).
% nocp_cpropagated
thf(fact_110_fmla_Osel_I1_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
( ( relati91604085239814319d1_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) )
= X11 ) ).
% fmla.sel(1)
thf(fact_111_fmla_Oexpand,axiom,
! [Fmla: relational_fmla_a_b,Fmla3: relational_fmla_a_b] :
( ( ( relati3644702733014758741ed_a_b @ Fmla )
= ( relati3644702733014758741ed_a_b @ Fmla3 ) )
=> ( ( ( relati3644702733014758741ed_a_b @ Fmla )
=> ( ( relati3644702733014758741ed_a_b @ Fmla3 )
=> ( ( ( relati91604085239814319d1_a_b @ Fmla )
= ( relati91604085239814319d1_a_b @ Fmla3 ) )
& ( ( relati5687822700427945008d2_a_b @ Fmla )
= ( relati5687822700427945008d2_a_b @ Fmla3 ) ) ) ) )
=> ( ( ( relati6551038146797045342ol_a_b @ Fmla )
= ( relati6551038146797045342ol_a_b @ Fmla3 ) )
=> ( ( ( relati6551038146797045342ol_a_b @ Fmla )
=> ( ( relati6551038146797045342ol_a_b @ Fmla3 )
=> ( ( relati2638701775882563405ol_a_b @ Fmla )
= ( relati2638701775882563405ol_a_b @ Fmla3 ) ) ) )
=> ( ( ( relational_is_Eq_a_b @ Fmla )
= ( relational_is_Eq_a_b @ Fmla3 ) )
=> ( ( ( relational_is_Eq_a_b @ Fmla )
=> ( ( relational_is_Eq_a_b @ Fmla3 )
=> ( ( ( relati5459635069493737188q1_a_b @ Fmla )
= ( relati5459635069493737188q1_a_b @ Fmla3 ) )
& ( ( relati1832481647827092069q2_a_b @ Fmla )
= ( relati1832481647827092069q2_a_b @ Fmla3 ) ) ) ) )
=> ( ( ( relati4321004860440572638eg_a_b @ Fmla )
= ( relati4321004860440572638eg_a_b @ Fmla3 ) )
=> ( ( ( relati4321004860440572638eg_a_b @ Fmla )
=> ( ( relati4321004860440572638eg_a_b @ Fmla3 )
=> ( ( relati5982302313924697647eg_a_b @ Fmla )
= ( relati5982302313924697647eg_a_b @ Fmla3 ) ) ) )
=> ( ( ( relati8168519172193746908nj_a_b @ Fmla )
= ( relati8168519172193746908nj_a_b @ Fmla3 ) )
=> ( ( ( relati8168519172193746908nj_a_b @ Fmla )
=> ( ( relati8168519172193746908nj_a_b @ Fmla3 )
=> ( ( ( relati5154284022127734760j1_a_b @ Fmla )
= ( relati5154284022127734760j1_a_b @ Fmla3 ) )
& ( ( relati1527130600461089641j2_a_b @ Fmla )
= ( relati1527130600461089641j2_a_b @ Fmla3 ) ) ) ) )
=> ( ( ( relati5350680195807439568sj_a_b @ Fmla )
= ( relati5350680195807439568sj_a_b @ Fmla3 ) )
=> ( ( ( relati5350680195807439568sj_a_b @ Fmla )
=> ( ( relati5350680195807439568sj_a_b @ Fmla3 )
=> ( ( ( relati3334262663314506228j1_a_b @ Fmla )
= ( relati3334262663314506228j1_a_b @ Fmla3 ) )
& ( ( relati8930481278502636917j2_a_b @ Fmla )
= ( relati8930481278502636917j2_a_b @ Fmla3 ) ) ) ) )
=> ( ( ( relati5212983245281121968ts_a_b @ Fmla )
=> ( ( relati5212983245281121968ts_a_b @ Fmla3 )
=> ( ( ( relati9218598872894977428s1_a_b @ Fmla )
= ( relati9218598872894977428s1_a_b @ Fmla3 ) )
& ( ( relati5591445451228332309s2_a_b @ Fmla )
= ( relati5591445451228332309s2_a_b @ Fmla3 ) ) ) ) )
=> ( Fmla = Fmla3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% fmla.expand
thf(fact_112_fmla_Ocase__eq__if,axiom,
( relati6637215556741570915_b_a_o
= ( ^ [F12: b > list_R6823256787227418703term_a > $o,F22: $o > $o,F32: nat > relational_term_a > $o,F42: relational_fmla_a_b > $o,F52: relational_fmla_a_b > relational_fmla_a_b > $o,F62: relational_fmla_a_b > relational_fmla_a_b > $o,F72: nat > relational_fmla_a_b > $o,Fmla2: relational_fmla_a_b] :
( ( ( relati3644702733014758741ed_a_b @ Fmla2 )
=> ( F12 @ ( relati91604085239814319d1_a_b @ Fmla2 ) @ ( relati5687822700427945008d2_a_b @ Fmla2 ) ) )
& ( ~ ( relati3644702733014758741ed_a_b @ Fmla2 )
=> ( ( ( relati6551038146797045342ol_a_b @ Fmla2 )
=> ( F22 @ ( relati2638701775882563405ol_a_b @ Fmla2 ) ) )
& ( ~ ( relati6551038146797045342ol_a_b @ Fmla2 )
=> ( ( ( relational_is_Eq_a_b @ Fmla2 )
=> ( F32 @ ( relati5459635069493737188q1_a_b @ Fmla2 ) @ ( relati1832481647827092069q2_a_b @ Fmla2 ) ) )
& ( ~ ( relational_is_Eq_a_b @ Fmla2 )
=> ( ( ( relati4321004860440572638eg_a_b @ Fmla2 )
=> ( F42 @ ( relati5982302313924697647eg_a_b @ Fmla2 ) ) )
& ( ~ ( relati4321004860440572638eg_a_b @ Fmla2 )
=> ( ( ( relati8168519172193746908nj_a_b @ Fmla2 )
=> ( F52 @ ( relati5154284022127734760j1_a_b @ Fmla2 ) @ ( relati1527130600461089641j2_a_b @ Fmla2 ) ) )
& ( ~ ( relati8168519172193746908nj_a_b @ Fmla2 )
=> ( ( ( relati5350680195807439568sj_a_b @ Fmla2 )
=> ( F62 @ ( relati3334262663314506228j1_a_b @ Fmla2 ) @ ( relati8930481278502636917j2_a_b @ Fmla2 ) ) )
& ( ~ ( relati5350680195807439568sj_a_b @ Fmla2 )
=> ( F72 @ ( relati9218598872894977428s1_a_b @ Fmla2 ) @ ( relati5591445451228332309s2_a_b @ Fmla2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% fmla.case_eq_if
thf(fact_113_fmla_Ocollapse_I1_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ Fmla )
=> ( ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) )
= Fmla ) ) ).
% fmla.collapse(1)
thf(fact_114_fmla_Ocollapse_I7_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5212983245281121968ts_a_b @ Fmla )
=> ( ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) )
= Fmla ) ) ).
% fmla.collapse(7)
thf(fact_115_fmla_Ocollapse_I6_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati5350680195807439568sj_a_b @ Fmla )
=> ( ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) )
= Fmla ) ) ).
% fmla.collapse(6)
thf(fact_116_fmla_Ocollapse_I5_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati8168519172193746908nj_a_b @ Fmla )
=> ( ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) )
= Fmla ) ) ).
% fmla.collapse(5)
thf(fact_117_fmla_Ocollapse_I4_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relati4321004860440572638eg_a_b @ Fmla )
=> ( ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) )
= Fmla ) ) ).
% fmla.collapse(4)
thf(fact_118_cpropagated__simps_I4_J,axiom,
! [Q: relational_fmla_a_b] :
( ( relati1591879772219623554ed_a_b @ ( relational_Neg_a_b @ Q ) )
= ( relational_nocp_a_b @ Q ) ) ).
% cpropagated_simps(4)
thf(fact_119_cpropagated__simps_I6_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relati1591879772219623554ed_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) )
= ( ( relational_nocp_a_b @ Q1 )
& ( relational_nocp_a_b @ Q22 ) ) ) ).
% cpropagated_simps(6)
thf(fact_120_fmla_Oinject_I4_J,axiom,
! [X4: relational_fmla_a_b,Y4: relational_fmla_a_b] :
( ( ( relational_Neg_a_b @ X4 )
= ( relational_Neg_a_b @ Y4 ) )
= ( X4 = Y4 ) ) ).
% fmla.inject(4)
thf(fact_121_fmla_Oinject_I6_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
( ( ( relational_Disj_a_b @ X61 @ X62 )
= ( relational_Disj_a_b @ Y61 @ Y62 ) )
= ( ( X61 = Y61 )
& ( X62 = Y62 ) ) ) ).
% fmla.inject(6)
thf(fact_122_fmla_Oinject_I5_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
( ( ( relational_Conj_a_b @ X51 @ X52 )
= ( relational_Conj_a_b @ Y51 @ Y52 ) )
= ( ( X51 = Y51 )
& ( X52 = Y52 ) ) ) ).
% fmla.inject(5)
thf(fact_123_fmla_Oinject_I7_J,axiom,
! [X71: nat,X72: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
( ( ( relati591517084277583526ts_a_b @ X71 @ X72 )
= ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) )
= ( ( X71 = Y71 )
& ( X72 = Y72 ) ) ) ).
% fmla.inject(7)
thf(fact_124_cpropagated__simps_I5_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relati1591879772219623554ed_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) )
= ( ( relational_nocp_a_b @ Q1 )
& ( relational_nocp_a_b @ Q22 ) ) ) ).
% cpropagated_simps(5)
thf(fact_125_fmla_Orel__distinct_I21_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X2: $o,Y71: nat,Y72: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X2 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).
% fmla.rel_distinct(21)
thf(fact_126_fmla_Orel__distinct_I22_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X2: $o] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.rel_distinct(22)
thf(fact_127_fmla_Orel__distinct_I17_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X2: $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X2 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).
% fmla.rel_distinct(17)
thf(fact_128_fmla_Orel__distinct_I18_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X2: $o] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.rel_distinct(18)
thf(fact_129_fmla_Orel__distinct_I19_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X2: $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X2 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).
% fmla.rel_distinct(19)
thf(fact_130_fmla_Orel__distinct_I20_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X2: $o] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.rel_distinct(20)
thf(fact_131_fmla_Orel__distinct_I15_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X2: $o,Y4: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X2 ) @ ( relational_Neg_a_b @ Y4 ) ) ).
% fmla.rel_distinct(15)
thf(fact_132_fmla_Orel__distinct_I16_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y4: relational_fmla_a_b,X2: $o] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ Y4 ) @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.rel_distinct(16)
thf(fact_133_fmla_Orel__distinct_I12_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.rel_distinct(12)
thf(fact_134_fmla_Orel__distinct_I11_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X11: b,X12: list_R6823256787227418703term_a,Y71: nat,Y72: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).
% fmla.rel_distinct(11)
thf(fact_135_fmla_Orel__distinct_I8_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.rel_distinct(8)
thf(fact_136_fmla_Orel__distinct_I7_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X11: b,X12: list_R6823256787227418703term_a,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).
% fmla.rel_distinct(7)
thf(fact_137_fmla_Orel__distinct_I10_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.rel_distinct(10)
thf(fact_138_fmla_Orel__distinct_I9_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X11: b,X12: list_R6823256787227418703term_a,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).
% fmla.rel_distinct(9)
thf(fact_139_fmla_Orel__distinct_I6_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y4: relational_fmla_a_b,X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ Y4 ) @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.rel_distinct(6)
thf(fact_140_fmla_Orel__distinct_I5_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X11: b,X12: list_R6823256787227418703term_a,Y4: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relational_Neg_a_b @ Y4 ) ) ).
% fmla.rel_distinct(5)
thf(fact_141_term_Orel__refl,axiom,
! [Ra: a > a > $o,X: relational_term_a] :
( ! [X5: a] : ( Ra @ X5 @ X5 )
=> ( relati3163788165526728396rm_a_a @ Ra @ X @ X ) ) ).
% term.rel_refl
thf(fact_142_fmla_Orel__refl,axiom,
! [R1a: a > a > $o,R2a: b > b > $o,X: relational_fmla_a_b] :
( ! [X5: a] : ( R1a @ X5 @ X5 )
=> ( ! [X5: b] : ( R2a @ X5 @ X5 )
=> ( relati8459511609072445516_a_b_b @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl
thf(fact_143_term_Orel__eq,axiom,
( ( relati3163788165526728396rm_a_a
@ ^ [Y: a,Z: a] : ( Y = Z ) )
= ( ^ [Y: relational_term_a,Z: relational_term_a] : ( Y = Z ) ) ) ).
% term.rel_eq
thf(fact_144_fmla_Orel__eq,axiom,
( ( relati8459511609072445516_a_b_b
@ ^ [Y: a,Z: a] : ( Y = Z )
@ ^ [Y: b,Z: b] : ( Y = Z ) )
= ( ^ [Y: relational_fmla_a_b,Z: relational_fmla_a_b] : ( Y = Z ) ) ) ).
% fmla.rel_eq
thf(fact_145_fmla_Orel__distinct_I31_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).
% fmla.rel_distinct(31)
thf(fact_146_fmla_Orel__distinct_I32_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X4: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.rel_distinct(32)
thf(fact_147_fmla_Orel__distinct_I33_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).
% fmla.rel_distinct(33)
thf(fact_148_fmla_Orel__distinct_I34_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X4: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.rel_distinct(34)
thf(fact_149_fmla_Orel__distinct_I35_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).
% fmla.rel_distinct(35)
thf(fact_150_fmla_Orel__distinct_I36_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X4: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.rel_distinct(36)
thf(fact_151_fmla_Orel__distinct_I37_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).
% fmla.rel_distinct(37)
thf(fact_152_fmla_Orel__distinct_I38_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.rel_distinct(38)
thf(fact_153_fmla_Orel__distinct_I39_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).
% fmla.rel_distinct(39)
thf(fact_154_fmla_Orel__distinct_I40_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.rel_distinct(40)
thf(fact_155_fmla_Orel__distinct_I41_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X61: relational_fmla_a_b,X62: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ X61 @ X62 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).
% fmla.rel_distinct(41)
thf(fact_156_fmla_Orel__distinct_I42_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.rel_distinct(42)
thf(fact_157_fmla_Orel__intros_I4_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y4: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X4 @ Y4 )
=> ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Neg_a_b @ Y4 ) ) ) ).
% fmla.rel_intros(4)
thf(fact_158_fmla_Orel__intros_I5_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,Y51: relational_fmla_a_b,X52: relational_fmla_a_b,Y52: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X51 @ Y51 )
=> ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X52 @ Y52 )
=> ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ) ) ).
% fmla.rel_intros(5)
thf(fact_159_fmla_Orel__intros_I6_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X61: relational_fmla_a_b,Y61: relational_fmla_a_b,X62: relational_fmla_a_b,Y62: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X61 @ Y61 )
=> ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X62 @ Y62 )
=> ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ X61 @ X62 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ) ) ).
% fmla.rel_intros(6)
thf(fact_160_fmla_Orel__intros_I7_J,axiom,
! [X71: nat,Y71: nat,R1: a > a > $o,R2: b > b > $o,X72: relational_fmla_a_b,Y72: relational_fmla_a_b] :
( ( X71 = Y71 )
=> ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X72 @ Y72 )
=> ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ) ) ).
% fmla.rel_intros(7)
thf(fact_161_fmla_Orel__inject_I4_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y4: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Neg_a_b @ Y4 ) )
= ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X4 @ Y4 ) ) ).
% fmla.rel_inject(4)
thf(fact_162_fmla_Orel__inject_I5_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) )
= ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X51 @ Y51 )
& ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X52 @ Y52 ) ) ) ).
% fmla.rel_inject(5)
thf(fact_163_fmla_Orel__inject_I6_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X61: relational_fmla_a_b,X62: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ X61 @ X62 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) )
= ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X61 @ Y61 )
& ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X62 @ Y62 ) ) ) ).
% fmla.rel_inject(6)
thf(fact_164_fmla_Orel__inject_I7_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X71: nat,X72: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) )
= ( ( X71 = Y71 )
& ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X72 @ Y72 ) ) ) ).
% fmla.rel_inject(7)
thf(fact_165_fmla_Odistinct_I31_J,axiom,
! [X4: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relational_Neg_a_b @ X4 )
!= ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.distinct(31)
thf(fact_166_fmla_Odistinct_I33_J,axiom,
! [X4: relational_fmla_a_b,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relational_Neg_a_b @ X4 )
!= ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.distinct(33)
thf(fact_167_fmla_Odistinct_I35_J,axiom,
! [X4: relational_fmla_a_b,X71: nat,X72: relational_fmla_a_b] :
( ( relational_Neg_a_b @ X4 )
!= ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.distinct(35)
thf(fact_168_fmla_Odistinct_I37_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relational_Conj_a_b @ X51 @ X52 )
!= ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.distinct(37)
thf(fact_169_fmla_Odistinct_I39_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b,X71: nat,X72: relational_fmla_a_b] :
( ( relational_Conj_a_b @ X51 @ X52 )
!= ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.distinct(39)
thf(fact_170_fmla_Odistinct_I41_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b,X71: nat,X72: relational_fmla_a_b] :
( ( relational_Disj_a_b @ X61 @ X62 )
!= ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.distinct(41)
thf(fact_171_fmla_Orel__inject_I1_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X11: b,X12: list_R6823256787227418703term_a,Y11: b,Y12: list_R6823256787227418703term_a] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relational_Pred_b_a @ Y11 @ Y12 ) )
= ( ( R2 @ X11 @ Y11 )
& ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ X12 @ Y12 ) ) ) ).
% fmla.rel_inject(1)
thf(fact_172_fmla_Orel__intros_I1_J,axiom,
! [R2: b > b > $o,X11: b,Y11: b,R1: a > a > $o,X12: list_R6823256787227418703term_a,Y12: list_R6823256787227418703term_a] :
( ( R2 @ X11 @ Y11 )
=> ( ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ X12 @ Y12 )
=> ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relational_Pred_b_a @ Y11 @ Y12 ) ) ) ) ).
% fmla.rel_intros(1)
thf(fact_173_fmla_Orel__inject_I2_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X2: $o,Y2: $o] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X2 ) @ ( relational_Bool_a_b @ Y2 ) )
= ( X2 = Y2 ) ) ).
% fmla.rel_inject(2)
thf(fact_174_fmla_Orel__intros_I2_J,axiom,
! [X2: $o,Y2: $o,R1: a > a > $o,R2: b > b > $o] :
( ( X2 = Y2 )
=> ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X2 ) @ ( relational_Bool_a_b @ Y2 ) ) ) ).
% fmla.rel_intros(2)
thf(fact_175_fmla_Odistinct_I21_J,axiom,
! [X2: $o,X71: nat,X72: relational_fmla_a_b] :
( ( relational_Bool_a_b @ X2 )
!= ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.distinct(21)
thf(fact_176_fmla_Odistinct_I17_J,axiom,
! [X2: $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relational_Bool_a_b @ X2 )
!= ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.distinct(17)
thf(fact_177_fmla_Odistinct_I19_J,axiom,
! [X2: $o,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relational_Bool_a_b @ X2 )
!= ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.distinct(19)
thf(fact_178_fmla_Odistinct_I11_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a,X71: nat,X72: relational_fmla_a_b] :
( ( relational_Pred_b_a @ X11 @ X12 )
!= ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.distinct(11)
thf(fact_179_fmla_Odistinct_I15_J,axiom,
! [X2: $o,X4: relational_fmla_a_b] :
( ( relational_Bool_a_b @ X2 )
!= ( relational_Neg_a_b @ X4 ) ) ).
% fmla.distinct(15)
thf(fact_180_fmla_Odistinct_I7_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relational_Pred_b_a @ X11 @ X12 )
!= ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.distinct(7)
thf(fact_181_fmla_Odistinct_I9_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relational_Pred_b_a @ X11 @ X12 )
!= ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.distinct(9)
thf(fact_182_fmla_Odistinct_I5_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a,X4: relational_fmla_a_b] :
( ( relational_Pred_b_a @ X11 @ X12 )
!= ( relational_Neg_a_b @ X4 ) ) ).
% fmla.distinct(5)
thf(fact_183_fmla_Osimps_I70_J,axiom,
! [F1: a > a,F2: b > b,X71: nat,X72: relational_fmla_a_b] :
( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) )
= ( relati591517084277583526ts_a_b @ X71 @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X72 ) ) ) ).
% fmla.simps(70)
thf(fact_184_fmla_Osimps_I68_J,axiom,
! [F1: a > a,F2: b > b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Conj_a_b @ X51 @ X52 ) )
= ( relational_Conj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X51 ) @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X52 ) ) ) ).
% fmla.simps(68)
thf(fact_185_fmla_Osimps_I69_J,axiom,
! [F1: a > a,F2: b > b,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Disj_a_b @ X61 @ X62 ) )
= ( relational_Disj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X61 ) @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X62 ) ) ) ).
% fmla.simps(69)
thf(fact_186_nocp_Osimps_I5_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relational_nocp_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) )
= ( ( relational_nocp_a_b @ Q1 )
& ( relational_nocp_a_b @ Q22 ) ) ) ).
% nocp.simps(5)
thf(fact_187_fmla_Osimps_I67_J,axiom,
! [F1: a > a,F2: b > b,X4: relational_fmla_a_b] :
( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Neg_a_b @ X4 ) )
= ( relational_Neg_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X4 ) ) ) ).
% fmla.simps(67)
thf(fact_188_nocp_Osimps_I6_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relational_nocp_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) )
= ( ( relational_nocp_a_b @ Q1 )
& ( relational_nocp_a_b @ Q22 ) ) ) ).
% nocp.simps(6)
thf(fact_189_fmla_Odisc_I14_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
~ ( relati6551038146797045342ol_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.disc(14)
thf(fact_190_nocp_Osimps_I4_J,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_nocp_a_b @ ( relational_Neg_a_b @ Q ) )
= ( relational_nocp_a_b @ Q ) ) ).
% nocp.simps(4)
thf(fact_191_fmla_Odisc_I12_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relati6551038146797045342ol_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.disc(12)
thf(fact_192_fmla_Odisc_I13_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
~ ( relati6551038146797045342ol_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.disc(13)
thf(fact_193_fmla_Odisc_I11_J,axiom,
! [X4: relational_fmla_a_b] :
~ ( relati6551038146797045342ol_a_b @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.disc(11)
thf(fact_194_qp__Conj,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
~ ( relational_qp_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) ) ).
% qp_Conj
thf(fact_195_fmla_Odisc_I35_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
~ ( relati8168519172193746908nj_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.disc(35)
thf(fact_196_fmla_Odisc_I42_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
~ ( relati5350680195807439568sj_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.disc(42)
thf(fact_197_qp__Disj,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
~ ( relational_qp_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) ) ).
% qp_Disj
thf(fact_198_fmla_Odisc_I7_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
~ ( relati3644702733014758741ed_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.disc(7)
thf(fact_199_is__Conj__def,axiom,
( relati8168519172193746908nj_a_b
= ( ^ [Fmla2: relational_fmla_a_b] :
? [X512: relational_fmla_a_b,X522: relational_fmla_a_b] :
( Fmla2
= ( relational_Conj_a_b @ X512 @ X522 ) ) ) ) ).
% is_Conj_def
thf(fact_200_fmla_OdiscI_I5_J,axiom,
! [Fmla: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( Fmla
= ( relational_Conj_a_b @ X51 @ X52 ) )
=> ( relati8168519172193746908nj_a_b @ Fmla ) ) ).
% fmla.discI(5)
thf(fact_201_fmla_Odisc_I33_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] : ( relati8168519172193746908nj_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.disc(33)
thf(fact_202_fmla_Odisc_I40_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relati5350680195807439568sj_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.disc(40)
thf(fact_203_fmla_Osimps_I56_J,axiom,
! [F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,X71: nat,X72: relational_fmla_a_b] :
( ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) )
= ( F7 @ X71 @ X72 ) ) ).
% fmla.simps(56)
thf(fact_204_fmla_Odisc_I21_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
~ ( relational_is_Eq_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.disc(21)
thf(fact_205_fmla_Odisc_I28_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
~ ( relati4321004860440572638eg_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.disc(28)
thf(fact_206_is__Disj__def,axiom,
( relati5350680195807439568sj_a_b
= ( ^ [Fmla2: relational_fmla_a_b] :
? [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
( Fmla2
= ( relational_Disj_a_b @ X612 @ X622 ) ) ) ) ).
% is_Disj_def
thf(fact_207_fmla_OdiscI_I6_J,axiom,
! [Fmla: relational_fmla_a_b,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( Fmla
= ( relational_Disj_a_b @ X61 @ X62 ) )
=> ( relati5350680195807439568sj_a_b @ Fmla ) ) ).
% fmla.discI(6)
thf(fact_208_fmla_Odisc_I34_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
~ ( relati8168519172193746908nj_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.disc(34)
thf(fact_209_fmla_Odisc_I41_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] : ( relati5350680195807439568sj_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.disc(41)
thf(fact_210_fmla_Odisc_I5_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relati3644702733014758741ed_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.disc(5)
thf(fact_211_qp__Neg,axiom,
! [Q: relational_fmla_a_b] :
~ ( relational_qp_a_b @ ( relational_Neg_a_b @ Q ) ) ).
% qp_Neg
thf(fact_212_fmla_Odisc_I6_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
~ ( relati3644702733014758741ed_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.disc(6)
thf(fact_213_fmla_Osimps_I54_J,axiom,
! [F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Conj_a_b @ X51 @ X52 ) )
= ( F5 @ X51 @ X52 ) ) ).
% fmla.simps(54)
thf(fact_214_fmla_Odisc_I19_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relational_is_Eq_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.disc(19)
thf(fact_215_fmla_Odisc_I26_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relati4321004860440572638eg_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.disc(26)
thf(fact_216_fmla_Osimps_I55_J,axiom,
! [F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Disj_a_b @ X61 @ X62 ) )
= ( F6 @ X61 @ X62 ) ) ).
% fmla.simps(55)
thf(fact_217_fmla_Odisc_I20_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
~ ( relational_is_Eq_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.disc(20)
thf(fact_218_fmla_Odisc_I27_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
~ ( relati4321004860440572638eg_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.disc(27)
thf(fact_219_fmla_Odisc_I32_J,axiom,
! [X4: relational_fmla_a_b] :
~ ( relati8168519172193746908nj_a_b @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.disc(32)
thf(fact_220_fmla_Odisc_I39_J,axiom,
! [X4: relational_fmla_a_b] :
~ ( relati5350680195807439568sj_a_b @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.disc(39)
thf(fact_221_is__Exists__def,axiom,
( relati5212983245281121968ts_a_b
= ( ^ [Fmla2: relational_fmla_a_b] :
? [X712: nat,X722: relational_fmla_a_b] :
( Fmla2
= ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ) ) ).
% is_Exists_def
thf(fact_222_fmla_OdiscI_I7_J,axiom,
! [Fmla: relational_fmla_a_b,X71: nat,X72: relational_fmla_a_b] :
( ( Fmla
= ( relati591517084277583526ts_a_b @ X71 @ X72 ) )
=> ( relati5212983245281121968ts_a_b @ Fmla ) ) ).
% fmla.discI(7)
thf(fact_223_fmla_Odisc_I49_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] : ( relati5212983245281121968ts_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.disc(49)
thf(fact_224_erase_Osimps_I7_J,axiom,
! [X: nat,Z2: nat,Q: relational_fmla_a_b] :
( ( ( X = Z2 )
=> ( ( relational_erase_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X )
= ( relati591517084277583526ts_a_b @ X @ Q ) ) )
& ( ( X != Z2 )
=> ( ( relational_erase_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X )
= ( relati591517084277583526ts_a_b @ Z2 @ ( relational_erase_a_b @ Q @ X ) ) ) ) ) ).
% erase.simps(7)
thf(fact_225_fmla_Odisc_I4_J,axiom,
! [X4: relational_fmla_a_b] :
~ ( relati3644702733014758741ed_a_b @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.disc(4)
thf(fact_226_fmla_Odisc_I47_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
~ ( relati5212983245281121968ts_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.disc(47)
thf(fact_227_is__Neg__def,axiom,
( relati4321004860440572638eg_a_b
= ( ^ [Fmla2: relational_fmla_a_b] :
? [X42: relational_fmla_a_b] :
( Fmla2
= ( relational_Neg_a_b @ X42 ) ) ) ) ).
% is_Neg_def
thf(fact_228_fmla_Osimps_I53_J,axiom,
! [F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,X4: relational_fmla_a_b] :
( ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Neg_a_b @ X4 ) )
= ( F4 @ X4 ) ) ).
% fmla.simps(53)
thf(fact_229_fmla_OdiscI_I4_J,axiom,
! [Fmla: relational_fmla_a_b,X4: relational_fmla_a_b] :
( ( Fmla
= ( relational_Neg_a_b @ X4 ) )
=> ( relati4321004860440572638eg_a_b @ Fmla ) ) ).
% fmla.discI(4)
thf(fact_230_fmla_Odisc_I18_J,axiom,
! [X4: relational_fmla_a_b] :
~ ( relational_is_Eq_a_b @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.disc(18)
thf(fact_231_fmla_Odisc_I25_J,axiom,
! [X4: relational_fmla_a_b] : ( relati4321004860440572638eg_a_b @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.disc(25)
thf(fact_232_fmla_Odisc_I48_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
~ ( relati5212983245281121968ts_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.disc(48)
thf(fact_233_erase_Osimps_I5_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,X: nat] :
( ( relational_erase_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ X )
= ( relational_Conj_a_b @ ( relational_erase_a_b @ Q1 @ X ) @ ( relational_erase_a_b @ Q22 @ X ) ) ) ).
% erase.simps(5)
thf(fact_234_erase_Osimps_I6_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,X: nat] :
( ( relational_erase_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ X )
= ( relational_Disj_a_b @ ( relational_erase_a_b @ Q1 @ X ) @ ( relational_erase_a_b @ Q22 @ X ) ) ) ).
% erase.simps(6)
thf(fact_235_fmla_Odisc_I46_J,axiom,
! [X4: relational_fmla_a_b] :
~ ( relati5212983245281121968ts_a_b @ ( relational_Neg_a_b @ X4 ) ) ).
% fmla.disc(46)
thf(fact_236_erase_Osimps_I4_J,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_erase_a_b @ ( relational_Neg_a_b @ Q ) @ X )
= ( relational_Neg_a_b @ ( relational_erase_a_b @ Q @ X ) ) ) ).
% erase.simps(4)
thf(fact_237_fmla_Osel_I12_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
( ( relati5591445451228332309s2_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) )
= X72 ) ).
% fmla.sel(12)
thf(fact_238_qp__impl_Osimps_I7_J,axiom,
! [V: relational_fmla_a_b,Va: relational_fmla_a_b] :
~ ( relati3725921752842749053pl_a_b @ ( relational_Conj_a_b @ V @ Va ) ) ).
% qp_impl.simps(7)
thf(fact_239_fmla_Osel_I7_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relati5154284022127734760j1_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
= X51 ) ).
% fmla.sel(7)
thf(fact_240_fmla_Osel_I8_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relati1527130600461089641j2_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
= X52 ) ).
% fmla.sel(8)
thf(fact_241_qp__impl_Osimps_I8_J,axiom,
! [V: relational_fmla_a_b,Va: relational_fmla_a_b] :
~ ( relati3725921752842749053pl_a_b @ ( relational_Disj_a_b @ V @ Va ) ) ).
% qp_impl.simps(8)
thf(fact_242_fmla_Osel_I9_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relati3334262663314506228j1_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) )
= X61 ) ).
% fmla.sel(9)
thf(fact_243_fmla_Osel_I10_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relati8930481278502636917j2_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) )
= X62 ) ).
% fmla.sel(10)
thf(fact_244_qp__impl_Osimps_I6_J,axiom,
! [V: relational_fmla_a_b] :
~ ( relati3725921752842749053pl_a_b @ ( relational_Neg_a_b @ V ) ) ).
% qp_impl.simps(6)
thf(fact_245_fmla_Osel_I6_J,axiom,
! [X4: relational_fmla_a_b] :
( ( relati5982302313924697647eg_a_b @ ( relational_Neg_a_b @ X4 ) )
= X4 ) ).
% fmla.sel(6)
thf(fact_246_fmla_Osel_I11_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
( ( relati9218598872894977428s1_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) )
= X71 ) ).
% fmla.sel(11)
thf(fact_247_fmla_Osel_I2_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
( ( relati5687822700427945008d2_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) )
= X12 ) ).
% fmla.sel(2)
thf(fact_248_fmla_Orel__distinct_I2_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y2: $o,X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ Y2 ) @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.rel_distinct(2)
thf(fact_249_fmla_Orel__distinct_I1_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X11: b,X12: list_R6823256787227418703term_a,Y2: $o] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relational_Bool_a_b @ Y2 ) ) ).
% fmla.rel_distinct(1)
thf(fact_250_fmla_Osplit__sel__asm,axiom,
! [P: $o > $o,F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,Fmla: relational_fmla_a_b] :
( ( P @ ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ Fmla ) )
= ( ~ ( ( ( Fmla
= ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) )
& ~ ( P @ ( F1 @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) ) )
| ( ( Fmla
= ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) ) )
& ~ ( P @ ( F2 @ ( relati2638701775882563405ol_a_b @ Fmla ) ) ) )
| ( ( Fmla
= ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) )
& ~ ( P @ ( F3 @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) ) )
| ( ( Fmla
= ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) ) )
& ~ ( P @ ( F4 @ ( relati5982302313924697647eg_a_b @ Fmla ) ) ) )
| ( ( Fmla
= ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) )
& ~ ( P @ ( F5 @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) ) )
| ( ( Fmla
= ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) )
& ~ ( P @ ( F6 @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) ) )
| ( ( Fmla
= ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) )
& ~ ( P @ ( F7 @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) ) ) ) ) ) ).
% fmla.split_sel_asm
thf(fact_251_fmla_Osplit__sel,axiom,
! [P: $o > $o,F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,Fmla: relational_fmla_a_b] :
( ( P @ ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ Fmla ) )
= ( ( ( Fmla
= ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) )
=> ( P @ ( F1 @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) ) )
& ( ( Fmla
= ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) ) )
=> ( P @ ( F2 @ ( relati2638701775882563405ol_a_b @ Fmla ) ) ) )
& ( ( Fmla
= ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) )
=> ( P @ ( F3 @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) ) )
& ( ( Fmla
= ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) ) )
=> ( P @ ( F4 @ ( relati5982302313924697647eg_a_b @ Fmla ) ) ) )
& ( ( Fmla
= ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) )
=> ( P @ ( F5 @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) ) )
& ( ( Fmla
= ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) )
=> ( P @ ( F6 @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) ) )
& ( ( Fmla
= ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) )
=> ( P @ ( F7 @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) ) ) ) ) ).
% fmla.split_sel
thf(fact_252_fmla_Oexhaust__sel,axiom,
! [Fmla: relational_fmla_a_b] :
( ( Fmla
!= ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) )
=> ( ( Fmla
!= ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) ) )
=> ( ( Fmla
!= ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) )
=> ( ( Fmla
!= ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) ) )
=> ( ( Fmla
!= ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) )
=> ( ( Fmla
!= ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) )
=> ( Fmla
= ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) ) ) ) ) ) ) ) ).
% fmla.exhaust_sel
thf(fact_253_fmla_Orel__induct,axiom,
! [R1: a > a > $o,R2: b > b > $o,X: relational_fmla_a_b,Y3: relational_fmla_a_b,Q: relational_fmla_a_b > relational_fmla_a_b > $o] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X @ Y3 )
=> ( ! [A11: b,A12: list_R6823256787227418703term_a,B11: b,B12: list_R6823256787227418703term_a] :
( ( R2 @ A11 @ B11 )
=> ( ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ A12 @ B12 )
=> ( Q @ ( relational_Pred_b_a @ A11 @ A12 ) @ ( relational_Pred_b_a @ B11 @ B12 ) ) ) )
=> ( ! [A22: $o,B2: $o] :
( ( A22 = B2 )
=> ( Q @ ( relational_Bool_a_b @ A22 ) @ ( relational_Bool_a_b @ B2 ) ) )
=> ( ! [A31: nat,A32: relational_term_a,B31: nat,B32: relational_term_a] :
( ( A31 = B31 )
=> ( ( relati3163788165526728396rm_a_a @ R1 @ A32 @ B32 )
=> ( Q @ ( relational_Eq_a_b @ A31 @ A32 ) @ ( relational_Eq_a_b @ B31 @ B32 ) ) ) )
=> ( ! [A4: relational_fmla_a_b,B4: relational_fmla_a_b] :
( ( Q @ A4 @ B4 )
=> ( Q @ ( relational_Neg_a_b @ A4 ) @ ( relational_Neg_a_b @ B4 ) ) )
=> ( ! [A51: relational_fmla_a_b,A52: relational_fmla_a_b,B51: relational_fmla_a_b,B52: relational_fmla_a_b] :
( ( Q @ A51 @ B51 )
=> ( ( Q @ A52 @ B52 )
=> ( Q @ ( relational_Conj_a_b @ A51 @ A52 ) @ ( relational_Conj_a_b @ B51 @ B52 ) ) ) )
=> ( ! [A61: relational_fmla_a_b,A62: relational_fmla_a_b,B61: relational_fmla_a_b,B62: relational_fmla_a_b] :
( ( Q @ A61 @ B61 )
=> ( ( Q @ A62 @ B62 )
=> ( Q @ ( relational_Disj_a_b @ A61 @ A62 ) @ ( relational_Disj_a_b @ B61 @ B62 ) ) ) )
=> ( ! [A71: nat,A72: relational_fmla_a_b,B71: nat,B72: relational_fmla_a_b] :
( ( A71 = B71 )
=> ( ( Q @ A72 @ B72 )
=> ( Q @ ( relati591517084277583526ts_a_b @ A71 @ A72 ) @ ( relati591517084277583526ts_a_b @ B71 @ B72 ) ) ) )
=> ( Q @ X @ Y3 ) ) ) ) ) ) ) ) ) ).
% fmla.rel_induct
thf(fact_254_fmla_Orel__cases,axiom,
! [R1: a > a > $o,R2: b > b > $o,A: relational_fmla_a_b,B: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ A @ B )
=> ( ! [X1: b,X2a: list_R6823256787227418703term_a] :
( ( A
= ( relational_Pred_b_a @ X1 @ X2a ) )
=> ! [Y1: b,Y2a: list_R6823256787227418703term_a] :
( ( B
= ( relational_Pred_b_a @ Y1 @ Y2a ) )
=> ( ( R2 @ X1 @ Y1 )
=> ~ ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ X2a @ Y2a ) ) ) )
=> ( ! [X5: $o] :
( ( A
= ( relational_Bool_a_b @ X5 ) )
=> ! [Y5: $o] :
( ( B
= ( relational_Bool_a_b @ Y5 ) )
=> ( X5 = (~ Y5) ) ) )
=> ( ! [X1a: nat,X2b: relational_term_a] :
( ( A
= ( relational_Eq_a_b @ X1a @ X2b ) )
=> ! [Y1a: nat,Y2b: relational_term_a] :
( ( B
= ( relational_Eq_a_b @ Y1a @ Y2b ) )
=> ( ( X1a = Y1a )
=> ~ ( relati3163788165526728396rm_a_a @ R1 @ X2b @ Y2b ) ) ) )
=> ( ! [Xa: relational_fmla_a_b] :
( ( A
= ( relational_Neg_a_b @ Xa ) )
=> ! [Ya: relational_fmla_a_b] :
( ( B
= ( relational_Neg_a_b @ Ya ) )
=> ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ Xa @ Ya ) ) )
=> ( ! [X1b: relational_fmla_a_b,X2c: relational_fmla_a_b] :
( ( A
= ( relational_Conj_a_b @ X1b @ X2c ) )
=> ! [Y1b: relational_fmla_a_b,Y2c: relational_fmla_a_b] :
( ( B
= ( relational_Conj_a_b @ Y1b @ Y2c ) )
=> ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X1b @ Y1b )
=> ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X2c @ Y2c ) ) ) )
=> ( ! [X1c: relational_fmla_a_b,X2d: relational_fmla_a_b] :
( ( A
= ( relational_Disj_a_b @ X1c @ X2d ) )
=> ! [Y1c: relational_fmla_a_b,Y2d: relational_fmla_a_b] :
( ( B
= ( relational_Disj_a_b @ Y1c @ Y2d ) )
=> ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X1c @ Y1c )
=> ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X2d @ Y2d ) ) ) )
=> ~ ! [X1d: nat,X2e: relational_fmla_a_b] :
( ( A
= ( relati591517084277583526ts_a_b @ X1d @ X2e ) )
=> ! [Y1d: nat,Y2e: relational_fmla_a_b] :
( ( B
= ( relati591517084277583526ts_a_b @ Y1d @ Y2e ) )
=> ( ( X1d = Y1d )
=> ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X2e @ Y2e ) ) ) ) ) ) ) ) ) ) ) ).
% fmla.rel_cases
thf(fact_255_fmla_Oexhaust,axiom,
! [Y3: relational_fmla_a_b] :
( ! [X113: b,X123: list_R6823256787227418703term_a] :
( Y3
!= ( relational_Pred_b_a @ X113 @ X123 ) )
=> ( ! [X23: $o] :
( Y3
!= ( relational_Bool_a_b @ X23 ) )
=> ( ! [X31: nat,X32: relational_term_a] :
( Y3
!= ( relational_Eq_a_b @ X31 @ X32 ) )
=> ( ! [X43: relational_fmla_a_b] :
( Y3
!= ( relational_Neg_a_b @ X43 ) )
=> ( ! [X513: relational_fmla_a_b,X523: relational_fmla_a_b] :
( Y3
!= ( relational_Conj_a_b @ X513 @ X523 ) )
=> ( ! [X613: relational_fmla_a_b,X623: relational_fmla_a_b] :
( Y3
!= ( relational_Disj_a_b @ X613 @ X623 ) )
=> ~ ! [X713: nat,X723: relational_fmla_a_b] :
( Y3
!= ( relati591517084277583526ts_a_b @ X713 @ X723 ) ) ) ) ) ) ) ) ).
% fmla.exhaust
thf(fact_256_fmla_Oinject_I3_J,axiom,
! [X312: nat,X322: relational_term_a,Y31: nat,Y32: relational_term_a] :
( ( ( relational_Eq_a_b @ X312 @ X322 )
= ( relational_Eq_a_b @ Y31 @ Y32 ) )
= ( ( X312 = Y31 )
& ( X322 = Y32 ) ) ) ).
% fmla.inject(3)
thf(fact_257_fmla_Ocollapse_I3_J,axiom,
! [Fmla: relational_fmla_a_b] :
( ( relational_is_Eq_a_b @ Fmla )
=> ( ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) )
= Fmla ) ) ).
% fmla.collapse(3)
thf(fact_258_fmla_Odistinct_I23_J,axiom,
! [X312: nat,X322: relational_term_a,X4: relational_fmla_a_b] :
( ( relational_Eq_a_b @ X312 @ X322 )
!= ( relational_Neg_a_b @ X4 ) ) ).
% fmla.distinct(23)
thf(fact_259_fmla_Odistinct_I27_J,axiom,
! [X312: nat,X322: relational_term_a,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relational_Eq_a_b @ X312 @ X322 )
!= ( relational_Disj_a_b @ X61 @ X62 ) ) ).
% fmla.distinct(27)
thf(fact_260_fmla_Odistinct_I25_J,axiom,
! [X312: nat,X322: relational_term_a,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relational_Eq_a_b @ X312 @ X322 )
!= ( relational_Conj_a_b @ X51 @ X52 ) ) ).
% fmla.distinct(25)
thf(fact_261_fmla_Odistinct_I29_J,axiom,
! [X312: nat,X322: relational_term_a,X71: nat,X72: relational_fmla_a_b] :
( ( relational_Eq_a_b @ X312 @ X322 )
!= ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ).
% fmla.distinct(29)
thf(fact_262_fmla_Odistinct_I13_J,axiom,
! [X2: $o,X312: nat,X322: relational_term_a] :
( ( relational_Bool_a_b @ X2 )
!= ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.distinct(13)
thf(fact_263_fmla_Odistinct_I3_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a,X312: nat,X322: relational_term_a] :
( ( relational_Pred_b_a @ X11 @ X12 )
!= ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.distinct(3)
thf(fact_264_fmla_Odisc_I10_J,axiom,
! [X312: nat,X322: relational_term_a] :
~ ( relati6551038146797045342ol_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.disc(10)
thf(fact_265_fmla_Odisc_I38_J,axiom,
! [X312: nat,X322: relational_term_a] :
~ ( relati5350680195807439568sj_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.disc(38)
thf(fact_266_fmla_Odisc_I31_J,axiom,
! [X312: nat,X322: relational_term_a] :
~ ( relati8168519172193746908nj_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.disc(31)
thf(fact_267_fmla_Odisc_I3_J,axiom,
! [X312: nat,X322: relational_term_a] :
~ ( relati3644702733014758741ed_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.disc(3)
thf(fact_268_fmla_Odisc_I24_J,axiom,
! [X312: nat,X322: relational_term_a] :
~ ( relati4321004860440572638eg_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.disc(24)
thf(fact_269_fmla_Odisc_I17_J,axiom,
! [X312: nat,X322: relational_term_a] : ( relational_is_Eq_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.disc(17)
thf(fact_270_fmla_OdiscI_I3_J,axiom,
! [Fmla: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
( ( Fmla
= ( relational_Eq_a_b @ X312 @ X322 ) )
=> ( relational_is_Eq_a_b @ Fmla ) ) ).
% fmla.discI(3)
thf(fact_271_fmla_Osimps_I52_J,axiom,
! [F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,X312: nat,X322: relational_term_a] :
( ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Eq_a_b @ X312 @ X322 ) )
= ( F3 @ X312 @ X322 ) ) ).
% fmla.simps(52)
thf(fact_272_is__Eq__def,axiom,
( relational_is_Eq_a_b
= ( ^ [Fmla2: relational_fmla_a_b] :
? [X313: nat,X323: relational_term_a] :
( Fmla2
= ( relational_Eq_a_b @ X313 @ X323 ) ) ) ) ).
% is_Eq_def
thf(fact_273_fmla_Odisc_I45_J,axiom,
! [X312: nat,X322: relational_term_a] :
~ ( relati5212983245281121968ts_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.disc(45)
thf(fact_274_fmla_Osel_I5_J,axiom,
! [X312: nat,X322: relational_term_a] :
( ( relati1832481647827092069q2_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) )
= X322 ) ).
% fmla.sel(5)
thf(fact_275_fmla_Osel_I4_J,axiom,
! [X312: nat,X322: relational_term_a] :
( ( relati5459635069493737188q1_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) )
= X312 ) ).
% fmla.sel(4)
thf(fact_276_fmla_Orel__distinct_I24_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y4: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ Y4 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.rel_distinct(24)
thf(fact_277_fmla_Orel__distinct_I23_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y4: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Neg_a_b @ Y4 ) ) ).
% fmla.rel_distinct(23)
thf(fact_278_fmla_Orel__distinct_I28_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.rel_distinct(28)
thf(fact_279_fmla_Orel__distinct_I27_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).
% fmla.rel_distinct(27)
thf(fact_280_fmla_Orel__distinct_I26_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.rel_distinct(26)
thf(fact_281_fmla_Orel__distinct_I25_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).
% fmla.rel_distinct(25)
thf(fact_282_fmla_Orel__distinct_I30_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).
% fmla.rel_distinct(30)
thf(fact_283_fmla_Orel__distinct_I29_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y71: nat,Y72: relational_fmla_a_b] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).
% fmla.rel_distinct(29)
thf(fact_284_fmla_Orel__distinct_I14_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y31: nat,Y32: relational_term_a,X2: $o] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ Y31 @ Y32 ) @ ( relational_Bool_a_b @ X2 ) ) ).
% fmla.rel_distinct(14)
thf(fact_285_fmla_Orel__distinct_I13_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X2: $o,Y31: nat,Y32: relational_term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X2 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) ) ).
% fmla.rel_distinct(13)
thf(fact_286_fmla_Orel__distinct_I3_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X11: b,X12: list_R6823256787227418703term_a,Y31: nat,Y32: relational_term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X11 @ X12 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) ) ).
% fmla.rel_distinct(3)
thf(fact_287_fmla_Orel__distinct_I4_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,Y31: nat,Y32: relational_term_a,X11: b,X12: list_R6823256787227418703term_a] :
~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ Y31 @ Y32 ) @ ( relational_Pred_b_a @ X11 @ X12 ) ) ).
% fmla.rel_distinct(4)
thf(fact_288_fmla_Orel__inject_I3_J,axiom,
! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y31: nat,Y32: relational_term_a] :
( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) )
= ( ( X312 = Y31 )
& ( relati3163788165526728396rm_a_a @ R1 @ X322 @ Y32 ) ) ) ).
% fmla.rel_inject(3)
thf(fact_289_fmla_Orel__intros_I3_J,axiom,
! [X312: nat,Y31: nat,R1: a > a > $o,X322: relational_term_a,Y32: relational_term_a,R2: b > b > $o] :
( ( X312 = Y31 )
=> ( ( relati3163788165526728396rm_a_a @ R1 @ X322 @ Y32 )
=> ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) ) ) ) ).
% fmla.rel_intros(3)
thf(fact_290_cp_Ocases,axiom,
! [X: relational_fmla_a_b] :
( ! [X5: nat,T2: relational_term_a] :
( X
!= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( ! [Q4: relational_fmla_a_b] :
( X
!= ( relational_Neg_a_b @ Q4 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( X
!= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( X
!= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( X
!= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ! [V2: b,Va2: list_R6823256787227418703term_a] :
( X
!= ( relational_Pred_b_a @ V2 @ Va2 ) )
=> ~ ! [V2: $o] :
( X
!= ( relational_Bool_a_b @ V2 ) ) ) ) ) ) ) ) ).
% cp.cases
thf(fact_291_fv_Ocases,axiom,
! [X: relational_fmla_a_b] :
( ! [Uu: b,Ts2: list_R6823256787227418703term_a] :
( X
!= ( relational_Pred_b_a @ Uu @ Ts2 ) )
=> ( ! [B3: $o] :
( X
!= ( relational_Bool_a_b @ B3 ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( X
!= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( ! [Phi: relational_fmla_a_b] :
( X
!= ( relational_Neg_a_b @ Phi ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( X
!= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( X
!= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( X
!= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) ) ) ) ) ) ) ) ).
% fv.cases
thf(fact_292_nocp_Ocases,axiom,
! [X: relational_fmla_a_b] :
( ! [B3: $o] :
( X
!= ( relational_Bool_a_b @ B3 ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( X
!= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( X
!= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( ! [Q4: relational_fmla_a_b] :
( X
!= ( relational_Neg_a_b @ Q4 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( X
!= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( X
!= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( X
!= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) ) ) ) ) ) ) ) ).
% nocp.cases
thf(fact_293_erase_Ocases,axiom,
! [X: produc7366699395886430672_b_nat] :
( ! [T2: $o,X5: nat] :
( X
!= ( produc4282057684358614024_b_nat @ ( relational_Bool_a_b @ T2 ) @ X5 ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a,X5: nat] :
( X
!= ( produc4282057684358614024_b_nat @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ X5 ) )
=> ( ! [Z3: nat,T2: relational_term_a,X5: nat] :
( X
!= ( produc4282057684358614024_b_nat @ ( relational_Eq_a_b @ Z3 @ T2 ) @ X5 ) )
=> ( ! [Q4: relational_fmla_a_b,X5: nat] :
( X
!= ( produc4282057684358614024_b_nat @ ( relational_Neg_a_b @ Q4 ) @ X5 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,X5: nat] :
( X
!= ( produc4282057684358614024_b_nat @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ X5 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,X5: nat] :
( X
!= ( produc4282057684358614024_b_nat @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ X5 ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b,X5: nat] :
( X
!= ( produc4282057684358614024_b_nat @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ X5 ) ) ) ) ) ) ) ) ).
% erase.cases
thf(fact_294_erase_Oelims,axiom,
! [X: relational_fmla_a_b,Xa2: nat,Y3: relational_fmla_a_b] :
( ( ( relational_erase_a_b @ X @ Xa2 )
= Y3 )
=> ( ! [T2: $o] :
( ( X
= ( relational_Bool_a_b @ T2 ) )
=> ( Y3
!= ( relational_Bool_a_b @ T2 ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ~ ( ( ( member_nat @ Xa2 @ ( relati4569515538964159125_set_a @ Ts2 ) )
=> ( Y3
= ( relational_Bool_a_b @ $false ) ) )
& ( ~ ( member_nat @ Xa2 @ ( relati4569515538964159125_set_a @ Ts2 ) )
=> ( Y3
= ( relational_Pred_b_a @ P3 @ Ts2 ) ) ) ) )
=> ( ! [Z3: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ Z3 @ T2 ) )
=> ~ ( ( ( T2
= ( relational_Var_a @ Z3 ) )
=> ( Y3
= ( relational_Bool_a_b @ $true ) ) )
& ( ( T2
!= ( relational_Var_a @ Z3 ) )
=> ( ( ( ( Xa2 = Z3 )
| ( member_nat @ Xa2 @ ( relati6004689760767320788_set_a @ T2 ) ) )
=> ( Y3
= ( relational_Bool_a_b @ $false ) ) )
& ( ~ ( ( Xa2 = Z3 )
| ( member_nat @ Xa2 @ ( relati6004689760767320788_set_a @ T2 ) ) )
=> ( Y3
= ( relational_Eq_a_b @ Z3 @ T2 ) ) ) ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( Y3
!= ( relational_Neg_a_b @ ( relational_erase_a_b @ Q4 @ Xa2 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( relational_Conj_a_b @ ( relational_erase_a_b @ Q12 @ Xa2 ) @ ( relational_erase_a_b @ Q23 @ Xa2 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( relational_Disj_a_b @ ( relational_erase_a_b @ Q12 @ Xa2 ) @ ( relational_erase_a_b @ Q23 @ Xa2 ) ) ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) )
=> ~ ( ( ( Xa2 = Z3 )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Xa2 @ Q4 ) ) )
& ( ( Xa2 != Z3 )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Z3 @ ( relational_erase_a_b @ Q4 @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% erase.elims
thf(fact_295_fmla_Oset__cases_I2_J,axiom,
! [E: b,A: relational_fmla_a_b] :
( ( member_b @ E @ ( relati8924981150291758614la_a_b @ A ) )
=> ( ! [Z22: list_R6823256787227418703term_a] :
( A
!= ( relational_Pred_b_a @ E @ Z22 ) )
=> ( ! [Z3: relational_fmla_a_b] :
( ( A
= ( relational_Neg_a_b @ Z3 ) )
=> ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z3 ) ) )
=> ( ! [Z1: relational_fmla_a_b] :
( ? [Z22: relational_fmla_a_b] :
( A
= ( relational_Conj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z1 ) ) )
=> ( ! [Z1: relational_fmla_a_b,Z22: relational_fmla_a_b] :
( ( A
= ( relational_Conj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z22 ) ) )
=> ( ! [Z1: relational_fmla_a_b] :
( ? [Z22: relational_fmla_a_b] :
( A
= ( relational_Disj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z1 ) ) )
=> ( ! [Z1: relational_fmla_a_b,Z22: relational_fmla_a_b] :
( ( A
= ( relational_Disj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z22 ) ) )
=> ~ ! [Z1: nat,Z22: relational_fmla_a_b] :
( ( A
= ( relati591517084277583526ts_a_b @ Z1 @ Z22 ) )
=> ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z22 ) ) ) ) ) ) ) ) ) ) ).
% fmla.set_cases(2)
thf(fact_296_rrb__def,axiom,
( relational_rrb_a_b
= ( ^ [Q3: relational_fmla_a_b] :
! [Y6: nat,Qy: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ Y6 @ Qy ) @ ( relational_sub_a_b @ Q3 ) )
=> ? [X6: set_Re381260168593705685la_a_b] : ( relational_gen_a_b @ Y6 @ Qy @ X6 ) ) ) ) ).
% rrb_def
thf(fact_297_fmla_Omap__sel_I5_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relational_is_Eq_a_b @ A )
=> ( ( relati1832481647827092069q2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( relati3585320759856631375rm_a_a @ F1 @ ( relati1832481647827092069q2_a_b @ A ) ) ) ) ).
% fmla.map_sel(5)
thf(fact_298_term_Oinject_I2_J,axiom,
! [X2: nat,Y2: nat] :
( ( ( relational_Var_a @ X2 )
= ( relational_Var_a @ Y2 ) )
= ( X2 = Y2 ) ) ).
% term.inject(2)
thf(fact_299_cp__idem,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_cp_a_b @ ( relational_cp_a_b @ Q ) )
= ( relational_cp_a_b @ Q ) ) ).
% cp_idem
thf(fact_300_gen__Bool__True,axiom,
! [X: nat,G: set_Re381260168593705685la_a_b] :
~ ( relational_gen_a_b @ X @ ( relational_Bool_a_b @ $true ) @ G ) ).
% gen_Bool_True
thf(fact_301_cpropagated__simps_I3_J,axiom,
! [X: nat,T: relational_term_a] :
( ( relati1591879772219623554ed_a_b @ ( relational_Eq_a_b @ X @ T ) )
= ( T
!= ( relational_Var_a @ X ) ) ) ).
% cpropagated_simps(3)
thf(fact_302_fv__term__set__cong,axiom,
! [F: a > a] :
( relati6004689760767320788_set_a
= ( ^ [T4: relational_term_a] : ( relati6004689760767320788_set_a @ ( relati3585320759856631375rm_a_a @ F @ T4 ) ) ) ) ).
% fv_term_set_cong
thf(fact_303_fv__term__setD,axiom,
! [N: nat,T: relational_term_a] :
( ( member_nat @ N @ ( relati6004689760767320788_set_a @ T ) )
=> ( T
= ( relational_Var_a @ N ) ) ) ).
% fv_term_setD
thf(fact_304_gen__Gen__cp,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X @ Q @ G )
=> ? [X_1: set_Re381260168593705685la_a_b] : ( relational_gen_a_b @ X @ ( relational_cp_a_b @ Q ) @ X_1 ) ) ).
% gen_Gen_cp
thf(fact_305_Gen__cp,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ? [X_12: set_Re381260168593705685la_a_b] : ( relational_gen_a_b @ X @ Q @ X_12 )
=> ? [X_1: set_Re381260168593705685la_a_b] : ( relational_gen_a_b @ X @ ( relational_cp_a_b @ Q ) @ X_1 ) ) ).
% Gen_cp
thf(fact_306_Relational__Calculus_Oterm_Osimps_I10_J,axiom,
! [F: a > a,X2: nat] :
( ( relati3585320759856631375rm_a_a @ F @ ( relational_Var_a @ X2 ) )
= ( relational_Var_a @ X2 ) ) ).
% Relational_Calculus.term.simps(10)
thf(fact_307_gen__cp__erase,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,Qqp: relational_fmla_a_b] :
( ( relational_gen_a_b @ X @ Q @ G )
=> ( ( member4680049679412964150la_a_b @ Qqp @ G )
=> ( ( relational_cp_a_b @ ( relational_erase_a_b @ Qqp @ X ) )
= ( relational_Bool_a_b @ $false ) ) ) ) ).
% gen_cp_erase
thf(fact_308_gen_Ointros_I3_J,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X @ Q @ G )
=> ( relational_gen_a_b @ X @ ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q ) ) @ G ) ) ).
% gen.intros(3)
thf(fact_309_gen_Ointros_I7_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,Q22: relational_fmla_a_b] :
( ( ( relational_gen_a_b @ X @ Q1 @ G )
| ( relational_gen_a_b @ X @ Q22 @ G ) )
=> ( relational_gen_a_b @ X @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ G ) ) ).
% gen.intros(7)
thf(fact_310_cp_Osimps_I7_J,axiom,
! [V: $o] :
( ( relational_cp_a_b @ ( relational_Bool_a_b @ V ) )
= ( relational_Bool_a_b @ V ) ) ).
% cp.simps(7)
thf(fact_311_cp_Osimps_I6_J,axiom,
! [V: b,Va: list_R6823256787227418703term_a] :
( ( relational_cp_a_b @ ( relational_Pred_b_a @ V @ Va ) )
= ( relational_Pred_b_a @ V @ Va ) ) ).
% cp.simps(6)
thf(fact_312_term_Orel__intros_I2_J,axiom,
! [X2: nat,Y2: nat,R: a > a > $o] :
( ( X2 = Y2 )
=> ( relati3163788165526728396rm_a_a @ R @ ( relational_Var_a @ X2 ) @ ( relational_Var_a @ Y2 ) ) ) ).
% term.rel_intros(2)
thf(fact_313_term_Orel__inject_I2_J,axiom,
! [R: a > a > $o,X2: nat,Y2: nat] :
( ( relati3163788165526728396rm_a_a @ R @ ( relational_Var_a @ X2 ) @ ( relational_Var_a @ Y2 ) )
= ( X2 = Y2 ) ) ).
% term.rel_inject(2)
thf(fact_314_nocp__cp__triv,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_nocp_a_b @ Q )
=> ( ( relational_cp_a_b @ Q )
= Q ) ) ).
% nocp_cp_triv
thf(fact_315_is__Bool__cp__triv,axiom,
! [Q: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ Q )
=> ( ( relational_cp_a_b @ Q )
= Q ) ) ).
% is_Bool_cp_triv
thf(fact_316_fmla_Oset__intros_I10_J,axiom,
! [Ys: b,X4: relational_fmla_a_b] :
( ( member_b @ Ys @ ( relati8924981150291758614la_a_b @ X4 ) )
=> ( member_b @ Ys @ ( relati8924981150291758614la_a_b @ ( relational_Neg_a_b @ X4 ) ) ) ) ).
% fmla.set_intros(10)
thf(fact_317_fmla_Osimps_I130_J,axiom,
! [X4: relational_fmla_a_b] :
( ( relati8924981150291758614la_a_b @ ( relational_Neg_a_b @ X4 ) )
= ( relati8924981150291758614la_a_b @ X4 ) ) ).
% fmla.simps(130)
thf(fact_318_gen__qp,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,Qqp: relational_fmla_a_b] :
( ( relational_gen_a_b @ X @ Q @ G )
=> ( ( member4680049679412964150la_a_b @ Qqp @ G )
=> ( relational_qp_a_b @ Qqp ) ) ) ).
% gen_qp
thf(fact_319_qp__cp__triv,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_qp_a_b @ Q )
=> ( ( relational_cp_a_b @ Q )
= Q ) ) ).
% qp_cp_triv
thf(fact_320_qp__cp,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_qp_a_b @ Q )
=> ( relational_qp_a_b @ ( relational_cp_a_b @ Q ) ) ) ).
% qp_cp
thf(fact_321_fmla_Oset__intros_I13_J,axiom,
! [Yy: b,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( member_b @ Yy @ ( relati8924981150291758614la_a_b @ X61 ) )
=> ( member_b @ Yy @ ( relati8924981150291758614la_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ) ) ).
% fmla.set_intros(13)
thf(fact_322_fmla_Oset__intros_I14_J,axiom,
! [Za: b,X62: relational_fmla_a_b,X61: relational_fmla_a_b] :
( ( member_b @ Za @ ( relati8924981150291758614la_a_b @ X62 ) )
=> ( member_b @ Za @ ( relati8924981150291758614la_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ) ) ).
% fmla.set_intros(14)
thf(fact_323_fmla_Oset__intros_I11_J,axiom,
! [Yu: b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( member_b @ Yu @ ( relati8924981150291758614la_a_b @ X51 ) )
=> ( member_b @ Yu @ ( relati8924981150291758614la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).
% fmla.set_intros(11)
thf(fact_324_fmla_Oset__intros_I12_J,axiom,
! [Yw: b,X52: relational_fmla_a_b,X51: relational_fmla_a_b] :
( ( member_b @ Yw @ ( relati8924981150291758614la_a_b @ X52 ) )
=> ( member_b @ Yw @ ( relati8924981150291758614la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).
% fmla.set_intros(12)
thf(fact_325_fmla_Oset__intros_I15_J,axiom,
! [Zc: b,X72: relational_fmla_a_b,X71: nat] :
( ( member_b @ Zc @ ( relati8924981150291758614la_a_b @ X72 ) )
=> ( member_b @ Zc @ ( relati8924981150291758614la_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ) ) ).
% fmla.set_intros(15)
thf(fact_326_fmla_Osimps_I133_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
( ( relati8924981150291758614la_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) )
= ( relati8924981150291758614la_a_b @ X72 ) ) ).
% fmla.simps(133)
thf(fact_327_fmla_Oset__intros_I9_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] : ( member_b @ X11 @ ( relati8924981150291758614la_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ) ).
% fmla.set_intros(9)
thf(fact_328_cpropagated__cp__triv,axiom,
! [Q: relational_fmla_a_b] :
( ( relati1591879772219623554ed_a_b @ Q )
=> ( ( relational_cp_a_b @ Q )
= Q ) ) ).
% cpropagated_cp_triv
thf(fact_329_cpropagated__cp,axiom,
! [Q: relational_fmla_a_b] : ( relati1591879772219623554ed_a_b @ ( relational_cp_a_b @ Q ) ) ).
% cpropagated_cp
thf(fact_330_erase_Osimps_I3_J,axiom,
! [T: relational_term_a,Z2: nat,X: nat] :
( ( ( T
= ( relational_Var_a @ Z2 ) )
=> ( ( relational_erase_a_b @ ( relational_Eq_a_b @ Z2 @ T ) @ X )
= ( relational_Bool_a_b @ $true ) ) )
& ( ( T
!= ( relational_Var_a @ Z2 ) )
=> ( ( ( ( X = Z2 )
| ( member_nat @ X @ ( relati6004689760767320788_set_a @ T ) ) )
=> ( ( relational_erase_a_b @ ( relational_Eq_a_b @ Z2 @ T ) @ X )
= ( relational_Bool_a_b @ $false ) ) )
& ( ~ ( ( X = Z2 )
| ( member_nat @ X @ ( relati6004689760767320788_set_a @ T ) ) )
=> ( ( relational_erase_a_b @ ( relational_Eq_a_b @ Z2 @ T ) @ X )
= ( relational_Eq_a_b @ Z2 @ T ) ) ) ) ) ) ).
% erase.simps(3)
thf(fact_331_nocp_Osimps_I3_J,axiom,
! [X: nat,T: relational_term_a] :
( ( relational_nocp_a_b @ ( relational_Eq_a_b @ X @ T ) )
= ( T
!= ( relational_Var_a @ X ) ) ) ).
% nocp.simps(3)
thf(fact_332_qp__eq,axiom,
! [X: nat,Y3: nat] :
~ ( relational_qp_a_b @ ( relational_Eq_a_b @ X @ ( relational_Var_a @ Y3 ) ) ) ).
% qp_eq
thf(fact_333_nocp__cp__or__is__Bool,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_nocp_a_b @ ( relational_cp_a_b @ Q ) )
| ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q ) ) ) ).
% nocp_cp_or_is_Bool
thf(fact_334_qp__impl_Osimps_I5_J,axiom,
! [V: nat,Vb: nat] :
~ ( relati3725921752842749053pl_a_b @ ( relational_Eq_a_b @ V @ ( relational_Var_a @ Vb ) ) ) ).
% qp_impl.simps(5)
thf(fact_335_fmla_Osimps_I66_J,axiom,
! [F1: a > a,F2: b > b,X312: nat,X322: relational_term_a] :
( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Eq_a_b @ X312 @ X322 ) )
= ( relational_Eq_a_b @ X312 @ ( relati3585320759856631375rm_a_a @ F1 @ X322 ) ) ) ).
% fmla.simps(66)
thf(fact_336_fmla_Oset__sel_I11_J,axiom,
! [A: relational_fmla_a_b,Xr: b] :
( ( relati8168519172193746908nj_a_b @ A )
=> ( ( member_b @ Xr @ ( relati8924981150291758614la_a_b @ ( relati5154284022127734760j1_a_b @ A ) ) )
=> ( member_b @ Xr @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).
% fmla.set_sel(11)
thf(fact_337_fmla_Oset__sel_I12_J,axiom,
! [A: relational_fmla_a_b,Xt: b] :
( ( relati8168519172193746908nj_a_b @ A )
=> ( ( member_b @ Xt @ ( relati8924981150291758614la_a_b @ ( relati1527130600461089641j2_a_b @ A ) ) )
=> ( member_b @ Xt @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).
% fmla.set_sel(12)
thf(fact_338_fmla_Oset__sel_I13_J,axiom,
! [A: relational_fmla_a_b,Xv: b] :
( ( relati5350680195807439568sj_a_b @ A )
=> ( ( member_b @ Xv @ ( relati8924981150291758614la_a_b @ ( relati3334262663314506228j1_a_b @ A ) ) )
=> ( member_b @ Xv @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).
% fmla.set_sel(13)
thf(fact_339_fmla_Oset__sel_I14_J,axiom,
! [A: relational_fmla_a_b,Xx: b] :
( ( relati5350680195807439568sj_a_b @ A )
=> ( ( member_b @ Xx @ ( relati8924981150291758614la_a_b @ ( relati8930481278502636917j2_a_b @ A ) ) )
=> ( member_b @ Xx @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).
% fmla.set_sel(14)
thf(fact_340_fmla_Oset__sel_I10_J,axiom,
! [A: relational_fmla_a_b,Xp: b] :
( ( relati4321004860440572638eg_a_b @ A )
=> ( ( member_b @ Xp @ ( relati8924981150291758614la_a_b @ ( relati5982302313924697647eg_a_b @ A ) ) )
=> ( member_b @ Xp @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).
% fmla.set_sel(10)
thf(fact_341_fmla_Oset__sel_I9_J,axiom,
! [A: relational_fmla_a_b] :
( ( relati3644702733014758741ed_a_b @ A )
=> ( member_b @ ( relati91604085239814319d1_a_b @ A ) @ ( relati8924981150291758614la_a_b @ A ) ) ) ).
% fmla.set_sel(9)
thf(fact_342_fmla_Oset__sel_I15_J,axiom,
! [A: relational_fmla_a_b,Xz: b] :
( ( relati5212983245281121968ts_a_b @ A )
=> ( ( member_b @ Xz @ ( relati8924981150291758614la_a_b @ ( relati5591445451228332309s2_a_b @ A ) ) )
=> ( member_b @ Xz @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).
% fmla.set_sel(15)
thf(fact_343_gen_Ointros_I4_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q1 ) @ ( relational_Neg_a_b @ Q22 ) ) @ G )
=> ( relational_gen_a_b @ X @ ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) ) @ G ) ) ).
% gen.intros(4)
thf(fact_344_gen_Ointros_I5_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q1 ) @ ( relational_Neg_a_b @ Q22 ) ) @ G )
=> ( relational_gen_a_b @ X @ ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) ) @ G ) ) ).
% gen.intros(5)
thf(fact_345_erase_Opelims,axiom,
! [X: relational_fmla_a_b,Xa2: nat,Y3: relational_fmla_a_b] :
( ( ( relational_erase_a_b @ X @ Xa2 )
= Y3 )
=> ( ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ X @ Xa2 ) )
=> ( ! [T2: $o] :
( ( X
= ( relational_Bool_a_b @ T2 ) )
=> ( ( Y3
= ( relational_Bool_a_b @ T2 ) )
=> ~ ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ ( relational_Bool_a_b @ T2 ) @ Xa2 ) ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( ( ( ( member_nat @ Xa2 @ ( relati4569515538964159125_set_a @ Ts2 ) )
=> ( Y3
= ( relational_Bool_a_b @ $false ) ) )
& ( ~ ( member_nat @ Xa2 @ ( relati4569515538964159125_set_a @ Ts2 ) )
=> ( Y3
= ( relational_Pred_b_a @ P3 @ Ts2 ) ) ) )
=> ~ ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ Xa2 ) ) ) )
=> ( ! [Z3: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ Z3 @ T2 ) )
=> ( ( ( ( T2
= ( relational_Var_a @ Z3 ) )
=> ( Y3
= ( relational_Bool_a_b @ $true ) ) )
& ( ( T2
!= ( relational_Var_a @ Z3 ) )
=> ( ( ( ( Xa2 = Z3 )
| ( member_nat @ Xa2 @ ( relati6004689760767320788_set_a @ T2 ) ) )
=> ( Y3
= ( relational_Bool_a_b @ $false ) ) )
& ( ~ ( ( Xa2 = Z3 )
| ( member_nat @ Xa2 @ ( relati6004689760767320788_set_a @ T2 ) ) )
=> ( Y3
= ( relational_Eq_a_b @ Z3 @ T2 ) ) ) ) ) )
=> ~ ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ ( relational_Eq_a_b @ Z3 @ T2 ) @ Xa2 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( ( Y3
= ( relational_Neg_a_b @ ( relational_erase_a_b @ Q4 @ Xa2 ) ) )
=> ~ ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ ( relational_Neg_a_b @ Q4 ) @ Xa2 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( relational_Conj_a_b @ ( relational_erase_a_b @ Q12 @ Xa2 ) @ ( relational_erase_a_b @ Q23 @ Xa2 ) ) )
=> ~ ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ Xa2 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( relational_Disj_a_b @ ( relational_erase_a_b @ Q12 @ Xa2 ) @ ( relational_erase_a_b @ Q23 @ Xa2 ) ) )
=> ~ ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ Xa2 ) ) ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) )
=> ( ( ( ( Xa2 = Z3 )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Xa2 @ Q4 ) ) )
& ( ( Xa2 != Z3 )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Z3 @ ( relational_erase_a_b @ Q4 @ Xa2 ) ) ) ) )
=> ~ ( accp_P4351966040938400857_b_nat @ relati5987653437628155313el_a_b @ ( produc4282057684358614024_b_nat @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% erase.pelims
thf(fact_346_qp__impl_Oelims_I3_J,axiom,
! [X: relational_fmla_a_b] :
( ~ ( relati3725921752842749053pl_a_b @ X )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_qp_a_b @ Q4 ) ) )
=> ( ! [V2: $o] :
( X
!= ( relational_Bool_a_b @ V2 ) )
=> ( ! [V2: nat,Vb2: nat] :
( X
!= ( relational_Eq_a_b @ V2 @ ( relational_Var_a @ Vb2 ) ) )
=> ( ! [V2: relational_fmla_a_b] :
( X
!= ( relational_Neg_a_b @ V2 ) )
=> ( ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( X
!= ( relational_Conj_a_b @ V2 @ Va2 ) )
=> ~ ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( X
!= ( relational_Disj_a_b @ V2 @ Va2 ) ) ) ) ) ) ) ) ).
% qp_impl.elims(3)
thf(fact_347_nocp_Oelims_I1_J,axiom,
! [X: relational_fmla_a_b,Y3: $o] :
( ( ( relational_nocp_a_b @ X )
= Y3 )
=> ( ( ? [B3: $o] :
( X
= ( relational_Bool_a_b @ B3 ) )
=> Y3 )
=> ( ( ? [P3: b,Ts2: list_R6823256787227418703term_a] :
( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ~ Y3 )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( Y3
= ( T2
= ( relational_Var_a @ X5 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( Y3
= ( ~ ( relational_nocp_a_b @ Q4 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( Y3
= ( ~ ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( Y3
= ( ~ ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) ) ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( Y3
= ( ~ ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_nocp_a_b @ Q4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% nocp.elims(1)
thf(fact_348_qp__impl_Ocases,axiom,
! [X: relational_fmla_a_b] :
( ! [X5: nat,C: a] :
( X
!= ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) )
=> ( ! [X5: b,Ts2: list_R6823256787227418703term_a] :
( X
!= ( relational_Pred_b_a @ X5 @ Ts2 ) )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( X
!= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ! [V2: $o] :
( X
!= ( relational_Bool_a_b @ V2 ) )
=> ( ! [V2: nat,Vb2: nat] :
( X
!= ( relational_Eq_a_b @ V2 @ ( relational_Var_a @ Vb2 ) ) )
=> ( ! [V2: relational_fmla_a_b] :
( X
!= ( relational_Neg_a_b @ V2 ) )
=> ( ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( X
!= ( relational_Conj_a_b @ V2 @ Va2 ) )
=> ~ ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( X
!= ( relational_Disj_a_b @ V2 @ Va2 ) ) ) ) ) ) ) ) ) ).
% qp_impl.cases
thf(fact_349_nocp_Oelims_I2_J,axiom,
! [X: relational_fmla_a_b] :
( ( relational_nocp_a_b @ X )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( X
!= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( T2
= ( relational_Var_a @ X5 ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ~ ( relational_nocp_a_b @ Q4 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ~ ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ~ ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ~ ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_nocp_a_b @ Q4 ) ) ) ) ) ) ) ) ) ).
% nocp.elims(2)
thf(fact_350_term_Oinject_I1_J,axiom,
! [X13: a,Y13: a] :
( ( ( relational_Const_a @ X13 )
= ( relational_Const_a @ Y13 ) )
= ( X13 = Y13 ) ) ).
% term.inject(1)
thf(fact_351_cpropagated__simps_I7_J,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relati1591879772219623554ed_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) )
= ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
& ( relational_nocp_a_b @ Q ) ) ) ).
% cpropagated_simps(7)
thf(fact_352_fv_Osimps_I4_J,axiom,
! [Phi2: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( relational_Neg_a_b @ Phi2 ) )
= ( relational_fv_a_b @ Phi2 ) ) ).
% fv.simps(4)
thf(fact_353_term_Odistinct_I1_J,axiom,
! [X13: a,X2: nat] :
( ( relational_Const_a @ X13 )
!= ( relational_Var_a @ X2 ) ) ).
% term.distinct(1)
thf(fact_354_Relational__Calculus_Oterm_Oexhaust,axiom,
! [Y3: relational_term_a] :
( ! [X1: a] :
( Y3
!= ( relational_Const_a @ X1 ) )
=> ~ ! [X23: nat] :
( Y3
!= ( relational_Var_a @ X23 ) ) ) ).
% Relational_Calculus.term.exhaust
thf(fact_355_fv__fo__term__list_Ocases,axiom,
! [X: relational_term_a] :
( ! [N2: nat] :
( X
!= ( relational_Var_a @ N2 ) )
=> ~ ! [V2: a] :
( X
!= ( relational_Const_a @ V2 ) ) ) ).
% fv_fo_term_list.cases
thf(fact_356_term_Orel__inject_I1_J,axiom,
! [R: a > a > $o,X13: a,Y13: a] :
( ( relati3163788165526728396rm_a_a @ R @ ( relational_Const_a @ X13 ) @ ( relational_Const_a @ Y13 ) )
= ( R @ X13 @ Y13 ) ) ).
% term.rel_inject(1)
thf(fact_357_term_Orel__intros_I1_J,axiom,
! [R: a > a > $o,X13: a,Y13: a] :
( ( R @ X13 @ Y13 )
=> ( relati3163788165526728396rm_a_a @ R @ ( relational_Const_a @ X13 ) @ ( relational_Const_a @ Y13 ) ) ) ).
% term.rel_intros(1)
thf(fact_358_Relational__Calculus_Oterm_Osimps_I9_J,axiom,
! [F: a > a,X13: a] :
( ( relati3585320759856631375rm_a_a @ F @ ( relational_Const_a @ X13 ) )
= ( relational_Const_a @ ( F @ X13 ) ) ) ).
% Relational_Calculus.term.simps(9)
thf(fact_359_nocp_Osimps_I7_J,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relational_nocp_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) )
= ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
& ( relational_nocp_a_b @ Q ) ) ) ).
% nocp.simps(7)
thf(fact_360_qp__ExistsE,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relational_qp_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) )
=> ~ ( ( relational_qp_a_b @ Q )
=> ~ ( member_nat @ X @ ( relational_fv_a_b @ Q ) ) ) ) ).
% qp_ExistsE
thf(fact_361_qp__Exists,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_qp_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( relational_qp_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) ) ) ) ).
% qp_Exists
thf(fact_362_qp__Gen,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_qp_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ? [X_1: set_Re381260168593705685la_a_b] : ( relational_gen_a_b @ X @ Q @ X_1 ) ) ) ).
% qp_Gen
thf(fact_363_term_Orel__induct,axiom,
! [R: a > a > $o,X: relational_term_a,Y3: relational_term_a,Q: relational_term_a > relational_term_a > $o] :
( ( relati3163788165526728396rm_a_a @ R @ X @ Y3 )
=> ( ! [A1: a,B1: a] :
( ( R @ A1 @ B1 )
=> ( Q @ ( relational_Const_a @ A1 ) @ ( relational_Const_a @ B1 ) ) )
=> ( ! [A22: nat,B2: nat] :
( ( A22 = B2 )
=> ( Q @ ( relational_Var_a @ A22 ) @ ( relational_Var_a @ B2 ) ) )
=> ( Q @ X @ Y3 ) ) ) ) ).
% term.rel_induct
thf(fact_364_term_Orel__cases,axiom,
! [R: a > a > $o,A: relational_term_a,B: relational_term_a] :
( ( relati3163788165526728396rm_a_a @ R @ A @ B )
=> ( ! [X5: a] :
( ( A
= ( relational_Const_a @ X5 ) )
=> ! [Y5: a] :
( ( B
= ( relational_Const_a @ Y5 ) )
=> ~ ( R @ X5 @ Y5 ) ) )
=> ~ ! [Xa: nat] :
( ( A
= ( relational_Var_a @ Xa ) )
=> ! [Ya: nat] :
( ( B
= ( relational_Var_a @ Ya ) )
=> ( Xa != Ya ) ) ) ) ) ).
% term.rel_cases
thf(fact_365_term_Orel__distinct_I1_J,axiom,
! [R: a > a > $o,X13: a,Y2: nat] :
~ ( relati3163788165526728396rm_a_a @ R @ ( relational_Const_a @ X13 ) @ ( relational_Var_a @ Y2 ) ) ).
% term.rel_distinct(1)
thf(fact_366_term_Orel__distinct_I2_J,axiom,
! [R: a > a > $o,Y2: nat,X13: a] :
~ ( relati3163788165526728396rm_a_a @ R @ ( relational_Var_a @ Y2 ) @ ( relational_Const_a @ X13 ) ) ).
% term.rel_distinct(2)
thf(fact_367_fv_Osimps_I1_J,axiom,
! [Uu2: b,Ts: list_R6823256787227418703term_a] :
( ( relational_fv_a_b @ ( relational_Pred_b_a @ Uu2 @ Ts ) )
= ( relati4569515538964159125_set_a @ Ts ) ) ).
% fv.simps(1)
thf(fact_368_cpropagated__nocp,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relati1591879772219623554ed_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( relational_nocp_a_b @ Q ) ) ) ).
% cpropagated_nocp
thf(fact_369_qp__impl_Osimps_I1_J,axiom,
! [X: nat,C2: a] : ( relati3725921752842749053pl_a_b @ ( relational_Eq_a_b @ X @ ( relational_Const_a @ C2 ) ) ) ).
% qp_impl.simps(1)
thf(fact_370_qp__impl_Oelims_I2_J,axiom,
! [X: relational_fmla_a_b] :
( ( relati3725921752842749053pl_a_b @ X )
=> ( ! [X5: nat,C: a] :
( X
!= ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) )
=> ( ! [X5: b,Ts2: list_R6823256787227418703term_a] :
( X
!= ( relational_Pred_b_a @ X5 @ Ts2 ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ~ ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_qp_a_b @ Q4 ) ) ) ) ) ) ).
% qp_impl.elims(2)
thf(fact_371_qp__impl_Osimps_I3_J,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relati3725921752842749053pl_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) )
= ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
& ( relational_qp_a_b @ Q ) ) ) ).
% qp_impl.simps(3)
thf(fact_372_qp__cp__erase,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_qp_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( ( relational_cp_a_b @ ( relational_erase_a_b @ Q @ X ) )
= ( relational_Bool_a_b @ $false ) ) ) ) ).
% qp_cp_erase
thf(fact_373_qp__impl_Oelims_I1_J,axiom,
! [X: relational_fmla_a_b,Y3: $o] :
( ( ( relati3725921752842749053pl_a_b @ X )
= Y3 )
=> ( ( ? [X5: nat,C: a] :
( X
= ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) )
=> ~ Y3 )
=> ( ( ? [X5: b,Ts2: list_R6823256787227418703term_a] :
( X
= ( relational_Pred_b_a @ X5 @ Ts2 ) )
=> ~ Y3 )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( Y3
= ( ~ ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_qp_a_b @ Q4 ) ) ) ) )
=> ( ( ? [V2: $o] :
( X
= ( relational_Bool_a_b @ V2 ) )
=> Y3 )
=> ( ( ? [V2: nat,Vb2: nat] :
( X
= ( relational_Eq_a_b @ V2 @ ( relational_Var_a @ Vb2 ) ) )
=> Y3 )
=> ( ( ? [V2: relational_fmla_a_b] :
( X
= ( relational_Neg_a_b @ V2 ) )
=> Y3 )
=> ( ( ? [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( X
= ( relational_Conj_a_b @ V2 @ Va2 ) )
=> Y3 )
=> ~ ( ? [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( X
= ( relational_Disj_a_b @ V2 @ Va2 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ).
% qp_impl.elims(1)
thf(fact_374_nocp_Oelims_I3_J,axiom,
! [X: relational_fmla_a_b] :
( ~ ( relational_nocp_a_b @ X )
=> ( ! [B3: $o] :
( X
!= ( relational_Bool_a_b @ B3 ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( T2
!= ( relational_Var_a @ X5 ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( relational_nocp_a_b @ Q4 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_nocp_a_b @ Q4 ) ) ) ) ) ) ) ) ) ).
% nocp.elims(3)
thf(fact_375_genempty_Osimps,axiom,
( relati5999705594545617851ty_a_b
= ( ^ [A3: relational_fmla_a_b] :
( ( A3
= ( relational_Bool_a_b @ $false ) )
| ? [Q3: relational_fmla_a_b] :
( ( A3
= ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q3 ) ) )
& ( relati5999705594545617851ty_a_b @ Q3 ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A3
= ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q13 @ Q24 ) ) )
& ( relati5999705594545617851ty_a_b @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q13 ) @ ( relational_Neg_a_b @ Q24 ) ) ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A3
= ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q13 @ Q24 ) ) )
& ( relati5999705594545617851ty_a_b @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q13 ) @ ( relational_Neg_a_b @ Q24 ) ) ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A3
= ( relational_Disj_a_b @ Q13 @ Q24 ) )
& ( relati5999705594545617851ty_a_b @ Q13 )
& ( relati5999705594545617851ty_a_b @ Q24 ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A3
= ( relational_Conj_a_b @ Q13 @ Q24 ) )
& ( ( relati5999705594545617851ty_a_b @ Q13 )
| ( relati5999705594545617851ty_a_b @ Q24 ) ) )
| ? [Q3: relational_fmla_a_b] :
( ? [X3: nat,Y6: nat] :
( A3
= ( relational_Conj_a_b @ Q3 @ ( relational_Eq_a_b @ X3 @ ( relational_Var_a @ Y6 ) ) ) )
& ( relati5999705594545617851ty_a_b @ Q3 ) )
| ? [Q3: relational_fmla_a_b] :
( ? [Y6: nat] :
( A3
= ( relati591517084277583526ts_a_b @ Y6 @ Q3 ) )
& ( relati5999705594545617851ty_a_b @ Q3 ) ) ) ) ) ).
% genempty.simps
thf(fact_376_genempty_Ocases,axiom,
! [A: relational_fmla_a_b] :
( ( relati5999705594545617851ty_a_b @ A )
=> ( ( A
!= ( relational_Bool_a_b @ $false ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( A
= ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q4 ) ) )
=> ~ ( relati5999705594545617851ty_a_b @ Q4 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A
= ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) ) )
=> ~ ( relati5999705594545617851ty_a_b @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A
= ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) ) )
=> ~ ( relati5999705594545617851ty_a_b @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( relati5999705594545617851ty_a_b @ Q12 )
=> ~ ( relati5999705594545617851ty_a_b @ Q23 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ~ ( ( relati5999705594545617851ty_a_b @ Q12 )
| ( relati5999705594545617851ty_a_b @ Q23 ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ? [X5: nat,Y5: nat] :
( A
= ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ X5 @ ( relational_Var_a @ Y5 ) ) ) )
=> ~ ( relati5999705594545617851ty_a_b @ Q4 ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ? [Y5: nat,X5: nat] :
( A
= ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ Y5 @ ( relational_Var_a @ X5 ) ) ) )
=> ~ ( relati5999705594545617851ty_a_b @ Q4 ) )
=> ~ ! [Q4: relational_fmla_a_b] :
( ? [Y5: nat] :
( A
= ( relati591517084277583526ts_a_b @ Y5 @ Q4 ) )
=> ~ ( relati5999705594545617851ty_a_b @ Q4 ) ) ) ) ) ) ) ) ) ) ) ).
% genempty.cases
thf(fact_377_qp__impl_Opelims_I1_J,axiom,
! [X: relational_fmla_a_b,Y3: $o] :
( ( ( relati3725921752842749053pl_a_b @ X )
= Y3 )
=> ( ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ X )
=> ( ! [X5: nat,C: a] :
( ( X
= ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) )
=> ( Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) ) ) )
=> ( ! [X5: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ X5 @ Ts2 ) )
=> ( Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Pred_b_a @ X5 @ Ts2 ) ) ) )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( Y3
= ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_qp_a_b @ Q4 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relati591517084277583526ts_a_b @ X5 @ Q4 ) ) ) )
=> ( ! [V2: $o] :
( ( X
= ( relational_Bool_a_b @ V2 ) )
=> ( ~ Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Bool_a_b @ V2 ) ) ) )
=> ( ! [V2: nat,Vb2: nat] :
( ( X
= ( relational_Eq_a_b @ V2 @ ( relational_Var_a @ Vb2 ) ) )
=> ( ~ Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Eq_a_b @ V2 @ ( relational_Var_a @ Vb2 ) ) ) ) )
=> ( ! [V2: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ V2 ) )
=> ( ~ Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Neg_a_b @ V2 ) ) ) )
=> ( ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ V2 @ Va2 ) )
=> ( ~ Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Conj_a_b @ V2 @ Va2 ) ) ) )
=> ~ ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ V2 @ Va2 ) )
=> ( ~ Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Disj_a_b @ V2 @ Va2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% qp_impl.pelims(1)
thf(fact_378_ap__cp__erase,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_ap_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( ( relational_cp_a_b @ ( relational_erase_a_b @ Q @ X ) )
= ( relational_Bool_a_b @ $false ) ) ) ) ).
% ap_cp_erase
thf(fact_379_qp__impl_Opelims_I3_J,axiom,
! [X: relational_fmla_a_b] :
( ~ ( relati3725921752842749053pl_a_b @ X )
=> ( ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ X )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_qp_a_b @ Q4 ) ) ) )
=> ( ! [V2: $o] :
( ( X
= ( relational_Bool_a_b @ V2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Bool_a_b @ V2 ) ) )
=> ( ! [V2: nat,Vb2: nat] :
( ( X
= ( relational_Eq_a_b @ V2 @ ( relational_Var_a @ Vb2 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Eq_a_b @ V2 @ ( relational_Var_a @ Vb2 ) ) ) )
=> ( ! [V2: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ V2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Neg_a_b @ V2 ) ) )
=> ( ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ V2 @ Va2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Conj_a_b @ V2 @ Va2 ) ) )
=> ~ ! [V2: relational_fmla_a_b,Va2: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ V2 @ Va2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Disj_a_b @ V2 @ Va2 ) ) ) ) ) ) ) ) ) ) ).
% qp_impl.pelims(3)
thf(fact_380_genempty_Ointros_I2_J,axiom,
! [Q: relational_fmla_a_b] :
( ( relati5999705594545617851ty_a_b @ Q )
=> ( relati5999705594545617851ty_a_b @ ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q ) ) ) ) ).
% genempty.intros(2)
thf(fact_381_genempty_Ointros_I5_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relati5999705594545617851ty_a_b @ Q1 )
=> ( ( relati5999705594545617851ty_a_b @ Q22 )
=> ( relati5999705594545617851ty_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) ) ) ) ).
% genempty.intros(5)
thf(fact_382_genempty_Ointros_I6_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( ( relati5999705594545617851ty_a_b @ Q1 )
| ( relati5999705594545617851ty_a_b @ Q22 ) )
=> ( relati5999705594545617851ty_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) ) ) ).
% genempty.intros(6)
thf(fact_383_genempty_Ointros_I9_J,axiom,
! [Q: relational_fmla_a_b,Y3: nat] :
( ( relati5999705594545617851ty_a_b @ Q )
=> ( relati5999705594545617851ty_a_b @ ( relati591517084277583526ts_a_b @ Y3 @ Q ) ) ) ).
% genempty.intros(9)
thf(fact_384_genempty_Ointros_I1_J,axiom,
relati5999705594545617851ty_a_b @ ( relational_Bool_a_b @ $false ) ).
% genempty.intros(1)
thf(fact_385_Pred,axiom,
! [P2: b,Ts: list_R6823256787227418703term_a] : ( relational_ap_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) ) ).
% Pred
thf(fact_386_ap__cp__triv,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_ap_a_b @ Q )
=> ( ( relational_cp_a_b @ Q )
= Q ) ) ).
% ap_cp_triv
thf(fact_387_ap__cp,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_ap_a_b @ Q )
=> ( relational_ap_a_b @ ( relational_cp_a_b @ Q ) ) ) ).
% ap_cp
thf(fact_388_ap,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_ap_a_b @ Q )
=> ( relational_qp_a_b @ Q ) ) ).
% ap
thf(fact_389_genempty__cp,axiom,
! [Q: relational_fmla_a_b] :
( ( relati5999705594545617851ty_a_b @ Q )
=> ( ( relational_cp_a_b @ Q )
= ( relational_Bool_a_b @ $false ) ) ) ).
% genempty_cp
thf(fact_390_Eqc,axiom,
! [X: nat,C2: a] : ( relational_ap_a_b @ ( relational_Eq_a_b @ X @ ( relational_Const_a @ C2 ) ) ) ).
% Eqc
thf(fact_391_genempty_Ointros_I3_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relati5999705594545617851ty_a_b @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q1 ) @ ( relational_Neg_a_b @ Q22 ) ) )
=> ( relati5999705594545617851ty_a_b @ ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) ) ) ) ).
% genempty.intros(3)
thf(fact_392_genempty_Ointros_I4_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relati5999705594545617851ty_a_b @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q1 ) @ ( relational_Neg_a_b @ Q22 ) ) )
=> ( relati5999705594545617851ty_a_b @ ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) ) ) ) ).
% genempty.intros(4)
thf(fact_393_genempty_Ointros_I8_J,axiom,
! [Q: relational_fmla_a_b,Y3: nat,X: nat] :
( ( relati5999705594545617851ty_a_b @ Q )
=> ( relati5999705594545617851ty_a_b @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ Y3 @ ( relational_Var_a @ X ) ) ) ) ) ).
% genempty.intros(8)
thf(fact_394_genempty_Ointros_I7_J,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relati5999705594545617851ty_a_b @ Q )
=> ( relati5999705594545617851ty_a_b @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ X @ ( relational_Var_a @ Y3 ) ) ) ) ) ).
% genempty.intros(7)
thf(fact_395_qp__impl_Opelims_I2_J,axiom,
! [X: relational_fmla_a_b] :
( ( relati3725921752842749053pl_a_b @ X )
=> ( ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ X )
=> ( ! [X5: nat,C: a] :
( ( X
= ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) ) )
=> ( ! [X5: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ X5 @ Ts2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relational_Pred_b_a @ X5 @ Ts2 ) ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati7364465619720499582el_a_b @ ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ~ ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_qp_a_b @ Q4 ) ) ) ) ) ) ) ) ).
% qp_impl.pelims(2)
thf(fact_396_ap_Ocases,axiom,
! [A: relational_fmla_a_b] :
( ( relational_ap_a_b @ A )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( A
!= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ~ ! [X5: nat,C: a] :
( A
!= ( relational_Eq_a_b @ X5 @ ( relational_Const_a @ C ) ) ) ) ) ).
% ap.cases
thf(fact_397_ap_Osimps,axiom,
( relational_ap_a_b
= ( ^ [A3: relational_fmla_a_b] :
( ? [P4: b,Ts3: list_R6823256787227418703term_a] :
( A3
= ( relational_Pred_b_a @ P4 @ Ts3 ) )
| ? [X3: nat,C3: a] :
( A3
= ( relational_Eq_a_b @ X3 @ ( relational_Const_a @ C3 ) ) ) ) ) ) ).
% ap.simps
thf(fact_398_nocp_Opelims_I1_J,axiom,
! [X: relational_fmla_a_b,Y3: $o] :
( ( ( relational_nocp_a_b @ X )
= Y3 )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ X )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ( ~ Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Bool_a_b @ B3 ) ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( Y3
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Pred_b_a @ P3 @ Ts2 ) ) ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( ( Y3
= ( T2
!= ( relational_Var_a @ X5 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Eq_a_b @ X5 @ T2 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( ( Y3
= ( relational_nocp_a_b @ Q4 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Neg_a_b @ Q4 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) ) ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( Y3
= ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_nocp_a_b @ Q4 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relati591517084277583526ts_a_b @ X5 @ Q4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% nocp.pelims(1)
thf(fact_399_nocp_Opelims_I2_J,axiom,
! [X: relational_fmla_a_b] :
( ( relational_nocp_a_b @ X )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ X )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Pred_b_a @ P3 @ Ts2 ) ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( T2
= ( relational_Var_a @ X5 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Neg_a_b @ Q4 ) )
=> ~ ( relational_nocp_a_b @ Q4 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ~ ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ~ ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ~ ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_nocp_a_b @ Q4 ) ) ) ) ) ) ) ) ) ) ) ).
% nocp.pelims(2)
thf(fact_400_nocp_Opelims_I3_J,axiom,
! [X: relational_fmla_a_b] :
( ~ ( relational_nocp_a_b @ X )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ X )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Bool_a_b @ B3 ) ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( T2
!= ( relational_Var_a @ X5 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Neg_a_b @ Q4 ) )
=> ( relational_nocp_a_b @ Q4 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( relational_nocp_a_b @ Q12 )
& ( relational_nocp_a_b @ Q23 ) ) ) )
=> ~ ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( accp_R989495437599811158la_a_b @ relati3149960101488570543el_a_b @ ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
& ( relational_nocp_a_b @ Q4 ) ) ) ) ) ) ) ) ) ) ) ).
% nocp.pelims(3)
thf(fact_401_fmla_Omap__sel_I2_J,axiom,
! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ( relati3644702733014758741ed_a_b @ A )
=> ( ( relati5687822700427945008d2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
= ( map_Re5736185711816362116term_a @ ( relati3585320759856631375rm_a_a @ F1 ) @ ( relati5687822700427945008d2_a_b @ A ) ) ) ) ).
% fmla.map_sel(2)
thf(fact_402_qp__subst__eq,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_qp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
= ( relational_qp_a_b @ Q ) ) ).
% qp_subst_eq
thf(fact_403_subst_Osimps_I4_J,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_subst_a_b @ ( relational_Neg_a_b @ Q ) @ X @ Y3 )
= ( relational_Neg_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ).
% subst.simps(4)
thf(fact_404_subst_Osimps_I6_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_subst_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ X @ Y3 )
= ( relational_Disj_a_b @ ( relational_subst_a_b @ Q1 @ X @ Y3 ) @ ( relational_subst_a_b @ Q22 @ X @ Y3 ) ) ) ).
% subst.simps(6)
thf(fact_405_subst_Osimps_I5_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_subst_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ X @ Y3 )
= ( relational_Conj_a_b @ ( relational_subst_a_b @ Q1 @ X @ Y3 ) @ ( relational_subst_a_b @ Q22 @ X @ Y3 ) ) ) ).
% subst.simps(5)
thf(fact_406_subst_Osimps_I1_J,axiom,
! [T: $o,X: nat,Y3: nat] :
( ( relational_subst_a_b @ ( relational_Bool_a_b @ T ) @ X @ Y3 )
= ( relational_Bool_a_b @ T ) ) ).
% subst.simps(1)
thf(fact_407_fresh2_I2_J,axiom,
! [Y3: nat,X: nat,Q: relational_fmla_a_b] :
( Y3
!= ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) ) ).
% fresh2(2)
thf(fact_408_fresh2_I1_J,axiom,
! [X: nat,Y3: nat,Q: relational_fmla_a_b] :
( X
!= ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) ) ).
% fresh2(1)
thf(fact_409_qp__subst,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_qp_a_b @ Q )
=> ( relational_qp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ).
% qp_subst
thf(fact_410_qp__subst_H,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_qp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
=> ( relational_qp_a_b @ Q ) ) ).
% qp_subst'
thf(fact_411_ap__subst_H,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_ap_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
=> ( relational_ap_a_b @ Q ) ) ).
% ap_subst'
thf(fact_412_fresh2_I3_J,axiom,
! [X: nat,Y3: nat,Q: relational_fmla_a_b] :
~ ( member_nat @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) @ ( relational_fv_a_b @ Q ) ) ).
% fresh2(3)
thf(fact_413_Gen__cp__subst,axiom,
! [Z2: nat,Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ? [X_12: set_Re381260168593705685la_a_b] : ( relational_gen_a_b @ Z2 @ Q @ X_12 )
=> ( ( Z2 != X )
=> ? [X_1: set_Re381260168593705685la_a_b] : ( relational_gen_a_b @ Z2 @ ( relational_cp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) @ X_1 ) ) ) ).
% Gen_cp_subst
thf(fact_414_qp__cp__subst__triv,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_qp_a_b @ Q )
=> ( ( relational_cp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
= ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ).
% qp_cp_subst_triv
thf(fact_415_ap__cp__subst__triv,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( relational_ap_a_b @ Q )
=> ( ( relational_cp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
= ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ).
% ap_cp_subst_triv
thf(fact_416_fv__terms__set__cong,axiom,
! [F: a > a] :
( relati4569515538964159125_set_a
= ( ^ [Ts3: list_R6823256787227418703term_a] : ( relati4569515538964159125_set_a @ ( map_Re5736185711816362116term_a @ ( relati3585320759856631375rm_a_a @ F ) @ Ts3 ) ) ) ) ).
% fv_terms_set_cong
thf(fact_417_fmla_Osimps_I64_J,axiom,
! [F1: a > a,F2: b > b,X11: b,X12: list_R6823256787227418703term_a] :
( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Pred_b_a @ X11 @ X12 ) )
= ( relational_Pred_b_a @ ( F2 @ X11 ) @ ( map_Re5736185711816362116term_a @ ( relati3585320759856631375rm_a_a @ F1 ) @ X12 ) ) ) ).
% fmla.simps(64)
thf(fact_418_subst_Oelims,axiom,
! [X: relational_fmla_a_b,Xa2: nat,Xb: nat,Y3: relational_fmla_a_b] :
( ( ( relational_subst_a_b @ X @ Xa2 @ Xb )
= Y3 )
=> ( ! [T2: $o] :
( ( X
= ( relational_Bool_a_b @ T2 ) )
=> ( Y3
!= ( relational_Bool_a_b @ T2 ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( Y3
!= ( relational_Pred_b_a @ P3
@ ( map_Re5736185711816362116term_a
@ ^ [T4: relational_term_a] : ( relati7175845559408349773term_a @ T4 @ Xa2 @ Xb )
@ Ts2 ) ) ) )
=> ( ! [Z3: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ Z3 @ T2 ) )
=> ( Y3
!= ( relational_Eq_a_b @ ( if_nat @ ( Z3 = Xa2 ) @ Xb @ Z3 ) @ ( relati7175845559408349773term_a @ T2 @ Xa2 @ Xb ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( Y3
!= ( relational_Neg_a_b @ ( relational_subst_a_b @ Q4 @ Xa2 @ Xb ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( relational_Conj_a_b @ ( relational_subst_a_b @ Q12 @ Xa2 @ Xb ) @ ( relational_subst_a_b @ Q23 @ Xa2 @ Xb ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( relational_Disj_a_b @ ( relational_subst_a_b @ Q12 @ Xa2 @ Xb ) @ ( relational_subst_a_b @ Q23 @ Xa2 @ Xb ) ) ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) )
=> ~ ( ( ( Xa2 = Z3 )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Xa2 @ Q4 ) ) )
& ( ( Xa2 != Z3 )
=> ( ( ( Z3 = Xb )
=> ( Y3
= ( relati591517084277583526ts_a_b @ ( relati2677767559083392098h2_a_b @ Xa2 @ Xb @ Q4 ) @ ( relational_subst_a_b @ ( relational_subst_a_b @ Q4 @ Z3 @ ( relati2677767559083392098h2_a_b @ Xa2 @ Xb @ Q4 ) ) @ Xa2 @ Xb ) ) ) )
& ( ( Z3 != Xb )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Z3 @ ( relational_subst_a_b @ Q4 @ Xa2 @ Xb ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% subst.elims
thf(fact_419_subst_Ocases,axiom,
! [X: produc8867654947514737559at_nat] :
( ! [T2: $o,X5: nat,Y5: nat] :
( X
!= ( produc6913411929637712585at_nat @ ( relational_Bool_a_b @ T2 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a,X5: nat,Y5: nat] :
( X
!= ( produc6913411929637712585at_nat @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ! [Z3: nat,T2: relational_term_a,X5: nat,Y5: nat] :
( X
!= ( produc6913411929637712585at_nat @ ( relational_Eq_a_b @ Z3 @ T2 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ! [Q4: relational_fmla_a_b,X5: nat,Y5: nat] :
( X
!= ( produc6913411929637712585at_nat @ ( relational_Neg_a_b @ Q4 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,X5: nat,Y5: nat] :
( X
!= ( produc6913411929637712585at_nat @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,X5: nat,Y5: nat] :
( X
!= ( produc6913411929637712585at_nat @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b,X5: nat,Y5: nat] :
( X
!= ( produc6913411929637712585at_nat @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) ) ) ) ) ) ) ) ).
% subst.cases
thf(fact_420_gen__empty__cp,axiom,
! [Z2: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ Z2 @ Q @ G )
=> ( ( G = bot_bo4495933725496725865la_a_b )
=> ( ( relational_cp_a_b @ Q )
= ( relational_Bool_a_b @ $false ) ) ) ) ).
% gen_empty_cp
thf(fact_421_list_Orel__eq,axiom,
( ( list_a3533670403825157575term_a
@ ^ [Y: relational_term_a,Z: relational_term_a] : ( Y = Z ) )
= ( ^ [Y: list_R6823256787227418703term_a,Z: list_R6823256787227418703term_a] : ( Y = Z ) ) ) ).
% list.rel_eq
thf(fact_422_list_Orel__refl,axiom,
! [Ra: relational_term_a > relational_term_a > $o,X: list_R6823256787227418703term_a] :
( ! [X5: relational_term_a] : ( Ra @ X5 @ X5 )
=> ( list_a3533670403825157575term_a @ Ra @ X @ X ) ) ).
% list.rel_refl
thf(fact_423_gen__Bool__False,axiom,
! [X: nat,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X @ ( relational_Bool_a_b @ $false ) @ G )
= ( G = bot_bo4495933725496725865la_a_b ) ) ).
% gen_Bool_False
thf(fact_424_list__all2__map2,axiom,
! [P: relational_term_a > relational_term_a > $o,As: list_R6823256787227418703term_a,F: relational_term_a > relational_term_a,Bs: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ As @ ( map_Re5736185711816362116term_a @ F @ Bs ) )
= ( list_a3533670403825157575term_a
@ ^ [X3: relational_term_a,Y6: relational_term_a] : ( P @ X3 @ ( F @ Y6 ) )
@ As
@ Bs ) ) ).
% list_all2_map2
thf(fact_425_list__all2__map1,axiom,
! [P: relational_term_a > relational_term_a > $o,F: relational_term_a > relational_term_a,As: list_R6823256787227418703term_a,Bs: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ ( map_Re5736185711816362116term_a @ F @ As ) @ Bs )
= ( list_a3533670403825157575term_a
@ ^ [X3: relational_term_a] : ( P @ ( F @ X3 ) )
@ As
@ Bs ) ) ).
% list_all2_map1
thf(fact_426_list_Orel__map_I1_J,axiom,
! [Sb: relational_term_a > relational_term_a > $o,I: relational_term_a > relational_term_a,X: list_R6823256787227418703term_a,Y3: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ Sb @ ( map_Re5736185711816362116term_a @ I @ X ) @ Y3 )
= ( list_a3533670403825157575term_a
@ ^ [X3: relational_term_a] : ( Sb @ ( I @ X3 ) )
@ X
@ Y3 ) ) ).
% list.rel_map(1)
thf(fact_427_list_Orel__map_I2_J,axiom,
! [Sa: relational_term_a > relational_term_a > $o,X: list_R6823256787227418703term_a,G2: relational_term_a > relational_term_a,Y3: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ Sa @ X @ ( map_Re5736185711816362116term_a @ G2 @ Y3 ) )
= ( list_a3533670403825157575term_a
@ ^ [X3: relational_term_a,Y6: relational_term_a] : ( Sa @ X3 @ ( G2 @ Y6 ) )
@ X
@ Y3 ) ) ).
% list.rel_map(2)
thf(fact_428_subst_Osimps_I2_J,axiom,
! [P2: b,Ts: list_R6823256787227418703term_a,X: nat,Y3: nat] :
( ( relational_subst_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) @ X @ Y3 )
= ( relational_Pred_b_a @ P2
@ ( map_Re5736185711816362116term_a
@ ^ [T4: relational_term_a] : ( relati7175845559408349773term_a @ T4 @ X @ Y3 )
@ Ts ) ) ) ).
% subst.simps(2)
thf(fact_429_fmla_Orel__map_I1_J,axiom,
! [S1b: a > a > $o,S2b: b > b > $o,I1: a > a,I2: b > b,X: relational_fmla_a_b,Y3: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ S1b @ S2b @ ( relati4520850492397955663_a_b_b @ I1 @ I2 @ X ) @ Y3 )
= ( relati8459511609072445516_a_b_b
@ ^ [X3: a] : ( S1b @ ( I1 @ X3 ) )
@ ^ [X3: b] : ( S2b @ ( I2 @ X3 ) )
@ X
@ Y3 ) ) ).
% fmla.rel_map(1)
thf(fact_430_fmla_Orel__map_I2_J,axiom,
! [S1a: a > a > $o,S2a: b > b > $o,X: relational_fmla_a_b,G1: a > a,G22: b > b,Y3: relational_fmla_a_b] :
( ( relati8459511609072445516_a_b_b @ S1a @ S2a @ X @ ( relati4520850492397955663_a_b_b @ G1 @ G22 @ Y3 ) )
= ( relati8459511609072445516_a_b_b
@ ^ [X3: a,Y6: a] : ( S1a @ X3 @ ( G1 @ Y6 ) )
@ ^ [X3: b,Y6: b] : ( S2a @ X3 @ ( G22 @ Y6 ) )
@ X
@ Y3 ) ) ).
% fmla.rel_map(2)
thf(fact_431_term_Orel__map_I1_J,axiom,
! [Sb: a > a > $o,I: a > a,X: relational_term_a,Y3: relational_term_a] :
( ( relati3163788165526728396rm_a_a @ Sb @ ( relati3585320759856631375rm_a_a @ I @ X ) @ Y3 )
= ( relati3163788165526728396rm_a_a
@ ^ [X3: a] : ( Sb @ ( I @ X3 ) )
@ X
@ Y3 ) ) ).
% term.rel_map(1)
thf(fact_432_term_Orel__map_I2_J,axiom,
! [Sa: a > a > $o,X: relational_term_a,G2: a > a,Y3: relational_term_a] :
( ( relati3163788165526728396rm_a_a @ Sa @ X @ ( relati3585320759856631375rm_a_a @ G2 @ Y3 ) )
= ( relati3163788165526728396rm_a_a
@ ^ [X3: a,Y6: a] : ( Sa @ X3 @ ( G2 @ Y6 ) )
@ X
@ Y3 ) ) ).
% term.rel_map(2)
thf(fact_433_fmla_Omap__ident,axiom,
! [T: relational_fmla_a_b] :
( ( relati4520850492397955663_a_b_b
@ ^ [X3: a] : X3
@ ^ [X3: b] : X3
@ T )
= T ) ).
% fmla.map_ident
thf(fact_434_fmla_Odisc__eq__case_I2_J,axiom,
( relati6551038146797045342ol_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu3: b,Uv: list_R6823256787227418703term_a] : $false
@ ^ [Uu3: $o] : $true
@ ^ [Uu3: nat,Uv: relational_term_a] : $false
@ ^ [Uu3: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: nat,Uv: relational_fmla_a_b] : $false ) ) ).
% fmla.disc_eq_case(2)
thf(fact_435_fmla_Odisc__eq__case_I6_J,axiom,
( relati5350680195807439568sj_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu3: b,Uv: list_R6823256787227418703term_a] : $false
@ ^ [Uu3: $o] : $false
@ ^ [Uu3: nat,Uv: relational_term_a] : $false
@ ^ [Uu3: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $true
@ ^ [Uu3: nat,Uv: relational_fmla_a_b] : $false ) ) ).
% fmla.disc_eq_case(6)
thf(fact_436_fmla_Odisc__eq__case_I5_J,axiom,
( relati8168519172193746908nj_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu3: b,Uv: list_R6823256787227418703term_a] : $false
@ ^ [Uu3: $o] : $false
@ ^ [Uu3: nat,Uv: relational_term_a] : $false
@ ^ [Uu3: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $true
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: nat,Uv: relational_fmla_a_b] : $false ) ) ).
% fmla.disc_eq_case(5)
thf(fact_437_fmla_Odisc__eq__case_I1_J,axiom,
( relati3644702733014758741ed_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu3: b,Uv: list_R6823256787227418703term_a] : $true
@ ^ [Uu3: $o] : $false
@ ^ [Uu3: nat,Uv: relational_term_a] : $false
@ ^ [Uu3: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: nat,Uv: relational_fmla_a_b] : $false ) ) ).
% fmla.disc_eq_case(1)
thf(fact_438_fmla_Odisc__eq__case_I4_J,axiom,
( relati4321004860440572638eg_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu3: b,Uv: list_R6823256787227418703term_a] : $false
@ ^ [Uu3: $o] : $false
@ ^ [Uu3: nat,Uv: relational_term_a] : $false
@ ^ [Uu3: relational_fmla_a_b] : $true
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: nat,Uv: relational_fmla_a_b] : $false ) ) ).
% fmla.disc_eq_case(4)
thf(fact_439_fmla_Odisc__eq__case_I3_J,axiom,
( relational_is_Eq_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu3: b,Uv: list_R6823256787227418703term_a] : $false
@ ^ [Uu3: $o] : $false
@ ^ [Uu3: nat,Uv: relational_term_a] : $true
@ ^ [Uu3: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: nat,Uv: relational_fmla_a_b] : $false ) ) ).
% fmla.disc_eq_case(3)
thf(fact_440_fmla_Ocase__distrib,axiom,
! [H: $o > $o,F1: b > list_R6823256787227418703term_a > $o,F2: $o > $o,F3: nat > relational_term_a > $o,F4: relational_fmla_a_b > $o,F5: relational_fmla_a_b > relational_fmla_a_b > $o,F6: relational_fmla_a_b > relational_fmla_a_b > $o,F7: nat > relational_fmla_a_b > $o,Fmla: relational_fmla_a_b] :
( ( H @ ( relati6637215556741570915_b_a_o @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ Fmla ) )
= ( relati6637215556741570915_b_a_o
@ ^ [X14: b,X22: list_R6823256787227418703term_a] : ( H @ ( F1 @ X14 @ X22 ) )
@ ^ [X3: $o] : ( H @ ( F2 @ X3 ) )
@ ^ [X14: nat,X22: relational_term_a] : ( H @ ( F3 @ X14 @ X22 ) )
@ ^ [X3: relational_fmla_a_b] : ( H @ ( F4 @ X3 ) )
@ ^ [X14: relational_fmla_a_b,X22: relational_fmla_a_b] : ( H @ ( F5 @ X14 @ X22 ) )
@ ^ [X14: relational_fmla_a_b,X22: relational_fmla_a_b] : ( H @ ( F6 @ X14 @ X22 ) )
@ ^ [X14: nat,X22: relational_fmla_a_b] : ( H @ ( F7 @ X14 @ X22 ) )
@ Fmla ) ) ).
% fmla.case_distrib
thf(fact_441_fmla_Odisc__eq__case_I7_J,axiom,
( relati5212983245281121968ts_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu3: b,Uv: list_R6823256787227418703term_a] : $false
@ ^ [Uu3: $o] : $false
@ ^ [Uu3: nat,Uv: relational_term_a] : $false
@ ^ [Uu3: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
@ ^ [Uu3: nat,Uv: relational_fmla_a_b] : $true ) ) ).
% fmla.disc_eq_case(7)
thf(fact_442_subst_Osimps_I7_J,axiom,
! [X: nat,Z2: nat,Q: relational_fmla_a_b,Y3: nat] :
( ( ( X = Z2 )
=> ( ( relational_subst_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati591517084277583526ts_a_b @ X @ Q ) ) )
& ( ( X != Z2 )
=> ( ( ( Z2 = Y3 )
=> ( ( relational_subst_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati591517084277583526ts_a_b @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) @ ( relational_subst_a_b @ ( relational_subst_a_b @ Q @ Z2 @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) ) @ X @ Y3 ) ) ) )
& ( ( Z2 != Y3 )
=> ( ( relational_subst_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati591517084277583526ts_a_b @ Z2 @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ) ) ) ) ).
% subst.simps(7)
thf(fact_443_subst__term_Osimps_I1_J,axiom,
! [Z2: nat,X: nat,Y3: nat] :
( ( relati7175845559408349773term_a @ ( relational_Var_a @ Z2 ) @ X @ Y3 )
= ( relational_Var_a @ ( if_nat @ ( X = Z2 ) @ Y3 @ Z2 ) ) ) ).
% subst_term.simps(1)
thf(fact_444_subst__term_Osimps_I2_J,axiom,
! [C2: a,X: nat,Y3: nat] :
( ( relati7175845559408349773term_a @ ( relational_Const_a @ C2 ) @ X @ Y3 )
= ( relational_Const_a @ C2 ) ) ).
% subst_term.simps(2)
thf(fact_445_subst__term__triv,axiom,
! [X: nat,T: relational_term_a,Y3: nat] :
( ~ ( member_nat @ X @ ( relati6004689760767320788_set_a @ T ) )
=> ( ( relati7175845559408349773term_a @ T @ X @ Y3 )
= T ) ) ).
% subst_term_triv
thf(fact_446_gen_Ointros_I1_J,axiom,
! [X: nat] : ( relational_gen_a_b @ X @ ( relational_Bool_a_b @ $false ) @ bot_bo4495933725496725865la_a_b ) ).
% gen.intros(1)
thf(fact_447_cp_Osimps_I2_J,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_cp_a_b @ ( relational_Neg_a_b @ Q ) )
= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q ) )
@ ( relational_Bool_a_b
@ ~ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q ) ) )
@ ( relational_Neg_a_b @ ( relational_cp_a_b @ Q ) ) ) ) ).
% cp.simps(2)
thf(fact_448_cp_Osimps_I4_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relational_cp_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) )
= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q1 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q1 ) ) @ ( relational_Bool_a_b @ $true ) @ ( relational_cp_a_b @ Q22 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q22 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q22 ) ) @ ( relational_Bool_a_b @ $true ) @ ( relational_cp_a_b @ Q1 ) ) @ ( relational_Disj_a_b @ ( relational_cp_a_b @ Q1 ) @ ( relational_cp_a_b @ Q22 ) ) ) ) ) ).
% cp.simps(4)
thf(fact_449_cp_Osimps_I3_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relational_cp_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) )
= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q1 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q1 ) ) @ ( relational_cp_a_b @ Q22 ) @ ( relational_Bool_a_b @ $false ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q22 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q22 ) ) @ ( relational_cp_a_b @ Q1 ) @ ( relational_Bool_a_b @ $false ) ) @ ( relational_Conj_a_b @ ( relational_cp_a_b @ Q1 ) @ ( relational_cp_a_b @ Q22 ) ) ) ) ) ).
% cp.simps(3)
thf(fact_450_fmla_Osimps_I128_J,axiom,
! [X2: $o] :
( ( relati8924981150291758614la_a_b @ ( relational_Bool_a_b @ X2 ) )
= bot_bot_set_b ) ).
% fmla.simps(128)
thf(fact_451_fmla_Osimps_I129_J,axiom,
! [X312: nat,X322: relational_term_a] :
( ( relati8924981150291758614la_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) )
= bot_bot_set_b ) ).
% fmla.simps(129)
thf(fact_452_gen__genempty,axiom,
! [Z2: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ Z2 @ Q @ G )
=> ( ( G = bot_bo4495933725496725865la_a_b )
=> ( relati5999705594545617851ty_a_b @ Q ) ) ) ).
% gen_genempty
thf(fact_453_subst_Osimps_I3_J,axiom,
! [Z2: nat,T: relational_term_a,X: nat,Y3: nat] :
( ( relational_subst_a_b @ ( relational_Eq_a_b @ Z2 @ T ) @ X @ Y3 )
= ( relational_Eq_a_b @ ( if_nat @ ( Z2 = X ) @ Y3 @ Z2 ) @ ( relati7175845559408349773term_a @ T @ X @ Y3 ) ) ) ).
% subst.simps(3)
thf(fact_454_subst__term_Oelims,axiom,
! [X: relational_term_a,Xa2: nat,Xb: nat,Y3: relational_term_a] :
( ( ( relati7175845559408349773term_a @ X @ Xa2 @ Xb )
= Y3 )
=> ( ! [Z3: nat] :
( ( X
= ( relational_Var_a @ Z3 ) )
=> ( Y3
!= ( relational_Var_a @ ( if_nat @ ( Xa2 = Z3 ) @ Xb @ Z3 ) ) ) )
=> ~ ! [C: a] :
( ( X
= ( relational_Const_a @ C ) )
=> ( Y3
!= ( relational_Const_a @ C ) ) ) ) ) ).
% subst_term.elims
thf(fact_455_list__all2__antisym,axiom,
! [P: relational_term_a > relational_term_a > $o,Q: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a,Ys: list_R6823256787227418703term_a] :
( ! [X5: relational_term_a,Y5: relational_term_a] :
( ( P @ X5 @ Y5 )
=> ( ( Q @ Y5 @ X5 )
=> ( X5 = Y5 ) ) )
=> ( ( list_a3533670403825157575term_a @ P @ Xs @ Ys )
=> ( ( list_a3533670403825157575term_a @ Q @ Ys @ Xs )
=> ( Xs = Ys ) ) ) ) ).
% list_all2_antisym
thf(fact_456_list__all2__trans,axiom,
! [P1: relational_term_a > relational_term_a > $o,P22: relational_term_a > relational_term_a > $o,P32: relational_term_a > relational_term_a > $o,As: list_R6823256787227418703term_a,Bs: list_R6823256787227418703term_a,Cs: list_R6823256787227418703term_a] :
( ! [A5: relational_term_a,B3: relational_term_a,C: relational_term_a] :
( ( P1 @ A5 @ B3 )
=> ( ( P22 @ B3 @ C )
=> ( P32 @ A5 @ C ) ) )
=> ( ( list_a3533670403825157575term_a @ P1 @ As @ Bs )
=> ( ( list_a3533670403825157575term_a @ P22 @ Bs @ Cs )
=> ( list_a3533670403825157575term_a @ P32 @ As @ Cs ) ) ) ) ).
% list_all2_trans
thf(fact_457_list__all2__refl,axiom,
! [P: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a] :
( ! [X5: relational_term_a] : ( P @ X5 @ X5 )
=> ( list_a3533670403825157575term_a @ P @ Xs @ Xs ) ) ).
% list_all2_refl
thf(fact_458_list__all2__mono,axiom,
! [P: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a,Ys: list_R6823256787227418703term_a,Q: relational_term_a > relational_term_a > $o] :
( ( list_a3533670403825157575term_a @ P @ Xs @ Ys )
=> ( ! [Xs2: relational_term_a,Ys2: relational_term_a] :
( ( P @ Xs2 @ Ys2 )
=> ( Q @ Xs2 @ Ys2 ) )
=> ( list_a3533670403825157575term_a @ Q @ Xs @ Ys ) ) ) ).
% list_all2_mono
thf(fact_459_list__all2__eq,axiom,
( ( ^ [Y: list_R6823256787227418703term_a,Z: list_R6823256787227418703term_a] : ( Y = Z ) )
= ( list_a3533670403825157575term_a
@ ^ [Y: relational_term_a,Z: relational_term_a] : ( Y = Z ) ) ) ).
% list_all2_eq
thf(fact_460_cp_Osimps_I1_J,axiom,
! [X: nat,T: relational_term_a] :
( ( relational_cp_a_b @ ( relational_Eq_a_b @ X @ T ) )
= ( relati582353067970734056la_a_b
@ ^ [A3: a] : ( relational_Eq_a_b @ X @ T )
@ ^ [Y6: nat] : ( if_Rel1279876242545935705la_a_b @ ( X = Y6 ) @ ( relational_Bool_a_b @ $true ) @ ( relational_Eq_a_b @ X @ ( relational_Var_a @ Y6 ) ) )
@ T ) ) ).
% cp.simps(1)
thf(fact_461_subst_Opelims,axiom,
! [X: relational_fmla_a_b,Xa2: nat,Xb: nat,Y3: relational_fmla_a_b] :
( ( ( relational_subst_a_b @ X @ Xa2 @ Xb )
= Y3 )
=> ( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ X @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) )
=> ( ! [T2: $o] :
( ( X
= ( relational_Bool_a_b @ T2 ) )
=> ( ( Y3
= ( relational_Bool_a_b @ T2 ) )
=> ~ ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Bool_a_b @ T2 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( ( Y3
= ( relational_Pred_b_a @ P3
@ ( map_Re5736185711816362116term_a
@ ^ [T4: relational_term_a] : ( relati7175845559408349773term_a @ T4 @ Xa2 @ Xb )
@ Ts2 ) ) )
=> ~ ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Z3: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ Z3 @ T2 ) )
=> ( ( Y3
= ( relational_Eq_a_b @ ( if_nat @ ( Z3 = Xa2 ) @ Xb @ Z3 ) @ ( relati7175845559408349773term_a @ T2 @ Xa2 @ Xb ) ) )
=> ~ ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Eq_a_b @ Z3 @ T2 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( ( Y3
= ( relational_Neg_a_b @ ( relational_subst_a_b @ Q4 @ Xa2 @ Xb ) ) )
=> ~ ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Neg_a_b @ Q4 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( relational_Conj_a_b @ ( relational_subst_a_b @ Q12 @ Xa2 @ Xb ) @ ( relational_subst_a_b @ Q23 @ Xa2 @ Xb ) ) )
=> ~ ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( relational_Disj_a_b @ ( relational_subst_a_b @ Q12 @ Xa2 @ Xb ) @ ( relational_subst_a_b @ Q23 @ Xa2 @ Xb ) ) )
=> ~ ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) )
=> ( ( ( ( Xa2 = Z3 )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Xa2 @ Q4 ) ) )
& ( ( Xa2 != Z3 )
=> ( ( ( Z3 = Xb )
=> ( Y3
= ( relati591517084277583526ts_a_b @ ( relati2677767559083392098h2_a_b @ Xa2 @ Xb @ Q4 ) @ ( relational_subst_a_b @ ( relational_subst_a_b @ Q4 @ Z3 @ ( relati2677767559083392098h2_a_b @ Xa2 @ Xb @ Q4 ) ) @ Xa2 @ Xb ) ) ) )
& ( ( Z3 != Xb )
=> ( Y3
= ( relati591517084277583526ts_a_b @ Z3 @ ( relational_subst_a_b @ Q4 @ Xa2 @ Xb ) ) ) ) ) ) )
=> ~ ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% subst.pelims
thf(fact_462_cp_Oelims,axiom,
! [X: relational_fmla_a_b,Y3: relational_fmla_a_b] :
( ( ( relational_cp_a_b @ X )
= Y3 )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( Y3
!= ( relati582353067970734056la_a_b
@ ^ [A3: a] : ( relational_Eq_a_b @ X5 @ T2 )
@ ^ [Y6: nat] : ( if_Rel1279876242545935705la_a_b @ ( X5 = Y6 ) @ ( relational_Bool_a_b @ $true ) @ ( relational_Eq_a_b @ X5 @ ( relational_Var_a @ Y6 ) ) )
@ T2 ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( Y3
!= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q4 ) )
@ ( relational_Bool_a_b
@ ~ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q4 ) ) )
@ ( relational_Neg_a_b @ ( relational_cp_a_b @ Q4 ) ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( relational_cp_a_b @ Q23 ) @ ( relational_Bool_a_b @ $false ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( relational_cp_a_b @ Q12 ) @ ( relational_Bool_a_b @ $false ) ) @ ( relational_Conj_a_b @ ( relational_cp_a_b @ Q12 ) @ ( relational_cp_a_b @ Q23 ) ) ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( relational_Bool_a_b @ $true ) @ ( relational_cp_a_b @ Q23 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( relational_Bool_a_b @ $true ) @ ( relational_cp_a_b @ Q12 ) ) @ ( relational_Disj_a_b @ ( relational_cp_a_b @ Q12 ) @ ( relational_cp_a_b @ Q23 ) ) ) ) ) )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( Y3
!= ( relati3989891337220013914ts_a_b @ X5 @ ( relational_cp_a_b @ Q4 ) ) ) )
=> ( ! [V2: b,Va2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ V2 @ Va2 ) )
=> ( Y3
!= ( relational_Pred_b_a @ V2 @ Va2 ) ) )
=> ~ ! [V2: $o] :
( ( X
= ( relational_Bool_a_b @ V2 ) )
=> ( Y3
!= ( relational_Bool_a_b @ V2 ) ) ) ) ) ) ) ) ) ) ).
% cp.elims
thf(fact_463_cp_Opelims,axiom,
! [X: relational_fmla_a_b,Y3: relational_fmla_a_b] :
( ( ( relational_cp_a_b @ X )
= Y3 )
=> ( ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ X )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( ( Y3
= ( relati582353067970734056la_a_b
@ ^ [A3: a] : ( relational_Eq_a_b @ X5 @ T2 )
@ ^ [Y6: nat] : ( if_Rel1279876242545935705la_a_b @ ( X5 = Y6 ) @ ( relational_Bool_a_b @ $true ) @ ( relational_Eq_a_b @ X5 @ ( relational_Var_a @ Y6 ) ) )
@ T2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ ( relational_Eq_a_b @ X5 @ T2 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( ( Y3
= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q4 ) )
@ ( relational_Bool_a_b
@ ~ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q4 ) ) )
@ ( relational_Neg_a_b @ ( relational_cp_a_b @ Q4 ) ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ ( relational_Neg_a_b @ Q4 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( relational_cp_a_b @ Q23 ) @ ( relational_Bool_a_b @ $false ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( relational_cp_a_b @ Q12 ) @ ( relational_Bool_a_b @ $false ) ) @ ( relational_Conj_a_b @ ( relational_cp_a_b @ Q12 ) @ ( relational_cp_a_b @ Q23 ) ) ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q12 ) ) @ ( relational_Bool_a_b @ $true ) @ ( relational_cp_a_b @ Q23 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati2638701775882563405ol_a_b @ ( relational_cp_a_b @ Q23 ) ) @ ( relational_Bool_a_b @ $true ) @ ( relational_cp_a_b @ Q12 ) ) @ ( relational_Disj_a_b @ ( relational_cp_a_b @ Q12 ) @ ( relational_cp_a_b @ Q23 ) ) ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) ) ) )
=> ( ! [X5: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ X5 @ Q4 ) )
=> ( ( Y3
= ( relati3989891337220013914ts_a_b @ X5 @ ( relational_cp_a_b @ Q4 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ ( relati591517084277583526ts_a_b @ X5 @ Q4 ) ) ) )
=> ( ! [V2: b,Va2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ V2 @ Va2 ) )
=> ( ( Y3
= ( relational_Pred_b_a @ V2 @ Va2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ ( relational_Pred_b_a @ V2 @ Va2 ) ) ) )
=> ~ ! [V2: $o] :
( ( X
= ( relational_Bool_a_b @ V2 ) )
=> ( ( Y3
= ( relational_Bool_a_b @ V2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5452380258257131376el_a_b @ ( relational_Bool_a_b @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% cp.pelims
thf(fact_464_subst_Opinduct,axiom,
! [A0: relational_fmla_a_b,A13: nat,A23: nat,P: relational_fmla_a_b > nat > nat > $o] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ A0 @ ( product_Pair_nat_nat @ A13 @ A23 ) ) )
=> ( ! [T2: $o,X5: nat,Y5: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Bool_a_b @ T2 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( P @ ( relational_Bool_a_b @ T2 ) @ X5 @ Y5 ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a,X5: nat,Y5: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( P @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ X5 @ Y5 ) )
=> ( ! [Z3: nat,T2: relational_term_a,X5: nat,Y5: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Eq_a_b @ Z3 @ T2 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( P @ ( relational_Eq_a_b @ Z3 @ T2 ) @ X5 @ Y5 ) )
=> ( ! [Q4: relational_fmla_a_b,X5: nat,Y5: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Neg_a_b @ Q4 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ( P @ Q4 @ X5 @ Y5 )
=> ( P @ ( relational_Neg_a_b @ Q4 ) @ X5 @ Y5 ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,X5: nat,Y5: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ( P @ Q12 @ X5 @ Y5 )
=> ( ( P @ Q23 @ X5 @ Y5 )
=> ( P @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ X5 @ Y5 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,X5: nat,Y5: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ( P @ Q12 @ X5 @ Y5 )
=> ( ( P @ Q23 @ X5 @ Y5 )
=> ( P @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ X5 @ Y5 ) ) ) )
=> ( ! [Z3: nat,Q4: relational_fmla_a_b,X5: nat,Y5: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ( ! [Xa3: nat] :
( ( X5 != Z3 )
=> ( ( Z3 = Y5 )
=> ( ( Xa3
= ( relati2677767559083392098h2_a_b @ X5 @ Y5 @ Q4 ) )
=> ( P @ Q4 @ Z3 @ Xa3 ) ) ) )
=> ( ! [Xa3: nat] :
( ( X5 != Z3 )
=> ( ( Z3 = Y5 )
=> ( ( Xa3
= ( relati2677767559083392098h2_a_b @ X5 @ Y5 @ Q4 ) )
=> ( P @ ( relational_subst_a_b @ Q4 @ Z3 @ Xa3 ) @ X5 @ Y5 ) ) ) )
=> ( ( ( X5 != Z3 )
=> ( ( Z3 != Y5 )
=> ( P @ Q4 @ X5 @ Y5 ) ) )
=> ( P @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ X5 @ Y5 ) ) ) ) )
=> ( P @ A0 @ A13 @ A23 ) ) ) ) ) ) ) ) ) ).
% subst.pinduct
thf(fact_465_cp__exists,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relational_cp_a_b @ ( relati3989891337220013914ts_a_b @ X @ Q ) )
= ( relati3989891337220013914ts_a_b @ X @ ( relational_cp_a_b @ Q ) ) ) ).
% cp_exists
thf(fact_466_nocp__exists,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relational_nocp_a_b @ ( relati3989891337220013914ts_a_b @ X @ Q ) )
= ( relational_nocp_a_b @ Q ) ) ).
% nocp_exists
thf(fact_467_is__Bool__exists,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relati6551038146797045342ol_a_b @ ( relati3989891337220013914ts_a_b @ X @ Q ) )
= ( relati6551038146797045342ol_a_b @ Q ) ) ).
% is_Bool_exists
thf(fact_468_Relational__Calculus_Oterm_Ocase__distrib,axiom,
! [H: relational_fmla_a_b > relational_fmla_a_b,F1: a > relational_fmla_a_b,F2: nat > relational_fmla_a_b,Term: relational_term_a] :
( ( H @ ( relati582353067970734056la_a_b @ F1 @ F2 @ Term ) )
= ( relati582353067970734056la_a_b
@ ^ [X3: a] : ( H @ ( F1 @ X3 ) )
@ ^ [X3: nat] : ( H @ ( F2 @ X3 ) )
@ Term ) ) ).
% Relational_Calculus.term.case_distrib
thf(fact_469_exists,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_qp_a_b @ Q )
=> ( relational_qp_a_b @ ( relati3989891337220013914ts_a_b @ X @ Q ) ) ) ).
% exists
thf(fact_470_fv_Osimps_I2_J,axiom,
! [B: $o] :
( ( relational_fv_a_b @ ( relational_Bool_a_b @ B ) )
= bot_bot_set_nat ) ).
% fv.simps(2)
thf(fact_471_subst_Opsimps_I4_J,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Neg_a_b @ Q ) @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( relational_subst_a_b @ ( relational_Neg_a_b @ Q ) @ X @ Y3 )
= ( relational_Neg_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ) ).
% subst.psimps(4)
thf(fact_472_subst_Opsimps_I6_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( relational_subst_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ X @ Y3 )
= ( relational_Disj_a_b @ ( relational_subst_a_b @ Q1 @ X @ Y3 ) @ ( relational_subst_a_b @ Q22 @ X @ Y3 ) ) ) ) ).
% subst.psimps(6)
thf(fact_473_subst_Opsimps_I5_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( relational_subst_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ X @ Y3 )
= ( relational_Conj_a_b @ ( relational_subst_a_b @ Q1 @ X @ Y3 ) @ ( relational_subst_a_b @ Q22 @ X @ Y3 ) ) ) ) ).
% subst.psimps(5)
thf(fact_474_subst_Opsimps_I1_J,axiom,
! [T: $o,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Bool_a_b @ T ) @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( relational_subst_a_b @ ( relational_Bool_a_b @ T ) @ X @ Y3 )
= ( relational_Bool_a_b @ T ) ) ) ).
% subst.psimps(1)
thf(fact_475_exists__Exists,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( ( relati3989891337220013914ts_a_b @ X @ Q )
= ( relati591517084277583526ts_a_b @ X @ Q ) ) ) ).
% exists_Exists
thf(fact_476_exists__def,axiom,
( relati3989891337220013914ts_a_b
= ( ^ [X3: nat,Q3: relational_fmla_a_b] : ( if_Rel1279876242545935705la_a_b @ ( member_nat @ X3 @ ( relational_fv_a_b @ Q3 ) ) @ ( relati591517084277583526ts_a_b @ X3 @ Q3 ) @ Q3 ) ) ) ).
% exists_def
thf(fact_477_cp_Osimps_I5_J,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relational_cp_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) )
= ( relati3989891337220013914ts_a_b @ X @ ( relational_cp_a_b @ Q ) ) ) ).
% cp.simps(5)
thf(fact_478_exists__cp__subst,axiom,
! [X: nat,Y3: nat,Q: relational_fmla_a_b] :
( ( X != Y3 )
=> ( ( relati3989891337220013914ts_a_b @ X @ ( relational_cp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) )
= ( relational_cp_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ) ).
% exists_cp_subst
thf(fact_479_fv__term__set_Osimps_I2_J,axiom,
! [V: a] :
( ( relati6004689760767320788_set_a @ ( relational_Const_a @ V ) )
= bot_bot_set_nat ) ).
% fv_term_set.simps(2)
thf(fact_480_Relational__Calculus_Oterm_Osimps_I6_J,axiom,
! [F1: a > relational_fmla_a_b,F2: nat > relational_fmla_a_b,X2: nat] :
( ( relati582353067970734056la_a_b @ F1 @ F2 @ ( relational_Var_a @ X2 ) )
= ( F2 @ X2 ) ) ).
% Relational_Calculus.term.simps(6)
thf(fact_481_exists__cp__erase,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relati3989891337220013914ts_a_b @ X @ ( relational_cp_a_b @ ( relational_erase_a_b @ Q @ X ) ) )
= ( relational_cp_a_b @ ( relational_erase_a_b @ Q @ X ) ) ) ).
% exists_cp_erase
thf(fact_482_Relational__Calculus_Oterm_Osimps_I5_J,axiom,
! [F1: a > relational_fmla_a_b,F2: nat > relational_fmla_a_b,X13: a] :
( ( relati582353067970734056la_a_b @ F1 @ F2 @ ( relational_Const_a @ X13 ) )
= ( F1 @ X13 ) ) ).
% Relational_Calculus.term.simps(5)
thf(fact_483_qp_Osimps,axiom,
( relational_qp_a_b
= ( ^ [A3: relational_fmla_a_b] :
( ? [Q3: relational_fmla_a_b] :
( ( A3 = Q3 )
& ( relational_ap_a_b @ Q3 ) )
| ? [Q3: relational_fmla_a_b,X3: nat] :
( ( A3
= ( relati3989891337220013914ts_a_b @ X3 @ Q3 ) )
& ( relational_qp_a_b @ Q3 ) ) ) ) ) ).
% qp.simps
thf(fact_484_qp_Ocases,axiom,
! [A: relational_fmla_a_b] :
( ( relational_qp_a_b @ A )
=> ( ~ ( relational_ap_a_b @ A )
=> ~ ! [Q4: relational_fmla_a_b] :
( ? [X5: nat] :
( A
= ( relati3989891337220013914ts_a_b @ X5 @ Q4 ) )
=> ~ ( relational_qp_a_b @ Q4 ) ) ) ) ).
% qp.cases
thf(fact_485_subst_Opsimps_I3_J,axiom,
! [Z2: nat,T: relational_term_a,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Eq_a_b @ Z2 @ T ) @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( relational_subst_a_b @ ( relational_Eq_a_b @ Z2 @ T ) @ X @ Y3 )
= ( relational_Eq_a_b @ ( if_nat @ ( Z2 = X ) @ Y3 @ Z2 ) @ ( relati7175845559408349773term_a @ T @ X @ Y3 ) ) ) ) ).
% subst.psimps(3)
thf(fact_486_subst_Opsimps_I7_J,axiom,
! [Z2: nat,Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( ( X = Z2 )
=> ( ( relational_subst_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati591517084277583526ts_a_b @ X @ Q ) ) )
& ( ( X != Z2 )
=> ( ( ( Z2 = Y3 )
=> ( ( relational_subst_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati591517084277583526ts_a_b @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) @ ( relational_subst_a_b @ ( relational_subst_a_b @ Q @ Z2 @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) ) @ X @ Y3 ) ) ) )
& ( ( Z2 != Y3 )
=> ( ( relational_subst_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati591517084277583526ts_a_b @ Z2 @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ) ) ) ) ) ).
% subst.psimps(7)
thf(fact_487_subst_Opsimps_I2_J,axiom,
! [P2: b,Ts: list_R6823256787227418703term_a,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ ( relational_Pred_b_a @ P2 @ Ts ) @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( relational_subst_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) @ X @ Y3 )
= ( relational_Pred_b_a @ P2
@ ( map_Re5736185711816362116term_a
@ ^ [T4: relational_term_a] : ( relati7175845559408349773term_a @ T4 @ X @ Y3 )
@ Ts ) ) ) ) ).
% subst.psimps(2)
thf(fact_488_subst__exists,axiom,
! [Z2: nat,Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( ( member_nat @ Z2 @ ( relational_fv_a_b @ Q ) )
=> ( ( ( X = Z2 )
=> ( ( relational_subst_a_b @ ( relati3989891337220013914ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati3989891337220013914ts_a_b @ X @ Q ) ) )
& ( ( X != Z2 )
=> ( ( ( Z2 = Y3 )
=> ( ( relational_subst_a_b @ ( relati3989891337220013914ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati3989891337220013914ts_a_b @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) @ ( relational_subst_a_b @ ( relational_subst_a_b @ Q @ Z2 @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) ) @ X @ Y3 ) ) ) )
& ( ( Z2 != Y3 )
=> ( ( relational_subst_a_b @ ( relati3989891337220013914ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relati3989891337220013914ts_a_b @ Z2 @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ) ) ) ) )
& ( ~ ( member_nat @ Z2 @ ( relational_fv_a_b @ Q ) )
=> ( ( relational_subst_a_b @ ( relati3989891337220013914ts_a_b @ Z2 @ Q ) @ X @ Y3 )
= ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ) ).
% subst_exists
thf(fact_489_size__subst__p,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( accp_P2470304046166516174at_nat @ relati8369873211719781654el_a_b @ ( produc6913411929637712585at_nat @ Q @ ( product_Pair_nat_nat @ X @ Y3 ) ) )
=> ( ( size_s453432777765377587la_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
= ( size_s453432777765377587la_a_b @ Q ) ) ) ).
% size_subst_p
thf(fact_490_gen_Ointros_I8_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b @ Y3 @ Q @ G )
=> ( relational_gen_a_b @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ X @ ( relational_Var_a @ Y3 ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Q3 @ Y3 @ X ) )
@ G ) ) ) ).
% gen.intros(8)
thf(fact_491_gen_Ointros_I9_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b @ Y3 @ Q @ G )
=> ( relational_gen_a_b @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ Y3 @ ( relational_Var_a @ X ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Q3 @ Y3 @ X ) )
@ G ) ) ) ).
% gen.intros(9)
thf(fact_492_gen__Pred,axiom,
! [Z2: nat,P2: b,Ts: list_R6823256787227418703term_a,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ Z2 @ ( relational_Pred_b_a @ P2 @ Ts ) @ G )
= ( ( member_nat @ Z2 @ ( relati4569515538964159125_set_a @ Ts ) )
& ( G
= ( insert7010464514620295119la_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) @ bot_bo4495933725496725865la_a_b ) ) ) ) ).
% gen_Pred
thf(fact_493_size__subst,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat] :
( ( size_s453432777765377587la_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
= ( size_s453432777765377587la_a_b @ Q ) ) ).
% size_subst
thf(fact_494_gen__Eq,axiom,
! [Z2: nat,A: nat,T: relational_term_a,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ Z2 @ ( relational_Eq_a_b @ A @ T ) @ G )
= ( ( Z2 = A )
& ? [C3: a] :
( ( T
= ( relational_Const_a @ C3 ) )
& ( G
= ( insert7010464514620295119la_a_b @ ( relational_Eq_a_b @ A @ T ) @ bot_bo4495933725496725865la_a_b ) ) ) ) ) ).
% gen_Eq
thf(fact_495_fmla_Oset__map_I2_J,axiom,
! [F1: a > a,F2: b > b,V: relational_fmla_a_b] :
( ( relati8924981150291758614la_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ V ) )
= ( image_b_b @ F2 @ ( relati8924981150291758614la_a_b @ V ) ) ) ).
% fmla.set_map(2)
thf(fact_496_sub_Osimps_I4_J,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_sub_a_b @ ( relational_Neg_a_b @ Q ) )
= ( insert7010464514620295119la_a_b @ ( relational_Neg_a_b @ Q ) @ ( relational_sub_a_b @ Q ) ) ) ).
% sub.simps(4)
thf(fact_497_sub_Osimps_I7_J,axiom,
! [Z2: nat,Q: relational_fmla_a_b] :
( ( relational_sub_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) )
= ( insert7010464514620295119la_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Q ) @ ( relational_sub_a_b @ Q ) ) ) ).
% sub.simps(7)
thf(fact_498_fmla_Osimps_I127_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
( ( relati8924981150291758614la_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) )
= ( insert_b @ X11 @ bot_bot_set_b ) ) ).
% fmla.simps(127)
thf(fact_499_gen_Ointros_I10_J,axiom,
! [X: nat,Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( X != Y3 )
=> ( ( relational_gen_a_b @ X @ Q @ G )
=> ( relational_gen_a_b @ X @ ( relati591517084277583526ts_a_b @ Y3 @ Q ) @ ( image_6790371041703824709la_a_b @ ( relati3989891337220013914ts_a_b @ Y3 ) @ G ) ) ) ) ).
% gen.intros(10)
thf(fact_500_sub_Osimps_I1_J,axiom,
! [T: $o] :
( ( relational_sub_a_b @ ( relational_Bool_a_b @ T ) )
= ( insert7010464514620295119la_a_b @ ( relational_Bool_a_b @ T ) @ bot_bo4495933725496725865la_a_b ) ) ).
% sub.simps(1)
thf(fact_501_sub_Osimps_I3_J,axiom,
! [X: nat,T: relational_term_a] :
( ( relational_sub_a_b @ ( relational_Eq_a_b @ X @ T ) )
= ( insert7010464514620295119la_a_b @ ( relational_Eq_a_b @ X @ T ) @ bot_bo4495933725496725865la_a_b ) ) ).
% sub.simps(3)
thf(fact_502_sub_Osimps_I2_J,axiom,
! [P2: b,Ts: list_R6823256787227418703term_a] :
( ( relational_sub_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) )
= ( insert7010464514620295119la_a_b @ ( relational_Pred_b_a @ P2 @ Ts ) @ bot_bo4495933725496725865la_a_b ) ) ).
% sub.simps(2)
thf(fact_503_qp__gen,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_qp_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( relational_gen_a_b @ X @ Q @ ( insert7010464514620295119la_a_b @ Q @ bot_bo4495933725496725865la_a_b ) ) ) ) ).
% qp_gen
thf(fact_504_gen_Ointros_I2_J,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_ap_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( relational_gen_a_b @ X @ Q @ ( insert7010464514620295119la_a_b @ Q @ bot_bo4495933725496725865la_a_b ) ) ) ) ).
% gen.intros(2)
thf(fact_505_gen__nocp__intros_I2_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b @ Y3 @ Q @ G )
=> ( relational_gen_a_b @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ Y3 @ ( relational_Var_a @ X ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_subst_a_b @ Q3 @ Y3 @ X )
@ G ) ) ) ).
% gen_nocp_intros(2)
thf(fact_506_gen__nocp__intros_I1_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b @ Y3 @ Q @ G )
=> ( relational_gen_a_b @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ X @ ( relational_Var_a @ Y3 ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_subst_a_b @ Q3 @ Y3 @ X )
@ G ) ) ) ).
% gen_nocp_intros(1)
thf(fact_507_gen_Ocases,axiom,
! [A13: nat,A23: relational_fmla_a_b,A33: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ A13 @ A23 @ A33 )
=> ( ( ( A23
= ( relational_Bool_a_b @ $false ) )
=> ( A33 != bot_bo4495933725496725865la_a_b ) )
=> ( ( ( A33
= ( insert7010464514620295119la_a_b @ A23 @ bot_bo4495933725496725865la_a_b ) )
=> ( ( relational_ap_a_b @ A23 )
=> ~ ( member_nat @ A13 @ ( relational_fv_a_b @ A23 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( A23
= ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q4 ) ) )
=> ~ ( relational_gen_a_b @ A13 @ Q4 @ A33 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) ) )
=> ~ ( relational_gen_a_b @ A13 @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ A33 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) ) )
=> ~ ( relational_gen_a_b @ A13 @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ A33 ) )
=> ( ! [Q12: relational_fmla_a_b,G12: set_Re381260168593705685la_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ! [G23: set_Re381260168593705685la_a_b] :
( ( A33
= ( sup_su5130108678486352897la_a_b @ G12 @ G23 ) )
=> ( ( relational_gen_a_b @ A13 @ Q12 @ G12 )
=> ~ ( relational_gen_a_b @ A13 @ Q23 @ G23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( A33 = G3 )
=> ~ ( ( relational_gen_a_b @ A13 @ Q12 @ G3 )
| ( relational_gen_a_b @ A13 @ Q23 @ G3 ) ) ) )
=> ( ! [Y5: nat,Q4: relational_fmla_a_b] :
( ( A23
= ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ A13 @ ( relational_Var_a @ Y5 ) ) ) )
=> ! [G3: set_Re381260168593705685la_a_b] :
( ( A33
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Qa @ Y5 @ A13 ) )
@ G3 ) )
=> ~ ( relational_gen_a_b @ Y5 @ Q4 @ G3 ) ) )
=> ( ! [Y5: nat,Q4: relational_fmla_a_b] :
( ( A23
= ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ Y5 @ ( relational_Var_a @ A13 ) ) ) )
=> ! [G3: set_Re381260168593705685la_a_b] :
( ( A33
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Qa @ Y5 @ A13 ) )
@ G3 ) )
=> ~ ( relational_gen_a_b @ Y5 @ Q4 @ G3 ) ) )
=> ~ ! [Y5: nat,Q4: relational_fmla_a_b] :
( ( A23
= ( relati591517084277583526ts_a_b @ Y5 @ Q4 ) )
=> ! [G3: set_Re381260168593705685la_a_b] :
( ( A33
= ( image_6790371041703824709la_a_b @ ( relati3989891337220013914ts_a_b @ Y5 ) @ G3 ) )
=> ( ( A13 != Y5 )
=> ~ ( relational_gen_a_b @ A13 @ Q4 @ G3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% gen.cases
thf(fact_508_gen_Osimps,axiom,
( relational_gen_a_b
= ( ^ [A14: nat,A24: relational_fmla_a_b,A34: set_Re381260168593705685la_a_b] :
( ( ( A24
= ( relational_Bool_a_b @ $false ) )
& ( A34 = bot_bo4495933725496725865la_a_b ) )
| ( ( A34
= ( insert7010464514620295119la_a_b @ A24 @ bot_bo4495933725496725865la_a_b ) )
& ( relational_ap_a_b @ A24 )
& ( member_nat @ A14 @ ( relational_fv_a_b @ A24 ) ) )
| ? [Q3: relational_fmla_a_b] :
( ( A24
= ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q3 ) ) )
& ( relational_gen_a_b @ A14 @ Q3 @ A34 ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q13 @ Q24 ) ) )
& ( relational_gen_a_b @ A14 @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q13 ) @ ( relational_Neg_a_b @ Q24 ) ) @ A34 ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q13 @ Q24 ) ) )
& ( relational_gen_a_b @ A14 @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q13 ) @ ( relational_Neg_a_b @ Q24 ) ) @ A34 ) )
| ? [Q13: relational_fmla_a_b,G13: set_Re381260168593705685la_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Disj_a_b @ Q13 @ Q24 ) )
& ? [G24: set_Re381260168593705685la_a_b] :
( ( A34
= ( sup_su5130108678486352897la_a_b @ G13 @ G24 ) )
& ( relational_gen_a_b @ A14 @ Q13 @ G13 )
& ( relational_gen_a_b @ A14 @ Q24 @ G24 ) ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Conj_a_b @ Q13 @ Q24 ) )
& ( ( relational_gen_a_b @ A14 @ Q13 @ A34 )
| ( relational_gen_a_b @ A14 @ Q24 @ A34 ) ) )
| ? [Y6: nat,Q3: relational_fmla_a_b] :
( ( A24
= ( relational_Conj_a_b @ Q3 @ ( relational_Eq_a_b @ A14 @ ( relational_Var_a @ Y6 ) ) ) )
& ? [G4: set_Re381260168593705685la_a_b] :
( ( A34
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Qa @ Y6 @ A14 ) )
@ G4 ) )
& ( relational_gen_a_b @ Y6 @ Q3 @ G4 ) ) )
| ? [Y6: nat,Q3: relational_fmla_a_b] :
( ( A24
= ( relational_Conj_a_b @ Q3 @ ( relational_Eq_a_b @ Y6 @ ( relational_Var_a @ A14 ) ) ) )
& ? [G4: set_Re381260168593705685la_a_b] :
( ( A34
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Qa @ Y6 @ A14 ) )
@ G4 ) )
& ( relational_gen_a_b @ Y6 @ Q3 @ G4 ) ) )
| ? [Y6: nat,Q3: relational_fmla_a_b] :
( ( A24
= ( relati591517084277583526ts_a_b @ Y6 @ Q3 ) )
& ? [G4: set_Re381260168593705685la_a_b] :
( ( A34
= ( image_6790371041703824709la_a_b @ ( relati3989891337220013914ts_a_b @ Y6 ) @ G4 ) )
& ( A14 != Y6 )
& ( relational_gen_a_b @ A14 @ Q3 @ G4 ) ) ) ) ) ) ).
% gen.simps
thf(fact_509_gen__induct,axiom,
! [X13: nat,X2: relational_fmla_a_b,X33: set_Re381260168593705685la_a_b,P: nat > relational_fmla_a_b > set_Re381260168593705685la_a_b > $o] :
( ( relational_gen_a_b @ X13 @ X2 @ X33 )
=> ( ! [X5: nat] : ( P @ X5 @ ( relational_Bool_a_b @ $false ) @ bot_bo4495933725496725865la_a_b )
=> ( ! [Q4: relational_fmla_a_b] :
( ( relational_ap_a_b @ Q4 )
=> ! [X5: nat] :
( ( member_nat @ X5 @ ( relational_fv_a_b @ Q4 ) )
=> ( P @ X5 @ Q4 @ ( insert7010464514620295119la_a_b @ Q4 @ bot_bo4495933725496725865la_a_b ) ) ) )
=> ( ! [X5: nat,Q4: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X5 @ Q4 @ G3 )
=> ( ( P @ X5 @ Q4 @ G3 )
=> ( P @ X5 @ ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q4 ) ) @ G3 ) ) )
=> ( ! [X5: nat,Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X5 @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ G3 )
=> ( ( P @ X5 @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ G3 )
=> ( P @ X5 @ ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) ) @ G3 ) ) )
=> ( ! [X5: nat,Q12: relational_fmla_a_b,Q23: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X5 @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ G3 )
=> ( ( P @ X5 @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ G3 )
=> ( P @ X5 @ ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) ) @ G3 ) ) )
=> ( ! [X5: nat,Q12: relational_fmla_a_b,G12: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X5 @ Q12 @ G12 )
=> ( ( P @ X5 @ Q12 @ G12 )
=> ! [Q23: relational_fmla_a_b,G23: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X5 @ Q23 @ G23 )
=> ( ( P @ X5 @ Q23 @ G23 )
=> ( P @ X5 @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ ( sup_su5130108678486352897la_a_b @ G12 @ G23 ) ) ) ) ) )
=> ( ! [X5: nat,Q12: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b,Q23: relational_fmla_a_b] :
( ( ( ( relational_gen_a_b @ X5 @ Q12 @ G3 )
& ( P @ X5 @ Q12 @ G3 ) )
| ( ( relational_gen_a_b @ X5 @ Q23 @ G3 )
& ( P @ X5 @ Q23 @ G3 ) ) )
=> ( P @ X5 @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ G3 ) )
=> ( ! [Y5: nat,Q4: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ Y5 @ Q4 @ G3 )
=> ( ( P @ Y5 @ Q4 @ G3 )
=> ! [X5: nat] :
( P @ X5 @ ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ X5 @ ( relational_Var_a @ Y5 ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_subst_a_b @ Qa @ Y5 @ X5 )
@ G3 ) ) ) )
=> ( ! [Y5: nat,Q4: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ Y5 @ Q4 @ G3 )
=> ( ( P @ Y5 @ Q4 @ G3 )
=> ! [X5: nat] :
( P @ X5 @ ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ Y5 @ ( relational_Var_a @ X5 ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_subst_a_b @ Qa @ Y5 @ X5 )
@ G3 ) ) ) )
=> ( ! [X5: nat,Y5: nat] :
( ( X5 != Y5 )
=> ! [Q4: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X5 @ Q4 @ G3 )
=> ( ( P @ X5 @ Q4 @ G3 )
=> ( P @ X5 @ ( relati591517084277583526ts_a_b @ Y5 @ Q4 ) @ ( image_6790371041703824709la_a_b @ ( relati3989891337220013914ts_a_b @ Y5 ) @ G3 ) ) ) ) )
=> ( P @ X13 @ X2 @ X33 ) ) ) ) ) ) ) ) ) ) ) ) ).
% gen_induct
thf(fact_510_gen_Ointros_I6_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,G14: set_Re381260168593705685la_a_b,Q22: relational_fmla_a_b,G25: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X @ Q1 @ G14 )
=> ( ( relational_gen_a_b @ X @ Q22 @ G25 )
=> ( relational_gen_a_b @ X @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ ( sup_su5130108678486352897la_a_b @ G14 @ G25 ) ) ) ) ).
% gen.intros(6)
thf(fact_511_fmla_Osimps_I132_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relati8924981150291758614la_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) )
= ( sup_sup_set_b @ ( relati8924981150291758614la_a_b @ X61 ) @ ( relati8924981150291758614la_a_b @ X62 ) ) ) ).
% fmla.simps(132)
thf(fact_512_fmla_Osimps_I131_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relati8924981150291758614la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
= ( sup_sup_set_b @ ( relati8924981150291758614la_a_b @ X51 ) @ ( relati8924981150291758614la_a_b @ X52 ) ) ) ).
% fmla.simps(131)
thf(fact_513_sub_Osimps_I6_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relational_sub_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) )
= ( insert7010464514620295119la_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ ( sup_su5130108678486352897la_a_b @ ( relational_sub_a_b @ Q1 ) @ ( relational_sub_a_b @ Q22 ) ) ) ) ).
% sub.simps(6)
thf(fact_514_sub_Osimps_I5_J,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relational_sub_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) )
= ( insert7010464514620295119la_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ ( sup_su5130108678486352897la_a_b @ ( relational_sub_a_b @ Q1 ) @ ( relational_sub_a_b @ Q22 ) ) ) ) ).
% sub.simps(5)
thf(fact_515_fv__term__set_Osimps_I1_J,axiom,
! [N: nat] :
( ( relati6004689760767320788_set_a @ ( relational_Var_a @ N ) )
= ( insert_nat @ N @ bot_bot_set_nat ) ) ).
% fv_term_set.simps(1)
thf(fact_516_fv__term__set_Oelims,axiom,
! [X: relational_term_a,Y3: set_nat] :
( ( ( relati6004689760767320788_set_a @ X )
= Y3 )
=> ( ! [N2: nat] :
( ( X
= ( relational_Var_a @ N2 ) )
=> ( Y3
!= ( insert_nat @ N2 @ bot_bot_set_nat ) ) )
=> ~ ( ? [V2: a] :
( X
= ( relational_Const_a @ V2 ) )
=> ( Y3 != bot_bot_set_nat ) ) ) ) ).
% fv_term_set.elims
thf(fact_517_sub_Oelims,axiom,
! [X: relational_fmla_a_b,Y3: set_Re381260168593705685la_a_b] :
( ( ( relational_sub_a_b @ X )
= Y3 )
=> ( ! [T2: $o] :
( ( X
= ( relational_Bool_a_b @ T2 ) )
=> ( Y3
!= ( insert7010464514620295119la_a_b @ ( relational_Bool_a_b @ T2 ) @ bot_bo4495933725496725865la_a_b ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( Y3
!= ( insert7010464514620295119la_a_b @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ bot_bo4495933725496725865la_a_b ) ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( Y3
!= ( insert7010464514620295119la_a_b @ ( relational_Eq_a_b @ X5 @ T2 ) @ bot_bo4495933725496725865la_a_b ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( Y3
!= ( insert7010464514620295119la_a_b @ ( relational_Neg_a_b @ Q4 ) @ ( relational_sub_a_b @ Q4 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( insert7010464514620295119la_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ ( sup_su5130108678486352897la_a_b @ ( relational_sub_a_b @ Q12 ) @ ( relational_sub_a_b @ Q23 ) ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( Y3
!= ( insert7010464514620295119la_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ ( sup_su5130108678486352897la_a_b @ ( relational_sub_a_b @ Q12 ) @ ( relational_sub_a_b @ Q23 ) ) ) ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) )
=> ( Y3
!= ( insert7010464514620295119la_a_b @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ ( relational_sub_a_b @ Q4 ) ) ) ) ) ) ) ) ) ) ) ).
% sub.elims
thf(fact_518_sub_Opelims,axiom,
! [X: relational_fmla_a_b,Y3: set_Re381260168593705685la_a_b] :
( ( ( relational_sub_a_b @ X )
= Y3 )
=> ( ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ X )
=> ( ! [T2: $o] :
( ( X
= ( relational_Bool_a_b @ T2 ) )
=> ( ( Y3
= ( insert7010464514620295119la_a_b @ ( relational_Bool_a_b @ T2 ) @ bot_bo4495933725496725865la_a_b ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ ( relational_Bool_a_b @ T2 ) ) ) )
=> ( ! [P3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ P3 @ Ts2 ) )
=> ( ( Y3
= ( insert7010464514620295119la_a_b @ ( relational_Pred_b_a @ P3 @ Ts2 ) @ bot_bo4495933725496725865la_a_b ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ ( relational_Pred_b_a @ P3 @ Ts2 ) ) ) )
=> ( ! [X5: nat,T2: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T2 ) )
=> ( ( Y3
= ( insert7010464514620295119la_a_b @ ( relational_Eq_a_b @ X5 @ T2 ) @ bot_bo4495933725496725865la_a_b ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ ( relational_Eq_a_b @ X5 @ T2 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Q4 ) )
=> ( ( Y3
= ( insert7010464514620295119la_a_b @ ( relational_Neg_a_b @ Q4 ) @ ( relational_sub_a_b @ Q4 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ ( relational_Neg_a_b @ Q4 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( insert7010464514620295119la_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) @ ( sup_su5130108678486352897la_a_b @ ( relational_sub_a_b @ Q12 ) @ ( relational_sub_a_b @ Q23 ) ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ( ( Y3
= ( insert7010464514620295119la_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) @ ( sup_su5130108678486352897la_a_b @ ( relational_sub_a_b @ Q12 ) @ ( relational_sub_a_b @ Q23 ) ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) ) ) )
=> ~ ! [Z3: nat,Q4: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) )
=> ( ( Y3
= ( insert7010464514620295119la_a_b @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) @ ( relational_sub_a_b @ Q4 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati7309537865537208983el_a_b @ ( relati591517084277583526ts_a_b @ Z3 @ Q4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sub.pelims
thf(fact_519_gen_H_Osimps,axiom,
( relational_gen_a_b2
= ( ^ [A14: nat,A24: relational_fmla_a_b,A34: set_Re381260168593705685la_a_b] :
( ( ( A24
= ( relational_Bool_a_b @ $false ) )
& ( A34 = bot_bo4495933725496725865la_a_b ) )
| ( ( A34
= ( insert7010464514620295119la_a_b @ A24 @ bot_bo4495933725496725865la_a_b ) )
& ( relational_ap_a_b @ A24 )
& ( member_nat @ A14 @ ( relational_fv_a_b @ A24 ) ) )
| ? [Q3: relational_fmla_a_b] :
( ( A24
= ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q3 ) ) )
& ( relational_gen_a_b2 @ A14 @ Q3 @ A34 ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q13 @ Q24 ) ) )
& ( relational_gen_a_b2 @ A14 @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q13 ) @ ( relational_Neg_a_b @ Q24 ) ) @ A34 ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q13 @ Q24 ) ) )
& ( relational_gen_a_b2 @ A14 @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q13 ) @ ( relational_Neg_a_b @ Q24 ) ) @ A34 ) )
| ? [Q13: relational_fmla_a_b,G13: set_Re381260168593705685la_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Disj_a_b @ Q13 @ Q24 ) )
& ? [G24: set_Re381260168593705685la_a_b] :
( ( A34
= ( sup_su5130108678486352897la_a_b @ G13 @ G24 ) )
& ( relational_gen_a_b2 @ A14 @ Q13 @ G13 )
& ( relational_gen_a_b2 @ A14 @ Q24 @ G24 ) ) )
| ? [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
( ( A24
= ( relational_Conj_a_b @ Q13 @ Q24 ) )
& ( ( relational_gen_a_b2 @ A14 @ Q13 @ A34 )
| ( relational_gen_a_b2 @ A14 @ Q24 @ A34 ) ) )
| ? [Y6: nat,Q3: relational_fmla_a_b] :
( ( A24
= ( relational_Conj_a_b @ Q3 @ ( relational_Eq_a_b @ A14 @ ( relational_Var_a @ Y6 ) ) ) )
& ? [G4: set_Re381260168593705685la_a_b] :
( ( A34
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_subst_a_b @ Qa @ Y6 @ A14 )
@ G4 ) )
& ( relational_gen_a_b2 @ Y6 @ Q3 @ G4 ) ) )
| ? [Y6: nat,Q3: relational_fmla_a_b] :
( ( A24
= ( relational_Conj_a_b @ Q3 @ ( relational_Eq_a_b @ Y6 @ ( relational_Var_a @ A14 ) ) ) )
& ? [G4: set_Re381260168593705685la_a_b] :
( ( A34
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_subst_a_b @ Qa @ Y6 @ A14 )
@ G4 ) )
& ( relational_gen_a_b2 @ Y6 @ Q3 @ G4 ) ) )
| ? [Y6: nat,Q3: relational_fmla_a_b] :
( ( A24
= ( relati591517084277583526ts_a_b @ Y6 @ Q3 ) )
& ? [G4: set_Re381260168593705685la_a_b] :
( ( A34
= ( image_6790371041703824709la_a_b @ ( relati3989891337220013914ts_a_b @ Y6 ) @ G4 ) )
& ( A14 != Y6 )
& ( relational_gen_a_b2 @ A14 @ Q3 @ G4 ) ) ) ) ) ) ).
% gen'.simps
thf(fact_520_gen_H_Ocases,axiom,
! [A13: nat,A23: relational_fmla_a_b,A33: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b2 @ A13 @ A23 @ A33 )
=> ( ( ( A23
= ( relational_Bool_a_b @ $false ) )
=> ( A33 != bot_bo4495933725496725865la_a_b ) )
=> ( ( ( A33
= ( insert7010464514620295119la_a_b @ A23 @ bot_bo4495933725496725865la_a_b ) )
=> ( ( relational_ap_a_b @ A23 )
=> ~ ( member_nat @ A13 @ ( relational_fv_a_b @ A23 ) ) ) )
=> ( ! [Q4: relational_fmla_a_b] :
( ( A23
= ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q4 ) ) )
=> ~ ( relational_gen_a_b2 @ A13 @ Q4 @ A33 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q12 @ Q23 ) ) )
=> ~ ( relational_gen_a_b2 @ A13 @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ A33 ) )
=> ( ! [Q12: relational_fmla_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q12 @ Q23 ) ) )
=> ~ ( relational_gen_a_b2 @ A13 @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q12 ) @ ( relational_Neg_a_b @ Q23 ) ) @ A33 ) )
=> ( ! [Q12: relational_fmla_a_b,G12: set_Re381260168593705685la_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Disj_a_b @ Q12 @ Q23 ) )
=> ! [G23: set_Re381260168593705685la_a_b] :
( ( A33
= ( sup_su5130108678486352897la_a_b @ G12 @ G23 ) )
=> ( ( relational_gen_a_b2 @ A13 @ Q12 @ G12 )
=> ~ ( relational_gen_a_b2 @ A13 @ Q23 @ G23 ) ) ) )
=> ( ! [Q12: relational_fmla_a_b,G3: set_Re381260168593705685la_a_b,Q23: relational_fmla_a_b] :
( ( A23
= ( relational_Conj_a_b @ Q12 @ Q23 ) )
=> ( ( A33 = G3 )
=> ~ ( ( relational_gen_a_b2 @ A13 @ Q12 @ G3 )
| ( relational_gen_a_b2 @ A13 @ Q23 @ G3 ) ) ) )
=> ( ! [Y5: nat,Q4: relational_fmla_a_b] :
( ( A23
= ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ A13 @ ( relational_Var_a @ Y5 ) ) ) )
=> ! [G3: set_Re381260168593705685la_a_b] :
( ( A33
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_subst_a_b @ Qa @ Y5 @ A13 )
@ G3 ) )
=> ~ ( relational_gen_a_b2 @ Y5 @ Q4 @ G3 ) ) )
=> ( ! [Y5: nat,Q4: relational_fmla_a_b] :
( ( A23
= ( relational_Conj_a_b @ Q4 @ ( relational_Eq_a_b @ Y5 @ ( relational_Var_a @ A13 ) ) ) )
=> ! [G3: set_Re381260168593705685la_a_b] :
( ( A33
= ( image_6790371041703824709la_a_b
@ ^ [Qa: relational_fmla_a_b] : ( relational_subst_a_b @ Qa @ Y5 @ A13 )
@ G3 ) )
=> ~ ( relational_gen_a_b2 @ Y5 @ Q4 @ G3 ) ) )
=> ~ ! [Y5: nat,Q4: relational_fmla_a_b] :
( ( A23
= ( relati591517084277583526ts_a_b @ Y5 @ Q4 ) )
=> ! [G3: set_Re381260168593705685la_a_b] :
( ( A33
= ( image_6790371041703824709la_a_b @ ( relati3989891337220013914ts_a_b @ Y5 ) @ G3 ) )
=> ( ( A13 != Y5 )
=> ~ ( relational_gen_a_b2 @ A13 @ Q4 @ G3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% gen'.cases
thf(fact_521_gen_H__gen,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b2 @ X @ Q @ G )
=> ( relational_gen_a_b @ X @ Q @ G ) ) ).
% gen'_gen
thf(fact_522_gen__gen_H,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b @ X @ Q @ G )
=> ( relational_gen_a_b2 @ X @ Q @ G ) ) ).
% gen_gen'
thf(fact_523_gen__eq__gen_H,axiom,
relational_gen_a_b = relational_gen_a_b2 ).
% gen_eq_gen'
thf(fact_524_gen_H__qp,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,Qqp: relational_fmla_a_b] :
( ( relational_gen_a_b2 @ X @ Q @ G )
=> ( ( member4680049679412964150la_a_b @ Qqp @ G )
=> ( relational_qp_a_b @ Qqp ) ) ) ).
% gen'_qp
thf(fact_525_gen_H_Ointros_I7_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,Q22: relational_fmla_a_b] :
( ( ( relational_gen_a_b2 @ X @ Q1 @ G )
| ( relational_gen_a_b2 @ X @ Q22 @ G ) )
=> ( relational_gen_a_b2 @ X @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ G ) ) ).
% gen'.intros(7)
thf(fact_526_gen_H_Ointros_I3_J,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b2 @ X @ Q @ G )
=> ( relational_gen_a_b2 @ X @ ( relational_Neg_a_b @ ( relational_Neg_a_b @ Q ) ) @ G ) ) ).
% gen'.intros(3)
thf(fact_527_fv_Osimps_I6_J,axiom,
! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
= ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( relational_fv_a_b @ Psi2 ) ) ) ).
% fv.simps(6)
thf(fact_528_fv_Osimps_I5_J,axiom,
! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
= ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( relational_fv_a_b @ Psi2 ) ) ) ).
% fv.simps(5)
thf(fact_529_gen_H_Ointros_I1_J,axiom,
! [X: nat] : ( relational_gen_a_b2 @ X @ ( relational_Bool_a_b @ $false ) @ bot_bo4495933725496725865la_a_b ) ).
% gen'.intros(1)
thf(fact_530_gen_H_Ointros_I6_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,G14: set_Re381260168593705685la_a_b,Q22: relational_fmla_a_b,G25: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b2 @ X @ Q1 @ G14 )
=> ( ( relational_gen_a_b2 @ X @ Q22 @ G25 )
=> ( relational_gen_a_b2 @ X @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ ( sup_su5130108678486352897la_a_b @ G14 @ G25 ) ) ) ) ).
% gen'.intros(6)
thf(fact_531_gen_H_Ointros_I4_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b2 @ X @ ( relational_Conj_a_b @ ( relational_Neg_a_b @ Q1 ) @ ( relational_Neg_a_b @ Q22 ) ) @ G )
=> ( relational_gen_a_b2 @ X @ ( relational_Neg_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) ) @ G ) ) ).
% gen'.intros(4)
thf(fact_532_gen_H_Ointros_I5_J,axiom,
! [X: nat,Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( relational_gen_a_b2 @ X @ ( relational_Disj_a_b @ ( relational_Neg_a_b @ Q1 ) @ ( relational_Neg_a_b @ Q22 ) ) @ G )
=> ( relational_gen_a_b2 @ X @ ( relational_Neg_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) ) @ G ) ) ).
% gen'.intros(5)
thf(fact_533_gen_H_Ointros_I10_J,axiom,
! [X: nat,Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b] :
( ( X != Y3 )
=> ( ( relational_gen_a_b2 @ X @ Q @ G )
=> ( relational_gen_a_b2 @ X @ ( relati591517084277583526ts_a_b @ Y3 @ Q ) @ ( image_6790371041703824709la_a_b @ ( relati3989891337220013914ts_a_b @ Y3 ) @ G ) ) ) ) ).
% gen'.intros(10)
thf(fact_534_fv_Osimps_I3_J,axiom,
! [X: nat,T5: relational_term_a] :
( ( relational_fv_a_b @ ( relational_Eq_a_b @ X @ T5 ) )
= ( sup_sup_set_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( relati6004689760767320788_set_a @ T5 ) ) ) ).
% fv.simps(3)
thf(fact_535_gen_H_Ointros_I2_J,axiom,
! [Q: relational_fmla_a_b,X: nat] :
( ( relational_ap_a_b @ Q )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( relational_gen_a_b2 @ X @ Q @ ( insert7010464514620295119la_a_b @ Q @ bot_bo4495933725496725865la_a_b ) ) ) ) ).
% gen'.intros(2)
thf(fact_536_gen_H_Ointros_I8_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b2 @ Y3 @ Q @ G )
=> ( relational_gen_a_b2 @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ X @ ( relational_Var_a @ Y3 ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_subst_a_b @ Q3 @ Y3 @ X )
@ G ) ) ) ).
% gen'.intros(8)
thf(fact_537_gen_H_Ointros_I9_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b2 @ Y3 @ Q @ G )
=> ( relational_gen_a_b2 @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ Y3 @ ( relational_Var_a @ X ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_subst_a_b @ Q3 @ Y3 @ X )
@ G ) ) ) ).
% gen'.intros(9)
thf(fact_538_gen_H__cp__intros_I1_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b2 @ Y3 @ Q @ G )
=> ( relational_gen_a_b2 @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ X @ ( relational_Var_a @ Y3 ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Q3 @ Y3 @ X ) )
@ G ) ) ) ).
% gen'_cp_intros(1)
thf(fact_539_gen_H__cp__intros_I2_J,axiom,
! [Y3: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,X: nat] :
( ( relational_gen_a_b2 @ Y3 @ Q @ G )
=> ( relational_gen_a_b2 @ X @ ( relational_Conj_a_b @ Q @ ( relational_Eq_a_b @ Y3 @ ( relational_Var_a @ X ) ) )
@ ( image_6790371041703824709la_a_b
@ ^ [Q3: relational_fmla_a_b] : ( relational_cp_a_b @ ( relational_subst_a_b @ Q3 @ Y3 @ X ) )
@ G ) ) ) ).
% gen'_cp_intros(2)
thf(fact_540_fv_Oelims,axiom,
! [X: relational_fmla_a_b,Y3: set_nat] :
( ( ( relational_fv_a_b @ X )
= Y3 )
=> ( ! [Uu: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ Uu @ Ts2 ) )
=> ( Y3
!= ( relati4569515538964159125_set_a @ Ts2 ) ) )
=> ( ( ? [B3: $o] :
( X
= ( relational_Bool_a_b @ B3 ) )
=> ( Y3 != bot_bot_set_nat ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( Y3
!= ( sup_sup_set_nat @ ( insert_nat @ X5 @ bot_bot_set_nat ) @ ( relati6004689760767320788_set_a @ T3 ) ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ( Y3
!= ( relational_fv_a_b @ Phi ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( Y3
!= ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi ) @ ( relational_fv_a_b @ Psi ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ( Y3
!= ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi ) @ ( relational_fv_a_b @ Psi ) ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ( Y3
!= ( minus_minus_set_nat @ ( relational_fv_a_b @ Phi ) @ ( insert_nat @ Z3 @ bot_bot_set_nat ) ) ) ) ) ) ) ) ) ) ) ).
% fv.elims
thf(fact_541_fv_Opelims,axiom,
! [X: relational_fmla_a_b,Y3: set_nat] :
( ( ( relational_fv_a_b @ X )
= Y3 )
=> ( ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ X )
=> ( ! [Uu: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ Uu @ Ts2 ) )
=> ( ( Y3
= ( relati4569515538964159125_set_a @ Ts2 ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Pred_b_a @ Uu @ Ts2 ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ( ( Y3 = bot_bot_set_nat )
=> ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Bool_a_b @ B3 ) ) ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( ( Y3
= ( sup_sup_set_nat @ ( insert_nat @ X5 @ bot_bot_set_nat ) @ ( relati6004689760767320788_set_a @ T3 ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Eq_a_b @ X5 @ T3 ) ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ( ( Y3
= ( relational_fv_a_b @ Phi ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Neg_a_b @ Phi ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( ( Y3
= ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi ) @ ( relational_fv_a_b @ Psi ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Conj_a_b @ Phi @ Psi ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ( ( Y3
= ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi ) @ ( relational_fv_a_b @ Psi ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Disj_a_b @ Phi @ Psi ) ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ( ( Y3
= ( minus_minus_set_nat @ ( relational_fv_a_b @ Phi ) @ ( insert_nat @ Z3 @ bot_bot_set_nat ) ) )
=> ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relati591517084277583526ts_a_b @ Z3 @ Phi ) ) ) ) ) ) ) ) ) ) ) ) ).
% fv.pelims
thf(fact_542_fv__subst__term,axiom,
! [X: nat,T: relational_term_a,Y3: nat] :
( ( ( member_nat @ X @ ( relati6004689760767320788_set_a @ T ) )
=> ( ( relati6004689760767320788_set_a @ ( relati7175845559408349773term_a @ T @ X @ Y3 ) )
= ( insert_nat @ Y3 @ ( minus_minus_set_nat @ ( relati6004689760767320788_set_a @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) )
& ( ~ ( member_nat @ X @ ( relati6004689760767320788_set_a @ T ) )
=> ( ( relati6004689760767320788_set_a @ ( relati7175845559408349773term_a @ T @ X @ Y3 ) )
= ( relati6004689760767320788_set_a @ T ) ) ) ) ).
% fv_subst_term
thf(fact_543_fv__exists,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( relati3989891337220013914ts_a_b @ X @ Q ) )
= ( minus_minus_set_nat @ ( relational_fv_a_b @ Q ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% fv_exists
thf(fact_544_fv_Osimps_I7_J,axiom,
! [Z2: nat,Phi2: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Phi2 ) )
= ( minus_minus_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( insert_nat @ Z2 @ bot_bot_set_nat ) ) ) ).
% fv.simps(7)
thf(fact_545_fv__subst,axiom,
! [X: nat,Q: relational_fmla_a_b,Y3: nat] :
( ( ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( ( relational_fv_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
= ( insert_nat @ Y3 @ ( minus_minus_set_nat @ ( relational_fv_a_b @ Q ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) )
& ( ~ ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( ( relational_fv_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) )
= ( relational_fv_a_b @ Q ) ) ) ) ).
% fv_subst
thf(fact_546_fv__erase,axiom,
! [Q: relational_fmla_a_b,X: nat] : ( ord_less_eq_set_nat @ ( relational_fv_a_b @ ( relational_erase_a_b @ Q @ X ) ) @ ( minus_minus_set_nat @ ( relational_fv_a_b @ Q ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% fv_erase
thf(fact_547_eval__subst,axiom,
! [Sigma: nat > a,T: relational_term_a,X: nat,Y3: nat] :
( ( relati1177013128715261720term_a @ Sigma @ ( relati7175845559408349773term_a @ T @ X @ Y3 ) )
= ( relati1177013128715261720term_a @ ( fun_upd_nat_a @ Sigma @ X @ ( Sigma @ Y3 ) ) @ T ) ) ).
% eval_subst
thf(fact_548_fv__term__set_Opelims,axiom,
! [X: relational_term_a,Y3: set_nat] :
( ( ( relati6004689760767320788_set_a @ X )
= Y3 )
=> ( ( accp_R1925461290012245842term_a @ relati7433707222316806765_rel_a @ X )
=> ( ! [N2: nat] :
( ( X
= ( relational_Var_a @ N2 ) )
=> ( ( Y3
= ( insert_nat @ N2 @ bot_bot_set_nat ) )
=> ~ ( accp_R1925461290012245842term_a @ relati7433707222316806765_rel_a @ ( relational_Var_a @ N2 ) ) ) )
=> ~ ! [V2: a] :
( ( X
= ( relational_Const_a @ V2 ) )
=> ( ( Y3 = bot_bot_set_nat )
=> ~ ( accp_R1925461290012245842term_a @ relati7433707222316806765_rel_a @ ( relational_Const_a @ V2 ) ) ) ) ) ) ) ).
% fv_term_set.pelims
thf(fact_549_fmla_Omap__comp,axiom,
! [G1: a > a,G22: b > b,F1: a > a,F2: b > b,V: relational_fmla_a_b] :
( ( relati4520850492397955663_a_b_b @ G1 @ G22 @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ V ) )
= ( relati4520850492397955663_a_b_b @ ( comp_a_a_a @ G1 @ F1 ) @ ( comp_b_b_b @ G22 @ F2 ) @ V ) ) ).
% fmla.map_comp
thf(fact_550_eval__term_Osimps_I2_J,axiom,
! [Sigma: nat > a,N: nat] :
( ( relati1177013128715261720term_a @ Sigma @ ( relational_Var_a @ N ) )
= ( Sigma @ N ) ) ).
% eval_term.simps(2)
thf(fact_551_eval__term_Osimps_I1_J,axiom,
! [Sigma: nat > a,C2: a] :
( ( relati1177013128715261720term_a @ Sigma @ ( relational_Const_a @ C2 ) )
= C2 ) ).
% eval_term.simps(1)
thf(fact_552_eval__term__cong,axiom,
! [T: relational_term_a,Sigma: nat > a,Sigma2: nat > a] :
( ! [N2: nat] :
( ( member_nat @ N2 @ ( relati6004689760767320788_set_a @ T ) )
=> ( ( Sigma @ N2 )
= ( Sigma2 @ N2 ) ) )
=> ( ( relati1177013128715261720term_a @ Sigma @ T )
= ( relati1177013128715261720term_a @ Sigma2 @ T ) ) ) ).
% eval_term_cong
thf(fact_553_gen__fv,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,Qqp: relational_fmla_a_b] :
( ( relational_gen_a_b @ X @ Q @ G )
=> ( ( member4680049679412964150la_a_b @ Qqp @ G )
=> ( ( member_nat @ X @ ( relational_fv_a_b @ Qqp ) )
& ( ord_less_eq_set_nat @ ( relational_fv_a_b @ Qqp ) @ ( relational_fv_a_b @ Q ) ) ) ) ) ).
% gen_fv
thf(fact_554_fv__cp,axiom,
! [Q: relational_fmla_a_b] : ( ord_less_eq_set_nat @ ( relational_fv_a_b @ ( relational_cp_a_b @ Q ) ) @ ( relational_fv_a_b @ Q ) ) ).
% fv_cp
thf(fact_555_eval__term_Oelims,axiom,
! [X: nat > a,Xa2: relational_term_a,Y3: a] :
( ( ( relati1177013128715261720term_a @ X @ Xa2 )
= Y3 )
=> ( ! [C: a] :
( ( Xa2
= ( relational_Const_a @ C ) )
=> ( Y3 != C ) )
=> ~ ! [N2: nat] :
( ( Xa2
= ( relational_Var_a @ N2 ) )
=> ( Y3
!= ( X @ N2 ) ) ) ) ) ).
% eval_term.elims
thf(fact_556_eval__terms__def,axiom,
( relati4772805863405912879erms_a
= ( ^ [Sigma3: nat > a] : ( map_Re419313091343012409rm_a_a @ ( relati1177013128715261720term_a @ Sigma3 ) ) ) ) ).
% eval_terms_def
thf(fact_557_fv__cp__foldr__Disj,axiom,
! [Qs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b,A2: set_nat] :
( ! [X5: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X5 @ ( sup_su5130108678486352897la_a_b @ ( set_Re9104216502384355786la_a_b @ Qs ) @ ( insert7010464514620295119la_a_b @ Q @ bot_bo4495933725496725865la_a_b ) ) )
=> ( ( relati1591879772219623554ed_a_b @ X5 )
& ( ( relational_fv_a_b @ X5 )
= A2 ) ) )
=> ( ( relational_fv_a_b @ ( relational_cp_a_b @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Qs @ Q ) ) )
= A2 ) ) ).
% fv_cp_foldr_Disj
thf(fact_558_sat_Oelims_I1_J,axiom,
! [X: relati7206184916280974613la_a_b,Xa2: produc7366699395886430672_b_nat > set_list_a,Xb: nat > a,Y3: $o] :
( ( ( relati5954879512608767636la_a_b @ X @ Xa2 @ Xb )
= Y3 )
=> ( ! [R3: relational_fmla_a_b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) )
=> ( Y3
= ( ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( produc4282057684358614024_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati3586412934113010954la_a_b @ B3 ) )
=> ( Y3 = (~ B3) ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relati4858397885352678280la_a_b @ X5 @ T3 ) )
=> ( Y3
= ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati3276862304027480822la_a_b @ Phi ) )
=> ( Y3
= ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2925905614403835404la_a_b @ Phi @ Psi ) )
=> ( Y3
= ( ~ ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
& ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2923897639004875288la_a_b @ Phi @ Psi ) )
=> ( Y3
= ( ~ ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
| ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [Z3: nat,Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati8887572811940184376la_a_b @ Z3 @ Phi ) )
=> ( Y3
= ( ~ ? [X3: a] : ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(1)
thf(fact_559_sat_Oelims_I1_J,axiom,
! [X: relati9047081815478866374_a_nat,Xa2: product_prod_nat_nat > set_list_a,Xb: nat > a,Y3: $o] :
( ( ( relational_sat_a_nat @ X @ Xa2 @ Xb )
= Y3 )
=> ( ! [R3: nat,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) )
=> ( Y3
= ( ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati9034565498597818939_a_nat @ B3 ) )
=> ( Y3 = (~ B3) ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_nat @ X5 @ T3 ) )
=> ( Y3
= ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relational_Neg_a_nat @ Phi ) )
=> ( Y3
= ( relational_sat_a_nat @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati2542520632142267709_a_nat @ Phi @ Psi ) )
=> ( Y3
= ( ~ ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati9106205213788308809_a_nat @ Phi @ Psi ) )
=> ( Y3
= ( ~ ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [Z3: nat,Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relati6314223733442460777_a_nat @ Z3 @ Phi ) )
=> ( Y3
= ( ~ ? [X3: a] : ( relational_sat_a_nat @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(1)
thf(fact_560_sat_Oelims_I1_J,axiom,
! [X: relational_fmla_a_b,Xa2: product_prod_b_nat > set_list_a,Xb: nat > a,Y3: $o] :
( ( ( relational_sat_a_b @ X @ Xa2 @ Xb )
= Y3 )
=> ( ! [R3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ R3 @ Ts2 ) )
=> ( Y3
= ( ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ( Y3 = (~ B3) ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( Y3
= ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ( Y3
= ( relational_sat_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( Y3
= ( ~ ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ( Y3
= ( ~ ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ( Y3
= ( ~ ? [X3: a] : ( relational_sat_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(1)
thf(fact_561_sat_Oelims_I2_J,axiom,
! [X: relati7206184916280974613la_a_b,Xa2: produc7366699395886430672_b_nat > set_list_a,Xb: nat > a] :
( ( relati5954879512608767636la_a_b @ X @ Xa2 @ Xb )
=> ( ! [R3: relational_fmla_a_b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) )
=> ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( produc4282057684358614024_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati3586412934113010954la_a_b @ B3 ) )
=> ~ B3 )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relati4858397885352678280la_a_b @ X5 @ T3 ) )
=> ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati3276862304027480822la_a_b @ Phi ) )
=> ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2925905614403835404la_a_b @ Phi @ Psi ) )
=> ~ ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
& ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2923897639004875288la_a_b @ Phi @ Psi ) )
=> ~ ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
| ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ! [Z3: nat,Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati8887572811940184376la_a_b @ Z3 @ Phi ) )
=> ~ ? [X5: a] : ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(2)
thf(fact_562_sat_Oelims_I2_J,axiom,
! [X: relati9047081815478866374_a_nat,Xa2: product_prod_nat_nat > set_list_a,Xb: nat > a] :
( ( relational_sat_a_nat @ X @ Xa2 @ Xb )
=> ( ! [R3: nat,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) )
=> ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati9034565498597818939_a_nat @ B3 ) )
=> ~ B3 )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_nat @ X5 @ T3 ) )
=> ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relational_Neg_a_nat @ Phi ) )
=> ( relational_sat_a_nat @ Phi @ Xa2 @ Xb ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati2542520632142267709_a_nat @ Phi @ Psi ) )
=> ~ ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati9106205213788308809_a_nat @ Phi @ Psi ) )
=> ~ ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) )
=> ~ ! [Z3: nat,Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relati6314223733442460777_a_nat @ Z3 @ Phi ) )
=> ~ ? [X5: a] : ( relational_sat_a_nat @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(2)
thf(fact_563_sat_Oelims_I2_J,axiom,
! [X: relational_fmla_a_b,Xa2: product_prod_b_nat > set_list_a,Xb: nat > a] :
( ( relational_sat_a_b @ X @ Xa2 @ Xb )
=> ( ! [R3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ R3 @ Ts2 ) )
=> ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ~ B3 )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ( relational_sat_a_b @ Phi @ Xa2 @ Xb ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ~ ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ~ ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ~ ? [X5: a] : ( relational_sat_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(2)
thf(fact_564_sat__cp,axiom,
! [Q: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_cp_a_b @ Q ) @ I3 @ Sigma )
= ( relational_sat_a_b @ Q @ I3 @ Sigma ) ) ).
% sat_cp
thf(fact_565_sat__subst,axiom,
! [Q: relational_fmla_a_b,X: nat,Y3: nat,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_subst_a_b @ Q @ X @ Y3 ) @ I3 @ Sigma )
= ( relational_sat_a_b @ Q @ I3 @ ( fun_upd_nat_a @ Sigma @ X @ ( Sigma @ Y3 ) ) ) ) ).
% sat_subst
thf(fact_566_sat__exists,axiom,
! [N: nat,Q: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relati3989891337220013914ts_a_b @ N @ Q ) @ I3 @ Sigma )
= ( ? [X3: a] : ( relational_sat_a_b @ Q @ I3 @ ( fun_upd_nat_a @ Sigma @ N @ X3 ) ) ) ) ).
% sat_exists
thf(fact_567_sat__foldr__Disj,axiom,
! [Xs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Xs @ Q ) @ I3 @ Sigma )
= ( ? [X3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X3 @ ( sup_su5130108678486352897la_a_b @ ( set_Re9104216502384355786la_a_b @ Xs ) @ ( insert7010464514620295119la_a_b @ Q @ bot_bo4495933725496725865la_a_b ) ) )
& ( relational_sat_a_b @ X3 @ I3 @ Sigma ) ) ) ) ).
% sat_foldr_Disj
thf(fact_568_sat_Osimps_I1_J,axiom,
! [R4: relational_fmla_a_b,Ts: list_R6823256787227418703term_a,I3: produc7366699395886430672_b_nat > set_list_a,Sigma: nat > a] :
( ( relati5954879512608767636la_a_b @ ( relati1568360951651578835_a_b_a @ R4 @ Ts ) @ I3 @ Sigma )
= ( member_list_a @ ( relati4772805863405912879erms_a @ Sigma @ Ts ) @ ( I3 @ ( produc4282057684358614024_b_nat @ R4 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) ).
% sat.simps(1)
thf(fact_569_sat_Osimps_I1_J,axiom,
! [R4: nat,Ts: list_R6823256787227418703term_a,I3: product_prod_nat_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_nat @ ( relati6362048942677509346_nat_a @ R4 @ Ts ) @ I3 @ Sigma )
= ( member_list_a @ ( relati4772805863405912879erms_a @ Sigma @ Ts ) @ ( I3 @ ( product_Pair_nat_nat @ R4 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) ).
% sat.simps(1)
thf(fact_570_sat_Osimps_I1_J,axiom,
! [R4: b,Ts: list_R6823256787227418703term_a,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_Pred_b_a @ R4 @ Ts ) @ I3 @ Sigma )
= ( member_list_a @ ( relati4772805863405912879erms_a @ Sigma @ Ts ) @ ( I3 @ ( product_Pair_b_nat @ R4 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) ).
% sat.simps(1)
thf(fact_571_list__all2__lengthD,axiom,
! [P: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a,Ys: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ Xs @ Ys )
=> ( ( size_s88622898042387131term_a @ Xs )
= ( size_s88622898042387131term_a @ Ys ) ) ) ).
% list_all2_lengthD
thf(fact_572_list_Orel__cong,axiom,
! [X: list_nat,Ya2: list_nat,Y3: list_nat,Xa2: list_nat,R: nat > nat > $o,Ra: nat > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: nat] :
( ( member_nat @ Z3 @ ( set_nat2 @ Ya2 ) )
=> ( ( member_nat @ Yb @ ( set_nat2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_nat_nat @ R @ X @ Y3 )
= ( list_all2_nat_nat @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_573_list_Orel__cong,axiom,
! [X: list_nat,Ya2: list_nat,Y3: list_b,Xa2: list_b,R: nat > b > $o,Ra: nat > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: b] :
( ( member_nat @ Z3 @ ( set_nat2 @ Ya2 ) )
=> ( ( member_b @ Yb @ ( set_b2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_nat_b @ R @ X @ Y3 )
= ( list_all2_nat_b @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_574_list_Orel__cong,axiom,
! [X: list_nat,Ya2: list_nat,Y3: list_a,Xa2: list_a,R: nat > a > $o,Ra: nat > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: a] :
( ( member_nat @ Z3 @ ( set_nat2 @ Ya2 ) )
=> ( ( member_a @ Yb @ ( set_a2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_nat_a @ R @ X @ Y3 )
= ( list_all2_nat_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_575_list_Orel__cong,axiom,
! [X: list_b,Ya2: list_b,Y3: list_nat,Xa2: list_nat,R: b > nat > $o,Ra: b > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: b,Yb: nat] :
( ( member_b @ Z3 @ ( set_b2 @ Ya2 ) )
=> ( ( member_nat @ Yb @ ( set_nat2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_b_nat @ R @ X @ Y3 )
= ( list_all2_b_nat @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_576_list_Orel__cong,axiom,
! [X: list_b,Ya2: list_b,Y3: list_b,Xa2: list_b,R: b > b > $o,Ra: b > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: b,Yb: b] :
( ( member_b @ Z3 @ ( set_b2 @ Ya2 ) )
=> ( ( member_b @ Yb @ ( set_b2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_b_b @ R @ X @ Y3 )
= ( list_all2_b_b @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_577_list_Orel__cong,axiom,
! [X: list_b,Ya2: list_b,Y3: list_a,Xa2: list_a,R: b > a > $o,Ra: b > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: b,Yb: a] :
( ( member_b @ Z3 @ ( set_b2 @ Ya2 ) )
=> ( ( member_a @ Yb @ ( set_a2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_b_a @ R @ X @ Y3 )
= ( list_all2_b_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_578_list_Orel__cong,axiom,
! [X: list_a,Ya2: list_a,Y3: list_nat,Xa2: list_nat,R: a > nat > $o,Ra: a > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: a,Yb: nat] :
( ( member_a @ Z3 @ ( set_a2 @ Ya2 ) )
=> ( ( member_nat @ Yb @ ( set_nat2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_a_nat @ R @ X @ Y3 )
= ( list_all2_a_nat @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_579_list_Orel__cong,axiom,
! [X: list_a,Ya2: list_a,Y3: list_b,Xa2: list_b,R: a > b > $o,Ra: a > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: a,Yb: b] :
( ( member_a @ Z3 @ ( set_a2 @ Ya2 ) )
=> ( ( member_b @ Yb @ ( set_b2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_a_b @ R @ X @ Y3 )
= ( list_all2_a_b @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_580_list_Orel__cong,axiom,
! [X: list_a,Ya2: list_a,Y3: list_a,Xa2: list_a,R: a > a > $o,Ra: a > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: a,Yb: a] :
( ( member_a @ Z3 @ ( set_a2 @ Ya2 ) )
=> ( ( member_a @ Yb @ ( set_a2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_a_a @ R @ X @ Y3 )
= ( list_all2_a_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_581_list_Orel__cong,axiom,
! [X: list_nat,Ya2: list_nat,Y3: list_list_a,Xa2: list_list_a,R: nat > list_a > $o,Ra: nat > list_a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: list_a] :
( ( member_nat @ Z3 @ ( set_nat2 @ Ya2 ) )
=> ( ( member_list_a @ Yb @ ( set_list_a2 @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( list_all2_nat_list_a @ R @ X @ Y3 )
= ( list_all2_nat_list_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% list.rel_cong
thf(fact_582_list_Orel__mono__strong,axiom,
! [R: nat > nat > $o,X: list_nat,Y3: list_nat,Ra: nat > nat > $o] :
( ( list_all2_nat_nat @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: nat] :
( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
=> ( ( member_nat @ Yb @ ( set_nat2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_nat_nat @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_583_list_Orel__mono__strong,axiom,
! [R: nat > b > $o,X: list_nat,Y3: list_b,Ra: nat > b > $o] :
( ( list_all2_nat_b @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: b] :
( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
=> ( ( member_b @ Yb @ ( set_b2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_nat_b @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_584_list_Orel__mono__strong,axiom,
! [R: nat > a > $o,X: list_nat,Y3: list_a,Ra: nat > a > $o] :
( ( list_all2_nat_a @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: a] :
( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
=> ( ( member_a @ Yb @ ( set_a2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_nat_a @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_585_list_Orel__mono__strong,axiom,
! [R: b > nat > $o,X: list_b,Y3: list_nat,Ra: b > nat > $o] :
( ( list_all2_b_nat @ R @ X @ Y3 )
=> ( ! [Z3: b,Yb: nat] :
( ( member_b @ Z3 @ ( set_b2 @ X ) )
=> ( ( member_nat @ Yb @ ( set_nat2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_b_nat @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_586_list_Orel__mono__strong,axiom,
! [R: b > b > $o,X: list_b,Y3: list_b,Ra: b > b > $o] :
( ( list_all2_b_b @ R @ X @ Y3 )
=> ( ! [Z3: b,Yb: b] :
( ( member_b @ Z3 @ ( set_b2 @ X ) )
=> ( ( member_b @ Yb @ ( set_b2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_b_b @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_587_list_Orel__mono__strong,axiom,
! [R: b > a > $o,X: list_b,Y3: list_a,Ra: b > a > $o] :
( ( list_all2_b_a @ R @ X @ Y3 )
=> ( ! [Z3: b,Yb: a] :
( ( member_b @ Z3 @ ( set_b2 @ X ) )
=> ( ( member_a @ Yb @ ( set_a2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_b_a @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_588_list_Orel__mono__strong,axiom,
! [R: a > nat > $o,X: list_a,Y3: list_nat,Ra: a > nat > $o] :
( ( list_all2_a_nat @ R @ X @ Y3 )
=> ( ! [Z3: a,Yb: nat] :
( ( member_a @ Z3 @ ( set_a2 @ X ) )
=> ( ( member_nat @ Yb @ ( set_nat2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_a_nat @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_589_list_Orel__mono__strong,axiom,
! [R: a > b > $o,X: list_a,Y3: list_b,Ra: a > b > $o] :
( ( list_all2_a_b @ R @ X @ Y3 )
=> ( ! [Z3: a,Yb: b] :
( ( member_a @ Z3 @ ( set_a2 @ X ) )
=> ( ( member_b @ Yb @ ( set_b2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_a_b @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_590_list_Orel__mono__strong,axiom,
! [R: a > a > $o,X: list_a,Y3: list_a,Ra: a > a > $o] :
( ( list_all2_a_a @ R @ X @ Y3 )
=> ( ! [Z3: a,Yb: a] :
( ( member_a @ Z3 @ ( set_a2 @ X ) )
=> ( ( member_a @ Yb @ ( set_a2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_a_a @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_591_list_Orel__mono__strong,axiom,
! [R: nat > list_a > $o,X: list_nat,Y3: list_list_a,Ra: nat > list_a > $o] :
( ( list_all2_nat_list_a @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: list_a] :
( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
=> ( ( member_list_a @ Yb @ ( set_list_a2 @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( list_all2_nat_list_a @ Ra @ X @ Y3 ) ) ) ).
% list.rel_mono_strong
thf(fact_592_list_Orel__refl__strong,axiom,
! [X: list_nat,Ra: nat > nat > $o] :
( ! [Z3: nat] :
( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( list_all2_nat_nat @ Ra @ X @ X ) ) ).
% list.rel_refl_strong
thf(fact_593_list_Orel__refl__strong,axiom,
! [X: list_b,Ra: b > b > $o] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_b2 @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( list_all2_b_b @ Ra @ X @ X ) ) ).
% list.rel_refl_strong
thf(fact_594_list_Orel__refl__strong,axiom,
! [X: list_list_a,Ra: list_a > list_a > $o] :
( ! [Z3: list_a] :
( ( member_list_a @ Z3 @ ( set_list_a2 @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( list_a3802133873445908231list_a @ Ra @ X @ X ) ) ).
% list.rel_refl_strong
thf(fact_595_list_Orel__refl__strong,axiom,
! [X: list_a,Ra: a > a > $o] :
( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_a2 @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( list_all2_a_a @ Ra @ X @ X ) ) ).
% list.rel_refl_strong
thf(fact_596_list_Orel__refl__strong,axiom,
! [X: list_R8263082107343818799la_a_b,Ra: relational_fmla_a_b > relational_fmla_a_b > $o] :
( ! [Z3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ Z3 @ ( set_Re9104216502384355786la_a_b @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( list_a2254996211694282183la_a_b @ Ra @ X @ X ) ) ).
% list.rel_refl_strong
thf(fact_597_list_Orel__refl__strong,axiom,
! [X: list_R6823256787227418703term_a,Ra: relational_term_a > relational_term_a > $o] :
( ! [Z3: relational_term_a] :
( ( member5466445112152945266term_a @ Z3 @ ( set_Re3569617851344498910term_a @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( list_a3533670403825157575term_a @ Ra @ X @ X ) ) ).
% list.rel_refl_strong
thf(fact_598_list__all2__same,axiom,
! [P: relational_fmla_a_b > relational_fmla_a_b > $o,Xs: list_R8263082107343818799la_a_b] :
( ( list_a2254996211694282183la_a_b @ P @ Xs @ Xs )
= ( ! [X3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X3 @ ( set_Re9104216502384355786la_a_b @ Xs ) )
=> ( P @ X3 @ X3 ) ) ) ) ).
% list_all2_same
thf(fact_599_list__all2__same,axiom,
! [P: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ Xs @ Xs )
= ( ! [X3: relational_term_a] :
( ( member5466445112152945266term_a @ X3 @ ( set_Re3569617851344498910term_a @ Xs ) )
=> ( P @ X3 @ X3 ) ) ) ) ).
% list_all2_same
thf(fact_600_sat_Osimps_I4_J,axiom,
! [Phi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_Neg_a_b @ Phi2 ) @ I3 @ Sigma )
= ( ~ ( relational_sat_a_b @ Phi2 @ I3 @ Sigma ) ) ) ).
% sat.simps(4)
thf(fact_601_sat_Osimps_I6_J,axiom,
! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_Disj_a_b @ Phi2 @ Psi2 ) @ I3 @ Sigma )
= ( ( relational_sat_a_b @ Phi2 @ I3 @ Sigma )
| ( relational_sat_a_b @ Psi2 @ I3 @ Sigma ) ) ) ).
% sat.simps(6)
thf(fact_602_sat_Osimps_I5_J,axiom,
! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_Conj_a_b @ Phi2 @ Psi2 ) @ I3 @ Sigma )
= ( ( relational_sat_a_b @ Phi2 @ I3 @ Sigma )
& ( relational_sat_a_b @ Psi2 @ I3 @ Sigma ) ) ) ).
% sat.simps(5)
thf(fact_603_sat_Osimps_I2_J,axiom,
! [B: $o,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_Bool_a_b @ B ) @ I3 @ Sigma )
= B ) ).
% sat.simps(2)
thf(fact_604_gen__sat,axiom,
! [X: nat,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_gen_a_b @ X @ Q @ G )
=> ( ( relational_sat_a_b @ Q @ I3 @ Sigma )
=> ? [X5: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X5 @ G )
& ( relational_sat_a_b @ X5 @ I3 @ Sigma ) ) ) ) ).
% gen_sat
thf(fact_605_sat__fv__cong,axiom,
! [Phi2: relational_fmla_a_b,Sigma: nat > a,Sigma2: nat > a,I3: product_prod_b_nat > set_list_a] :
( ! [N2: nat] :
( ( member_nat @ N2 @ ( relational_fv_a_b @ Phi2 ) )
=> ( ( Sigma @ N2 )
= ( Sigma2 @ N2 ) ) )
=> ( ( relational_sat_a_b @ Phi2 @ I3 @ Sigma )
= ( relational_sat_a_b @ Phi2 @ I3 @ Sigma2 ) ) ) ).
% sat_fv_cong
thf(fact_606_Exists__in__sub__foldr__Disj,axiom,
! [X: nat,Q2: relational_fmla_a_b,Qs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Qs @ Q ) ) )
=> ( ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ Q ) )
| ? [X5: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X5 @ ( set_Re9104216502384355786la_a_b @ Qs ) )
& ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ X5 ) ) ) ) ) ).
% Exists_in_sub_foldr_Disj
thf(fact_607_Exists__in__sub__cp__foldr__Disj,axiom,
! [X: nat,Q2: relational_fmla_a_b,Qs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( relational_cp_a_b @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Qs @ Q ) ) ) )
=> ( ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( relational_cp_a_b @ Q ) ) )
| ? [X5: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X5 @ ( set_Re9104216502384355786la_a_b @ Qs ) )
& ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( relational_cp_a_b @ X5 ) ) ) ) ) ) ).
% Exists_in_sub_cp_foldr_Disj
thf(fact_608_sat_Osimps_I3_J,axiom,
! [X: nat,T5: relational_term_a,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relational_Eq_a_b @ X @ T5 ) @ I3 @ Sigma )
= ( ( Sigma @ X )
= ( relati1177013128715261720term_a @ Sigma @ T5 ) ) ) ).
% sat.simps(3)
thf(fact_609_sat_Osimps_I7_J,axiom,
! [Z2: nat,Phi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relati591517084277583526ts_a_b @ Z2 @ Phi2 ) @ I3 @ Sigma )
= ( ? [X3: a] : ( relational_sat_a_b @ Phi2 @ I3 @ ( fun_upd_nat_a @ Sigma @ Z2 @ X3 ) ) ) ) ).
% sat.simps(7)
thf(fact_610_sat__fun__upd,axiom,
! [N: nat,Q: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a,Z2: a] :
( ~ ( member_nat @ N @ ( relational_fv_a_b @ Q ) )
=> ( ( relational_sat_a_b @ Q @ I3 @ ( fun_upd_nat_a @ Sigma @ N @ Z2 ) )
= ( relational_sat_a_b @ Q @ I3 @ Sigma ) ) ) ).
% sat_fun_upd
thf(fact_611_sat__erase,axiom,
! [Q: relational_fmla_a_b,X: nat,I3: product_prod_b_nat > set_list_a,Sigma: nat > a,Z2: a] :
( ( relational_sat_a_b @ ( relational_erase_a_b @ Q @ X ) @ I3 @ ( fun_upd_nat_a @ Sigma @ X @ Z2 ) )
= ( relational_sat_a_b @ ( relational_erase_a_b @ Q @ X ) @ I3 @ Sigma ) ) ).
% sat_erase
thf(fact_612_eval__terms__cong,axiom,
! [Ts: list_R6823256787227418703term_a,Sigma: nat > a,Sigma2: nat > a] :
( ! [N2: nat] :
( ( member_nat @ N2 @ ( relati4569515538964159125_set_a @ Ts ) )
=> ( ( Sigma @ N2 )
= ( Sigma2 @ N2 ) ) )
=> ( ( relati4772805863405912879erms_a @ Sigma @ Ts )
= ( relati4772805863405912879erms_a @ Sigma2 @ Ts ) ) ) ).
% eval_terms_cong
thf(fact_613_eval__terms__fv__terms__set,axiom,
! [Sigma: nat > a,Ts: list_R6823256787227418703term_a,Sigma2: nat > a,N: nat] :
( ( ( relati4772805863405912879erms_a @ Sigma @ Ts )
= ( relati4772805863405912879erms_a @ Sigma2 @ Ts ) )
=> ( ( member_nat @ N @ ( relati4569515538964159125_set_a @ Ts ) )
=> ( ( Sigma @ N )
= ( Sigma2 @ N ) ) ) ) ).
% eval_terms_fv_terms_set
thf(fact_614_sat_Oelims_I3_J,axiom,
! [X: relati7206184916280974613la_a_b,Xa2: produc7366699395886430672_b_nat > set_list_a,Xb: nat > a] :
( ~ ( relati5954879512608767636la_a_b @ X @ Xa2 @ Xb )
=> ( ! [R3: relational_fmla_a_b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) )
=> ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( produc4282057684358614024_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati3586412934113010954la_a_b @ B3 ) )
=> B3 )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relati4858397885352678280la_a_b @ X5 @ T3 ) )
=> ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati3276862304027480822la_a_b @ Phi ) )
=> ~ ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2925905614403835404la_a_b @ Phi @ Psi ) )
=> ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
& ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2923897639004875288la_a_b @ Phi @ Psi ) )
=> ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
| ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ! [Z3: nat,Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati8887572811940184376la_a_b @ Z3 @ Phi ) )
=> ? [X7: a] : ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X7 ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(3)
thf(fact_615_sat_Oelims_I3_J,axiom,
! [X: relati9047081815478866374_a_nat,Xa2: product_prod_nat_nat > set_list_a,Xb: nat > a] :
( ~ ( relational_sat_a_nat @ X @ Xa2 @ Xb )
=> ( ! [R3: nat,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) )
=> ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati9034565498597818939_a_nat @ B3 ) )
=> B3 )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_nat @ X5 @ T3 ) )
=> ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relational_Neg_a_nat @ Phi ) )
=> ~ ( relational_sat_a_nat @ Phi @ Xa2 @ Xb ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati2542520632142267709_a_nat @ Phi @ Psi ) )
=> ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati9106205213788308809_a_nat @ Phi @ Psi ) )
=> ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) )
=> ~ ! [Z3: nat,Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relati6314223733442460777_a_nat @ Z3 @ Phi ) )
=> ? [X7: a] : ( relational_sat_a_nat @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X7 ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(3)
thf(fact_616_sat_Oelims_I3_J,axiom,
! [X: relational_fmla_a_b,Xa2: product_prod_b_nat > set_list_a,Xb: nat > a] :
( ~ ( relational_sat_a_b @ X @ Xa2 @ Xb )
=> ( ! [R3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ R3 @ Ts2 ) )
=> ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> B3 )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ~ ( relational_sat_a_b @ Phi @ Xa2 @ Xb ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ? [X7: a] : ( relational_sat_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X7 ) ) ) ) ) ) ) ) ) ) ).
% sat.elims(3)
thf(fact_617_fv__cp__foldr1__Disj,axiom,
! [Qs: list_R8263082107343818799la_a_b,A2: set_nat] :
( ( ( relational_cp_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ ( relational_Bool_a_b @ $false ) ) )
!= ( relational_Bool_a_b @ $false ) )
=> ( ! [X5: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X5 @ ( set_Re9104216502384355786la_a_b @ Qs ) )
=> ( ( relati1591879772219623554ed_a_b @ X5 )
& ( ( relational_fv_a_b @ X5 )
= A2 ) ) )
=> ( ( relational_fv_a_b @ ( relational_cp_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ ( relational_Bool_a_b @ $false ) ) ) )
= A2 ) ) ) ).
% fv_cp_foldr1_Disj
thf(fact_618_fv__foldr__Disj,axiom,
! [Qs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Qs @ Q ) )
= ( sup_sup_set_nat @ ( relational_fv_a_b @ Q ) @ ( comple7399068483239264473et_nat @ ( image_8719518604786020652et_nat @ relational_fv_a_b @ ( set_Re9104216502384355786la_a_b @ Qs ) ) ) ) ) ).
% fv_foldr_Disj
thf(fact_619_foldr__Disj__equiv,axiom,
! [Q: relational_fmla_a_b,Qs: list_R8263082107343818799la_a_b,Q2: relational_fmla_a_b,Qs2: list_R8263082107343818799la_a_b] :
( ( ( insert7010464514620295119la_a_b @ Q @ ( set_Re9104216502384355786la_a_b @ Qs ) )
= ( insert7010464514620295119la_a_b @ Q2 @ ( set_Re9104216502384355786la_a_b @ Qs2 ) ) )
=> ( relational_equiv_a_b @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Qs @ Q ) @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Qs2 @ Q2 ) ) ) ).
% foldr_Disj_equiv
thf(fact_620_equiv__refl,axiom,
! [Q: relational_fmla_a_b] : ( relational_equiv_a_b @ Q @ Q ) ).
% equiv_refl
thf(fact_621_fv__terms__set__def,axiom,
( relati4569515538964159125_set_a
= ( ^ [Ts3: list_R6823256787227418703term_a] : ( comple7399068483239264473et_nat @ ( set_set_nat2 @ ( map_Re7922678280114582411et_nat @ relati6004689760767320788_set_a @ Ts3 ) ) ) ) ) ).
% fv_terms_set_def
thf(fact_622_equiv__Neg__cong,axiom,
! [Q: relational_fmla_a_b,Q2: relational_fmla_a_b] :
( ( relational_equiv_a_b @ Q @ Q2 )
=> ( relational_equiv_a_b @ ( relational_Neg_a_b @ Q ) @ ( relational_Neg_a_b @ Q2 ) ) ) ).
% equiv_Neg_cong
thf(fact_623_equiv__Disj__cong,axiom,
! [Q1: relational_fmla_a_b,Q14: relational_fmla_a_b,Q22: relational_fmla_a_b,Q25: relational_fmla_a_b] :
( ( relational_equiv_a_b @ Q1 @ Q14 )
=> ( ( relational_equiv_a_b @ Q22 @ Q25 )
=> ( relational_equiv_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ ( relational_Disj_a_b @ Q14 @ Q25 ) ) ) ) ).
% equiv_Disj_cong
thf(fact_624_equiv__Disj__Assoc,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,Q32: relational_fmla_a_b] : ( relational_equiv_a_b @ ( relational_Disj_a_b @ ( relational_Disj_a_b @ Q1 @ Q22 ) @ Q32 ) @ ( relational_Disj_a_b @ Q1 @ ( relational_Disj_a_b @ Q22 @ Q32 ) ) ) ).
% equiv_Disj_Assoc
thf(fact_625_equiv__Conj__cong,axiom,
! [Q1: relational_fmla_a_b,Q14: relational_fmla_a_b,Q22: relational_fmla_a_b,Q25: relational_fmla_a_b] :
( ( relational_equiv_a_b @ Q1 @ Q14 )
=> ( ( relational_equiv_a_b @ Q22 @ Q25 )
=> ( relational_equiv_a_b @ ( relational_Conj_a_b @ Q1 @ Q22 ) @ ( relational_Conj_a_b @ Q14 @ Q25 ) ) ) ) ).
% equiv_Conj_cong
thf(fact_626_equiv__Exists__cong,axiom,
! [Q: relational_fmla_a_b,Q2: relational_fmla_a_b,X: nat] :
( ( relational_equiv_a_b @ Q @ Q2 )
=> ( relational_equiv_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) @ ( relati591517084277583526ts_a_b @ X @ Q2 ) ) ) ).
% equiv_Exists_cong
thf(fact_627_equiv__trans,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b,Q32: relational_fmla_a_b] :
( ( relational_equiv_a_b @ Q1 @ Q22 )
=> ( ( relational_equiv_a_b @ Q22 @ Q32 )
=> ( relational_equiv_a_b @ Q1 @ Q32 ) ) ) ).
% equiv_trans
thf(fact_628_equiv__sym,axiom,
! [Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] :
( ( relational_equiv_a_b @ Q1 @ Q22 )
=> ( relational_equiv_a_b @ Q22 @ Q1 ) ) ).
% equiv_sym
thf(fact_629_foldr1__Disj__equiv__cong,axiom,
! [Xs: list_R8263082107343818799la_a_b,Ys: list_R8263082107343818799la_a_b,B: relational_fmla_a_b,C2: relational_fmla_a_b] :
( ( list_a2254996211694282183la_a_b @ relational_equiv_a_b @ Xs @ Ys )
=> ( ( relational_equiv_a_b @ B @ C2 )
=> ( relational_equiv_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Xs @ B ) @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Ys @ C2 ) ) ) ) ).
% foldr1_Disj_equiv_cong
thf(fact_630_equiv__cp,axiom,
! [Q: relational_fmla_a_b] : ( relational_equiv_a_b @ ( relational_cp_a_b @ Q ) @ Q ) ).
% equiv_cp
thf(fact_631_equiv__cp__cong,axiom,
! [Q: relational_fmla_a_b,Q2: relational_fmla_a_b] :
( ( relational_equiv_a_b @ Q @ Q2 )
=> ( relational_equiv_a_b @ ( relational_cp_a_b @ Q ) @ ( relational_cp_a_b @ Q2 ) ) ) ).
% equiv_cp_cong
thf(fact_632_Exists__foldr1__Disj,axiom,
! [X: nat,Xs: list_R8263082107343818799la_a_b,B: relational_fmla_a_b] : ( relational_equiv_a_b @ ( relati591517084277583526ts_a_b @ X @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Xs @ B ) ) @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ ( map_Re5057026939262599940la_a_b @ ( relati3989891337220013914ts_a_b @ X ) @ Xs ) @ ( relati3989891337220013914ts_a_b @ X @ B ) ) ) ).
% Exists_foldr1_Disj
thf(fact_633_foldr1__Disj__equiv,axiom,
! [Qs: list_R8263082107343818799la_a_b,Qs2: list_R8263082107343818799la_a_b] :
( ( ( set_Re9104216502384355786la_a_b @ Qs )
= ( set_Re9104216502384355786la_a_b @ Qs2 ) )
=> ( relational_equiv_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ ( relational_Bool_a_b @ $false ) ) @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs2 @ ( relational_Bool_a_b @ $false ) ) ) ) ).
% foldr1_Disj_equiv
thf(fact_634_equiv__Exists__Disj,axiom,
! [X: nat,Q1: relational_fmla_a_b,Q22: relational_fmla_a_b] : ( relational_equiv_a_b @ ( relati591517084277583526ts_a_b @ X @ ( relational_Disj_a_b @ Q1 @ Q22 ) ) @ ( relational_Disj_a_b @ ( relati591517084277583526ts_a_b @ X @ Q1 ) @ ( relati591517084277583526ts_a_b @ X @ Q22 ) ) ) ).
% equiv_Exists_Disj
thf(fact_635_fv__terms__setD,axiom,
! [M: nat,Ts: list_R6823256787227418703term_a] :
( ( member_nat @ M @ ( relati4569515538964159125_set_a @ Ts ) )
=> ( member5466445112152945266term_a @ ( relational_Var_a @ M ) @ ( set_Re3569617851344498910term_a @ Ts ) ) ) ).
% fv_terms_setD
thf(fact_636_fv__terms__setI,axiom,
! [M: nat,Ts: list_R6823256787227418703term_a] :
( ( member5466445112152945266term_a @ ( relational_Var_a @ M ) @ ( set_Re3569617851344498910term_a @ Ts ) )
=> ( member_nat @ M @ ( relati4569515538964159125_set_a @ Ts ) ) ) ).
% fv_terms_setI
thf(fact_637_Exists__nonfree__equiv,axiom,
! [X: nat,Q: relational_fmla_a_b] :
( ~ ( member_nat @ X @ ( relational_fv_a_b @ Q ) )
=> ( relational_equiv_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) @ Q ) ) ).
% Exists_nonfree_equiv
thf(fact_638_equiv__Exists__exists__cong,axiom,
! [Q: relational_fmla_a_b,Q2: relational_fmla_a_b,X: nat] :
( ( relational_equiv_a_b @ Q @ Q2 )
=> ( relational_equiv_a_b @ ( relati591517084277583526ts_a_b @ X @ Q ) @ ( relati3989891337220013914ts_a_b @ X @ Q2 ) ) ) ).
% equiv_Exists_exists_cong
thf(fact_639_foldr__Disj__equiv__cong,axiom,
! [Xs: list_R8263082107343818799la_a_b,Ys: list_R8263082107343818799la_a_b,B: relational_fmla_a_b,C2: relational_fmla_a_b] :
( ( list_a2254996211694282183la_a_b @ relational_equiv_a_b @ Xs @ Ys )
=> ( ( relational_equiv_a_b @ B @ C2 )
=> ( relational_equiv_a_b @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Xs @ B ) @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Ys @ C2 ) ) ) ) ).
% foldr_Disj_equiv_cong
thf(fact_640_Exists__foldr__Disj,axiom,
! [X: nat,Xs: list_R8263082107343818799la_a_b,B: relational_fmla_a_b] : ( relational_equiv_a_b @ ( relati591517084277583526ts_a_b @ X @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Xs @ B ) ) @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ ( map_Re5057026939262599940la_a_b @ ( relati3989891337220013914ts_a_b @ X ) @ Xs ) @ ( relati3989891337220013914ts_a_b @ X @ B ) ) ) ).
% Exists_foldr_Disj
thf(fact_641_fv__foldr1__Disj,axiom,
! [Qs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b] :
( ( ( Qs = nil_Re6358386334527539737la_a_b )
=> ( ( relational_fv_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ Q ) )
= ( relational_fv_a_b @ Q ) ) )
& ( ( Qs != nil_Re6358386334527539737la_a_b )
=> ( ( relational_fv_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ Q ) )
= ( comple7399068483239264473et_nat @ ( image_8719518604786020652et_nat @ relational_fv_a_b @ ( set_Re9104216502384355786la_a_b @ Qs ) ) ) ) ) ) ).
% fv_foldr1_Disj
thf(fact_642_Exists__in__sub__cp__foldr1__Disj,axiom,
! [X: nat,Q2: relational_fmla_a_b,Qs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( relational_cp_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ Q ) ) ) )
=> ( ( ( Qs = nil_Re6358386334527539737la_a_b )
& ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( relational_cp_a_b @ Q ) ) ) )
| ? [X5: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X5 @ ( set_Re9104216502384355786la_a_b @ Qs ) )
& ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( relational_cp_a_b @ X5 ) ) ) ) ) ) ).
% Exists_in_sub_cp_foldr1_Disj
thf(fact_643_fv__EXISTS,axiom,
! [Xs: list_nat,Q: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( relati7004044288120072026TS_a_b @ Xs @ Q ) )
= ( minus_minus_set_nat @ ( relational_fv_a_b @ Q ) @ ( set_nat2 @ Xs ) ) ) ).
% fv_EXISTS
thf(fact_644_list__all2__Nil,axiom,
! [P: relational_term_a > relational_term_a > $o,Ys: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ nil_Re7785829565976577615term_a @ Ys )
= ( Ys = nil_Re7785829565976577615term_a ) ) ).
% list_all2_Nil
thf(fact_645_list__all2__Nil2,axiom,
! [P: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ Xs @ nil_Re7785829565976577615term_a )
= ( Xs = nil_Re7785829565976577615term_a ) ) ).
% list_all2_Nil2
thf(fact_646_sat__foldr1__Disj,axiom,
! [Xs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma: nat > a] :
( ( relational_sat_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Xs @ Q ) @ I3 @ Sigma )
= ( ( ( Xs = nil_Re6358386334527539737la_a_b )
=> ( relational_sat_a_b @ Q @ I3 @ Sigma ) )
& ( ( Xs != nil_Re6358386334527539737la_a_b )
=> ? [X3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X3 @ ( set_Re9104216502384355786la_a_b @ Xs ) )
& ( relational_sat_a_b @ X3 @ I3 @ Sigma ) ) ) ) ) ).
% sat_foldr1_Disj
thf(fact_647_foldr1_Osimps_I2_J,axiom,
! [F: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,Z2: relational_fmla_a_b] :
( ( relati1724936043867567613la_a_b @ F @ nil_Re6358386334527539737la_a_b @ Z2 )
= Z2 ) ).
% foldr1.simps(2)
thf(fact_648_list_Octr__transfer_I1_J,axiom,
! [R: relational_term_a > relational_term_a > $o] : ( list_a3533670403825157575term_a @ R @ nil_Re7785829565976577615term_a @ nil_Re7785829565976577615term_a ) ).
% list.ctr_transfer(1)
thf(fact_649_Exists__in__sub__foldr1__Disj,axiom,
! [X: nat,Q2: relational_fmla_a_b,Qs: list_R8263082107343818799la_a_b,Q: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ Q ) ) )
=> ( ( ( Qs = nil_Re6358386334527539737la_a_b )
& ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ Q ) ) )
| ? [X5: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ X5 @ ( set_Re9104216502384355786la_a_b @ Qs ) )
& ( member4680049679412964150la_a_b @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ ( relational_sub_a_b @ X5 ) ) ) ) ) ).
% Exists_in_sub_foldr1_Disj
thf(fact_650_fv__close,axiom,
! [Q: relational_fmla_a_b] :
( ( relational_fv_a_b @ ( relati7004044288120072026TS_a_b @ ( linord2614967742042102400et_nat @ ( relational_fv_a_b @ Q ) ) @ Q ) )
= bot_bot_set_nat ) ).
% fv_close
thf(fact_651_gen__foldr1__Disj,axiom,
! [X: nat,Qs: list_R8263082107343818799la_a_b,Gs: list_s3671366213839843941la_a_b,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,GG: set_Re381260168593705685la_a_b] :
( ( list_a1880901387755353853la_a_b @ ( relational_gen_a_b @ X ) @ Qs @ Gs )
=> ( ( relational_gen_a_b @ X @ Q @ G )
=> ( ( ( ( Qs = nil_Re6358386334527539737la_a_b )
=> ( GG = G ) )
& ( ( Qs != nil_Re6358386334527539737la_a_b )
=> ( GG
= ( comple8442120529048846632la_a_b
@ ( image_7051608999182166449la_a_b
@ ^ [G4: set_Re381260168593705685la_a_b] : G4
@ ( set_se5111286776497155840la_a_b @ Gs ) ) ) ) ) )
=> ( relational_gen_a_b @ X @ ( relati1724936043867567613la_a_b @ relational_Disj_a_b @ Qs @ Q ) @ GG ) ) ) ) ).
% gen_foldr1_Disj
thf(fact_652_gen__foldr__Disj,axiom,
! [X: nat,Qs: list_R8263082107343818799la_a_b,Gs: list_s3671366213839843941la_a_b,Q: relational_fmla_a_b,G: set_Re381260168593705685la_a_b,GG: set_Re381260168593705685la_a_b] :
( ( list_a1880901387755353853la_a_b @ ( relational_gen_a_b @ X ) @ Qs @ Gs )
=> ( ( relational_gen_a_b @ X @ Q @ G )
=> ( ( GG
= ( sup_su5130108678486352897la_a_b @ G
@ ( comple8442120529048846632la_a_b
@ ( image_7051608999182166449la_a_b
@ ^ [G4: set_Re381260168593705685la_a_b] : G4
@ ( set_se5111286776497155840la_a_b @ Gs ) ) ) ) )
=> ( relational_gen_a_b @ X @ ( foldr_789212930732525799la_a_b @ relational_Disj_a_b @ Qs @ Q ) @ GG ) ) ) ) ).
% gen_foldr_Disj
thf(fact_653_fmla_Oset__cases_I1_J,axiom,
! [E: a,A: relational_fmla_a_b] :
( ( member_a @ E @ ( relati3071123380395136021la_a_b @ A ) )
=> ( ! [Z1: b,Z22: list_R6823256787227418703term_a] :
( ( A
= ( relational_Pred_b_a @ Z1 @ Z22 ) )
=> ! [X5: relational_term_a] :
( ( member5466445112152945266term_a @ X5 @ ( set_Re3569617851344498910term_a @ Z22 ) )
=> ~ ( member_a @ E @ ( relati2096729434547099208term_a @ X5 ) ) ) )
=> ( ! [Z1: nat,Z22: relational_term_a] :
( ( A
= ( relational_Eq_a_b @ Z1 @ Z22 ) )
=> ~ ( member_a @ E @ ( relati2096729434547099208term_a @ Z22 ) ) )
=> ( ! [Z3: relational_fmla_a_b] :
( ( A
= ( relational_Neg_a_b @ Z3 ) )
=> ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z3 ) ) )
=> ( ! [Z1: relational_fmla_a_b] :
( ? [Z22: relational_fmla_a_b] :
( A
= ( relational_Conj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z1 ) ) )
=> ( ! [Z1: relational_fmla_a_b,Z22: relational_fmla_a_b] :
( ( A
= ( relational_Conj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z22 ) ) )
=> ( ! [Z1: relational_fmla_a_b] :
( ? [Z22: relational_fmla_a_b] :
( A
= ( relational_Disj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z1 ) ) )
=> ( ! [Z1: relational_fmla_a_b,Z22: relational_fmla_a_b] :
( ( A
= ( relational_Disj_a_b @ Z1 @ Z22 ) )
=> ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z22 ) ) )
=> ~ ! [Z1: nat,Z22: relational_fmla_a_b] :
( ( A
= ( relati591517084277583526ts_a_b @ Z1 @ Z22 ) )
=> ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).
% fmla.set_cases(1)
thf(fact_654_fmla_Oset__intros_I1_J,axiom,
! [Y3: relational_term_a,X12: list_R6823256787227418703term_a,Ya2: a,X11: b] :
( ( member5466445112152945266term_a @ Y3 @ ( set_Re3569617851344498910term_a @ X12 ) )
=> ( ( member_a @ Ya2 @ ( relati2096729434547099208term_a @ Y3 ) )
=> ( member_a @ Ya2 @ ( relati3071123380395136021la_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) ) ) ) ) ).
% fmla.set_intros(1)
thf(fact_655_term_Orel__refl__strong,axiom,
! [X: relati112041753218324778la_a_b,Ra: relational_fmla_a_b > relational_fmla_a_b > $o] :
( ! [Z3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ Z3 @ ( relati7240241301533008341la_a_b @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( relati4738647720883422732la_a_b @ Ra @ X @ X ) ) ).
% term.rel_refl_strong
thf(fact_656_term_Orel__refl__strong,axiom,
! [X: relational_term_nat,Ra: nat > nat > $o] :
( ! [Z3: nat] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( relati2881564729679077486at_nat @ Ra @ X @ X ) ) ).
% term.rel_refl_strong
thf(fact_657_term_Orel__refl__strong,axiom,
! [X: relational_term_b,Ra: b > b > $o] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( relati376332583554052364rm_b_b @ Ra @ X @ X ) ) ).
% term.rel_refl_strong
thf(fact_658_term_Orel__refl__strong,axiom,
! [X: relati383187284260386255list_a,Ra: list_a > list_a > $o] :
( ! [Z3: list_a] :
( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( relati8847882339280608716list_a @ Ra @ X @ X ) ) ).
% term.rel_refl_strong
thf(fact_659_term_Orel__refl__strong,axiom,
! [X: relational_term_a,Ra: a > a > $o] :
( ! [Z3: a] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( relati3163788165526728396rm_a_a @ Ra @ X @ X ) ) ).
% term.rel_refl_strong
thf(fact_660_term_Orel__mono__strong,axiom,
! [R: nat > nat > $o,X: relational_term_nat,Y3: relational_term_nat,Ra: nat > nat > $o] :
( ( relati2881564729679077486at_nat @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: nat] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X ) )
=> ( ( member_nat @ Yb @ ( relati7416457470477713926rm_nat @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati2881564729679077486at_nat @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_661_term_Orel__mono__strong,axiom,
! [R: nat > b > $o,X: relational_term_nat,Y3: relational_term_b,Ra: nat > b > $o] :
( ( relati6955175908526440929_nat_b @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: b] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X ) )
=> ( ( member_b @ Yb @ ( relati2096729434547099209term_b @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati6955175908526440929_nat_b @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_662_term_Orel__mono__strong,axiom,
! [R: b > nat > $o,X: relational_term_b,Y3: relational_term_nat,Ra: b > nat > $o] :
( ( relati4158688736304548995_b_nat @ R @ X @ Y3 )
=> ( ! [Z3: b,Yb: nat] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X ) )
=> ( ( member_nat @ Yb @ ( relati7416457470477713926rm_nat @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati4158688736304548995_b_nat @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_663_term_Orel__mono__strong,axiom,
! [R: b > b > $o,X: relational_term_b,Y3: relational_term_b,Ra: b > b > $o] :
( ( relati376332583554052364rm_b_b @ R @ X @ Y3 )
=> ( ! [Z3: b,Yb: b] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X ) )
=> ( ( member_b @ Yb @ ( relati2096729434547099209term_b @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati376332583554052364rm_b_b @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_664_term_Orel__mono__strong,axiom,
! [R: nat > a > $o,X: relational_term_nat,Y3: relational_term_a,Ra: nat > a > $o] :
( ( relati6955175908526440928_nat_a @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: a] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X ) )
=> ( ( member_a @ Yb @ ( relati2096729434547099208term_a @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati6955175908526440928_nat_a @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_665_term_Orel__mono__strong,axiom,
! [R: b > a > $o,X: relational_term_b,Y3: relational_term_a,Ra: b > a > $o] :
( ( relati376332583554052363rm_b_a @ R @ X @ Y3 )
=> ( ! [Z3: b,Yb: a] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X ) )
=> ( ( member_a @ Yb @ ( relati2096729434547099208term_a @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati376332583554052363rm_b_a @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_666_term_Orel__mono__strong,axiom,
! [R: a > nat > $o,X: relational_term_a,Y3: relational_term_nat,Ra: a > nat > $o] :
( ( relati2923244407348154498_a_nat @ R @ X @ Y3 )
=> ( ! [Z3: a,Yb: nat] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X ) )
=> ( ( member_nat @ Yb @ ( relati7416457470477713926rm_nat @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati2923244407348154498_a_nat @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_667_term_Orel__mono__strong,axiom,
! [R: a > b > $o,X: relational_term_a,Y3: relational_term_b,Ra: a > b > $o] :
( ( relati3163788165526728397rm_a_b @ R @ X @ Y3 )
=> ( ! [Z3: a,Yb: b] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X ) )
=> ( ( member_b @ Yb @ ( relati2096729434547099209term_b @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati3163788165526728397rm_a_b @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_668_term_Orel__mono__strong,axiom,
! [R: a > a > $o,X: relational_term_a,Y3: relational_term_a,Ra: a > a > $o] :
( ( relati3163788165526728396rm_a_a @ R @ X @ Y3 )
=> ( ! [Z3: a,Yb: a] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X ) )
=> ( ( member_a @ Yb @ ( relati2096729434547099208term_a @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati3163788165526728396rm_a_a @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_669_term_Orel__mono__strong,axiom,
! [R: nat > list_a > $o,X: relational_term_nat,Y3: relati383187284260386255list_a,Ra: nat > list_a > $o] :
( ( relati4525196732223128934list_a @ R @ X @ Y3 )
=> ( ! [Z3: nat,Yb: list_a] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X ) )
=> ( ( member_list_a @ Yb @ ( relati1115505217504806350list_a @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( relati4525196732223128934list_a @ Ra @ X @ Y3 ) ) ) ).
% term.rel_mono_strong
thf(fact_670_term_Orel__cong,axiom,
! [X: relational_term_nat,Ya2: relational_term_nat,Y3: relational_term_nat,Xa2: relational_term_nat,R: nat > nat > $o,Ra: nat > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: nat] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya2 ) )
=> ( ( member_nat @ Yb @ ( relati7416457470477713926rm_nat @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati2881564729679077486at_nat @ R @ X @ Y3 )
= ( relati2881564729679077486at_nat @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_671_term_Orel__cong,axiom,
! [X: relational_term_nat,Ya2: relational_term_nat,Y3: relational_term_b,Xa2: relational_term_b,R: nat > b > $o,Ra: nat > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: b] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya2 ) )
=> ( ( member_b @ Yb @ ( relati2096729434547099209term_b @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati6955175908526440929_nat_b @ R @ X @ Y3 )
= ( relati6955175908526440929_nat_b @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_672_term_Orel__cong,axiom,
! [X: relational_term_b,Ya2: relational_term_b,Y3: relational_term_nat,Xa2: relational_term_nat,R: b > nat > $o,Ra: b > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: b,Yb: nat] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya2 ) )
=> ( ( member_nat @ Yb @ ( relati7416457470477713926rm_nat @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati4158688736304548995_b_nat @ R @ X @ Y3 )
= ( relati4158688736304548995_b_nat @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_673_term_Orel__cong,axiom,
! [X: relational_term_b,Ya2: relational_term_b,Y3: relational_term_b,Xa2: relational_term_b,R: b > b > $o,Ra: b > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: b,Yb: b] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya2 ) )
=> ( ( member_b @ Yb @ ( relati2096729434547099209term_b @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati376332583554052364rm_b_b @ R @ X @ Y3 )
= ( relati376332583554052364rm_b_b @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_674_term_Orel__cong,axiom,
! [X: relational_term_nat,Ya2: relational_term_nat,Y3: relational_term_a,Xa2: relational_term_a,R: nat > a > $o,Ra: nat > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: a] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya2 ) )
=> ( ( member_a @ Yb @ ( relati2096729434547099208term_a @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati6955175908526440928_nat_a @ R @ X @ Y3 )
= ( relati6955175908526440928_nat_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_675_term_Orel__cong,axiom,
! [X: relational_term_b,Ya2: relational_term_b,Y3: relational_term_a,Xa2: relational_term_a,R: b > a > $o,Ra: b > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: b,Yb: a] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya2 ) )
=> ( ( member_a @ Yb @ ( relati2096729434547099208term_a @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati376332583554052363rm_b_a @ R @ X @ Y3 )
= ( relati376332583554052363rm_b_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_676_term_Orel__cong,axiom,
! [X: relational_term_a,Ya2: relational_term_a,Y3: relational_term_nat,Xa2: relational_term_nat,R: a > nat > $o,Ra: a > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: a,Yb: nat] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya2 ) )
=> ( ( member_nat @ Yb @ ( relati7416457470477713926rm_nat @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati2923244407348154498_a_nat @ R @ X @ Y3 )
= ( relati2923244407348154498_a_nat @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_677_term_Orel__cong,axiom,
! [X: relational_term_a,Ya2: relational_term_a,Y3: relational_term_b,Xa2: relational_term_b,R: a > b > $o,Ra: a > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: a,Yb: b] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya2 ) )
=> ( ( member_b @ Yb @ ( relati2096729434547099209term_b @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati3163788165526728397rm_a_b @ R @ X @ Y3 )
= ( relati3163788165526728397rm_a_b @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_678_term_Orel__cong,axiom,
! [X: relational_term_a,Ya2: relational_term_a,Y3: relational_term_a,Xa2: relational_term_a,R: a > a > $o,Ra: a > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: a,Yb: a] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya2 ) )
=> ( ( member_a @ Yb @ ( relati2096729434547099208term_a @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati3163788165526728396rm_a_a @ R @ X @ Y3 )
= ( relati3163788165526728396rm_a_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_679_term_Orel__cong,axiom,
! [X: relational_term_nat,Ya2: relational_term_nat,Y3: relati383187284260386255list_a,Xa2: relati383187284260386255list_a,R: nat > list_a > $o,Ra: nat > list_a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: nat,Yb: list_a] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya2 ) )
=> ( ( member_list_a @ Yb @ ( relati1115505217504806350list_a @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( relati4525196732223128934list_a @ R @ X @ Y3 )
= ( relati4525196732223128934list_a @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% term.rel_cong
thf(fact_680_term_Oset__intros,axiom,
! [X13: relational_fmla_a_b] : ( member4680049679412964150la_a_b @ X13 @ ( relati7240241301533008341la_a_b @ ( relati3340789340644911146la_a_b @ X13 ) ) ) ).
% term.set_intros
thf(fact_681_term_Oset__intros,axiom,
! [X13: nat] : ( member_nat @ X13 @ ( relati7416457470477713926rm_nat @ ( relational_Const_nat @ X13 ) ) ) ).
% term.set_intros
thf(fact_682_term_Oset__intros,axiom,
! [X13: b] : ( member_b @ X13 @ ( relati2096729434547099209term_b @ ( relational_Const_b @ X13 ) ) ) ).
% term.set_intros
thf(fact_683_term_Oset__intros,axiom,
! [X13: list_a] : ( member_list_a @ X13 @ ( relati1115505217504806350list_a @ ( relati8210483018086767673list_a @ X13 ) ) ) ).
% term.set_intros
thf(fact_684_term_Oset__intros,axiom,
! [X13: a] : ( member_a @ X13 @ ( relati2096729434547099208term_a @ ( relational_Const_a @ X13 ) ) ) ).
% term.set_intros
thf(fact_685_term_Oset__cases,axiom,
! [E: relational_fmla_a_b,A: relati112041753218324778la_a_b] :
( ( member4680049679412964150la_a_b @ E @ ( relati7240241301533008341la_a_b @ A ) )
=> ( A
= ( relati3340789340644911146la_a_b @ E ) ) ) ).
% term.set_cases
thf(fact_686_term_Oset__cases,axiom,
! [E: nat,A: relational_term_nat] :
( ( member_nat @ E @ ( relati7416457470477713926rm_nat @ A ) )
=> ( A
= ( relational_Const_nat @ E ) ) ) ).
% term.set_cases
thf(fact_687_term_Oset__cases,axiom,
! [E: b,A: relational_term_b] :
( ( member_b @ E @ ( relati2096729434547099209term_b @ A ) )
=> ( A
= ( relational_Const_b @ E ) ) ) ).
% term.set_cases
thf(fact_688_term_Oset__cases,axiom,
! [E: list_a,A: relati383187284260386255list_a] :
( ( member_list_a @ E @ ( relati1115505217504806350list_a @ A ) )
=> ( A
= ( relati8210483018086767673list_a @ E ) ) ) ).
% term.set_cases
thf(fact_689_term_Oset__cases,axiom,
! [E: a,A: relational_term_a] :
( ( member_a @ E @ ( relati2096729434547099208term_a @ A ) )
=> ( A
= ( relational_Const_a @ E ) ) ) ).
% term.set_cases
thf(fact_690_finite__set__term,axiom,
! [T: relational_term_a] : ( finite_finite_a @ ( relati2096729434547099208term_a @ T ) ) ).
% finite_set_term
thf(fact_691_fmla_Oset__intros_I2_J,axiom,
! [Yb2: a,X322: relational_term_a,X312: nat] :
( ( member_a @ Yb2 @ ( relati2096729434547099208term_a @ X322 ) )
=> ( member_a @ Yb2 @ ( relati3071123380395136021la_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ) ) ).
% fmla.set_intros(2)
thf(fact_692_fmla_Osimps_I122_J,axiom,
! [X312: nat,X322: relational_term_a] :
( ( relati3071123380395136021la_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) )
= ( relati2096729434547099208term_a @ X322 ) ) ).
% fmla.simps(122)
thf(fact_693_fmla_Oset__intros_I8_J,axiom,
! [Ym: a,X72: relational_fmla_a_b,X71: nat] :
( ( member_a @ Ym @ ( relati3071123380395136021la_a_b @ X72 ) )
=> ( member_a @ Ym @ ( relati3071123380395136021la_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ) ) ).
% fmla.set_intros(8)
thf(fact_694_fmla_Osimps_I126_J,axiom,
! [X71: nat,X72: relational_fmla_a_b] :
( ( relati3071123380395136021la_a_b @ ( relati591517084277583526ts_a_b @ X71 @ X72 ) )
= ( relati3071123380395136021la_a_b @ X72 ) ) ).
% fmla.simps(126)
thf(fact_695_fmla_Oset__intros_I4_J,axiom,
! [Ye: a,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( member_a @ Ye @ ( relati3071123380395136021la_a_b @ X51 ) )
=> ( member_a @ Ye @ ( relati3071123380395136021la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).
% fmla.set_intros(4)
thf(fact_696_fmla_Oset__intros_I5_J,axiom,
! [Yg: a,X52: relational_fmla_a_b,X51: relational_fmla_a_b] :
( ( member_a @ Yg @ ( relati3071123380395136021la_a_b @ X52 ) )
=> ( member_a @ Yg @ ( relati3071123380395136021la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).
% fmla.set_intros(5)
thf(fact_697_fmla_Oset__intros_I6_J,axiom,
! [Yi: a,X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( member_a @ Yi @ ( relati3071123380395136021la_a_b @ X61 ) )
=> ( member_a @ Yi @ ( relati3071123380395136021la_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ) ) ).
% fmla.set_intros(6)
thf(fact_698_fmla_Oset__intros_I7_J,axiom,
! [Yk: a,X62: relational_fmla_a_b,X61: relational_fmla_a_b] :
( ( member_a @ Yk @ ( relati3071123380395136021la_a_b @ X62 ) )
=> ( member_a @ Yk @ ( relati3071123380395136021la_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) ) ) ) ).
% fmla.set_intros(7)
thf(fact_699_fmla_Oset__intros_I3_J,axiom,
! [Yc: a,X4: relational_fmla_a_b] :
( ( member_a @ Yc @ ( relati3071123380395136021la_a_b @ X4 ) )
=> ( member_a @ Yc @ ( relati3071123380395136021la_a_b @ ( relational_Neg_a_b @ X4 ) ) ) ) ).
% fmla.set_intros(3)
thf(fact_700_fmla_Osimps_I123_J,axiom,
! [X4: relational_fmla_a_b] :
( ( relati3071123380395136021la_a_b @ ( relational_Neg_a_b @ X4 ) )
= ( relati3071123380395136021la_a_b @ X4 ) ) ).
% fmla.simps(123)
thf(fact_701_fmla_Oset__sel_I2_J,axiom,
! [A: relational_fmla_a_b,Xb: a] :
( ( relational_is_Eq_a_b @ A )
=> ( ( member_a @ Xb @ ( relati2096729434547099208term_a @ ( relati1832481647827092069q2_a_b @ A ) ) )
=> ( member_a @ Xb @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).
% fmla.set_sel(2)
thf(fact_702_term_Omap__ident__strong,axiom,
! [T: relati112041753218324778la_a_b,F: relational_fmla_a_b > relational_fmla_a_b] :
( ! [Z3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ Z3 @ ( relati7240241301533008341la_a_b @ T ) )
=> ( ( F @ Z3 )
= Z3 ) )
=> ( ( relati8623550108501193999la_a_b @ F @ T )
= T ) ) ).
% term.map_ident_strong
thf(fact_703_term_Omap__ident__strong,axiom,
! [T: relational_term_nat,F: nat > nat] :
( ! [Z3: nat] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ T ) )
=> ( ( F @ Z3 )
= Z3 ) )
=> ( ( relati2575597170284168561at_nat @ F @ T )
= T ) ) ).
% term.map_ident_strong
thf(fact_704_term_Omap__ident__strong,axiom,
! [T: relational_term_b,F: b > b] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ T ) )
=> ( ( F @ Z3 )
= Z3 ) )
=> ( ( relati797865177883955343rm_b_b @ F @ T )
= T ) ) ).
% term.map_ident_strong
thf(fact_705_term_Omap__ident__strong,axiom,
! [T: relati383187284260386255list_a,F: list_a > list_a] :
( ! [Z3: list_a] :
( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ T ) )
=> ( ( F @ Z3 )
= Z3 ) )
=> ( ( relati6186803337415672399list_a @ F @ T )
= T ) ) ).
% term.map_ident_strong
thf(fact_706_term_Omap__ident__strong,axiom,
! [T: relational_term_a,F: a > a] :
( ! [Z3: a] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ T ) )
=> ( ( F @ Z3 )
= Z3 ) )
=> ( ( relati3585320759856631375rm_a_a @ F @ T )
= T ) ) ).
% term.map_ident_strong
thf(fact_707_fmla_Osimps_I120_J,axiom,
! [X11: b,X12: list_R6823256787227418703term_a] :
( ( relati3071123380395136021la_a_b @ ( relational_Pred_b_a @ X11 @ X12 ) )
= ( comple2307003609928055243_set_a @ ( image_1080223610614215258_set_a @ relati2096729434547099208term_a @ ( set_Re3569617851344498910term_a @ X12 ) ) ) ) ).
% fmla.simps(120)
thf(fact_708_fmla_Oset__sel_I1_J,axiom,
! [A: relational_fmla_a_b,X: relational_term_a,Xa2: a] :
( ( relati3644702733014758741ed_a_b @ A )
=> ( ( member5466445112152945266term_a @ X @ ( set_Re3569617851344498910term_a @ ( relati5687822700427945008d2_a_b @ A ) ) )
=> ( ( member_a @ Xa2 @ ( relati2096729434547099208term_a @ X ) )
=> ( member_a @ Xa2 @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ) ).
% fmla.set_sel(1)
thf(fact_709_fmla_Osimps_I121_J,axiom,
! [X2: $o] :
( ( relati3071123380395136021la_a_b @ ( relational_Bool_a_b @ X2 ) )
= bot_bot_set_a ) ).
% fmla.simps(121)
thf(fact_710_fmla_Osimps_I125_J,axiom,
! [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
( ( relati3071123380395136021la_a_b @ ( relational_Disj_a_b @ X61 @ X62 ) )
= ( sup_sup_set_a @ ( relati3071123380395136021la_a_b @ X61 ) @ ( relati3071123380395136021la_a_b @ X62 ) ) ) ).
% fmla.simps(125)
thf(fact_711_fmla_Osimps_I124_J,axiom,
! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
( ( relati3071123380395136021la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
= ( sup_sup_set_a @ ( relati3071123380395136021la_a_b @ X51 ) @ ( relati3071123380395136021la_a_b @ X52 ) ) ) ).
% fmla.simps(124)
thf(fact_712_fmla_Oset__map_I1_J,axiom,
! [F1: a > a,F2: b > b,V: relational_fmla_a_b] :
( ( relati3071123380395136021la_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ V ) )
= ( image_a_a @ F1 @ ( relati3071123380395136021la_a_b @ V ) ) ) ).
% fmla.set_map(1)
thf(fact_713_fmla_Orel__refl__strong,axiom,
! [X: relati7126052417554554232at_nat,R1a: nat > nat > $o,R2a: nat > nat > $o] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati3787705992210192720at_nat @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_714_fmla_Orel__refl__strong,axiom,
! [X: relati3061873246650996333_nat_b,R1a: nat > nat > $o,R2a: b > b > $o] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati4008535345494810862at_b_b @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_715_fmla_Orel__refl__strong,axiom,
! [X: relati3061873242347767532_nat_a,R1a: nat > nat > $o,R2a: a > a > $o] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati6795990927467486894at_a_a @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_716_fmla_Orel__refl__strong,axiom,
! [X: relati1059154107580485063_b_nat,R1a: b > b > $o,R2a: nat > nat > $o] :
( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati700162154543277371_b_nat @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati6801122105465879022at_nat @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_717_fmla_Orel__refl__strong,axiom,
! [X: relational_fmla_b_b,R1a: b > b > $o,R2a: b > b > $o] :
( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459988la_b_b @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati6320320224700598924_b_b_b @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_718_fmla_Orel__refl__strong,axiom,
! [X: relational_fmla_b_a,R1a: b > b > $o,R2a: a > a > $o] :
( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459987la_b_a @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati9107775806673274956_b_a_a @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_719_fmla_Orel__refl__strong,axiom,
! [X: relati9047081815478866374_a_nat,R1a: a > a > $o,R2a: nat > nat > $o] :
( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati8688089862441658682_a_nat @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati1061155776830437294at_nat @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_720_fmla_Orel__refl__strong,axiom,
! [X: relational_fmla_a_a,R1a: a > a > $o,R2a: a > a > $o] :
( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136020la_a_a @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati2023595154190345740_a_a_a @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_721_fmla_Orel__refl__strong,axiom,
! [X: relational_fmla_a_b,R1a: a > a > $o,R2a: b > b > $o] :
( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136021la_a_b @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati8459511609072445516_a_b_b @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_722_fmla_Orel__refl__strong,axiom,
! [X: relati6521690034043994866list_a,R1a: nat > nat > $o,R2a: list_a > list_a > $o] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3899910203474895390list_a @ X ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z22: list_a] :
( ( member_list_a @ Z22 @ ( relati3314577606465187421list_a @ X ) )
=> ( R2a @ Z22 @ Z22 ) )
=> ( relati4686781790491089838list_a @ R1a @ R2a @ X @ X ) ) ) ).
% fmla.rel_refl_strong
thf(fact_723_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: nat > nat > $o,X: relati7126052417554554232at_nat,Y3: relati7126052417554554232at_nat,R1a: nat > nat > $o,R2a: nat > nat > $o] :
( ( relati3787705992210192720at_nat @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ X ) )
=> ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X ) )
=> ( ( member_nat @ Y22 @ ( relati2567137625159299127at_nat @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati3787705992210192720at_nat @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_724_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: nat > b > $o,X: relati7126052417554554232at_nat,Y3: relati3061873246650996333_nat_b,R1a: nat > nat > $o,R2a: nat > b > $o] :
( ( relati2215349188705123711_nat_b @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ X ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: b] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X ) )
=> ( ( member_b @ Y22 @ ( relati410893084775174744_nat_b @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati2215349188705123711_nat_b @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_725_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: nat > a > $o,X: relati7126052417554554232at_nat,Y3: relati3061873242347767532_nat_a,R1a: nat > nat > $o,R2a: nat > a > $o] :
( ( relati2215349188705123710_nat_a @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ X ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: a] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X ) )
=> ( ( member_a @ Y22 @ ( relati410893084775174743_nat_a @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati2215349188705123710_nat_a @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_726_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: b > nat > $o,X: relati3061873246650996333_nat_b,Y3: relati7126052417554554232at_nat,R1a: nat > nat > $o,R2a: b > nat > $o] :
( ( relati8642234053338007585_b_nat @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ X ) )
=> ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: b,Y22: nat] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X ) )
=> ( ( member_nat @ Y22 @ ( relati2567137625159299127at_nat @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati8642234053338007585_b_nat @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_727_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: b > b > $o,X: relati3061873246650996333_nat_b,Y3: relati3061873246650996333_nat_b,R1a: nat > nat > $o,R2a: b > b > $o] :
( ( relati4008535345494810862at_b_b @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ X ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: b,Y22: b] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X ) )
=> ( ( member_b @ Y22 @ ( relati410893084775174744_nat_b @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati4008535345494810862at_b_b @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_728_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: b > a > $o,X: relati3061873246650996333_nat_b,Y3: relati3061873242347767532_nat_a,R1a: nat > nat > $o,R2a: b > a > $o] :
( ( relati4008535345494810861at_b_a @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ X ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: b,Y22: a] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X ) )
=> ( ( member_a @ Y22 @ ( relati410893084775174743_nat_a @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati4008535345494810861at_b_a @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_729_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: a > nat > $o,X: relati3061873242347767532_nat_a,Y3: relati7126052417554554232at_nat,R1a: nat > nat > $o,R2a: a > nat > $o] :
( ( relati7406789724381613088_a_nat @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ X ) )
=> ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: a,Y22: nat] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X ) )
=> ( ( member_nat @ Y22 @ ( relati2567137625159299127at_nat @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati7406789724381613088_a_nat @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_730_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: a > b > $o,X: relati3061873242347767532_nat_a,Y3: relati3061873246650996333_nat_b,R1a: nat > nat > $o,R2a: a > b > $o] :
( ( relati6795990927467486895at_a_b @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ X ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: a,Y22: b] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X ) )
=> ( ( member_b @ Y22 @ ( relati410893084775174744_nat_b @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati6795990927467486895at_a_b @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_731_fmla_Orel__mono__strong,axiom,
! [R1: nat > nat > $o,R2: a > a > $o,X: relati3061873242347767532_nat_a,Y3: relati3061873242347767532_nat_a,R1a: nat > nat > $o,R2a: a > a > $o] :
( ( relati6795990927467486894at_a_a @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ X ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: a,Y22: a] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X ) )
=> ( ( member_a @ Y22 @ ( relati410893084775174743_nat_a @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati6795990927467486894at_a_a @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_732_fmla_Orel__mono__strong,axiom,
! [R1: nat > b > $o,R2: nat > nat > $o,X: relati7126052417554554232at_nat,Y3: relati1059154107580485063_b_nat,R1a: nat > b > $o,R2a: nat > nat > $o] :
( ( relati8728868609221888707at_nat @ R1 @ R2 @ X @ Y3 )
=> ( ! [Z1: nat,Y1: b] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ X ) )
=> ( ( member_b @ Y1 @ ( relati700162154543277371_b_nat @ Y3 ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X ) )
=> ( ( member_nat @ Y22 @ ( relati6837777949408058618_b_nat @ Y3 ) )
=> ( ( R2 @ Z22 @ Y22 )
=> ( R2a @ Z22 @ Y22 ) ) ) )
=> ( relati8728868609221888707at_nat @ R1a @ R2a @ X @ Y3 ) ) ) ) ).
% fmla.rel_mono_strong
thf(fact_733_fmla_Orel__cong,axiom,
! [X: relati7126052417554554232at_nat,Ya2: relati7126052417554554232at_nat,Y3: relati7126052417554554232at_nat,Xa2: relati7126052417554554232at_nat,R1: nat > nat > $o,R1a: nat > nat > $o,R2: nat > nat > $o,R2a: nat > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya2 ) )
=> ( ( member_nat @ Y22 @ ( relati2567137625159299127at_nat @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X @ Y3 )
= ( relati3787705992210192720at_nat @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_734_fmla_Orel__cong,axiom,
! [X: relati7126052417554554232at_nat,Ya2: relati7126052417554554232at_nat,Y3: relati3061873246650996333_nat_b,Xa2: relati3061873246650996333_nat_b,R1: nat > nat > $o,R1a: nat > nat > $o,R2: nat > b > $o,R2a: nat > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: b] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya2 ) )
=> ( ( member_b @ Y22 @ ( relati410893084775174744_nat_b @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati2215349188705123711_nat_b @ R1 @ R2 @ X @ Y3 )
= ( relati2215349188705123711_nat_b @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_735_fmla_Orel__cong,axiom,
! [X: relati7126052417554554232at_nat,Ya2: relati7126052417554554232at_nat,Y3: relati3061873242347767532_nat_a,Xa2: relati3061873242347767532_nat_a,R1: nat > nat > $o,R1a: nat > nat > $o,R2: nat > a > $o,R2a: nat > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: a] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya2 ) )
=> ( ( member_a @ Y22 @ ( relati410893084775174743_nat_a @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati2215349188705123710_nat_a @ R1 @ R2 @ X @ Y3 )
= ( relati2215349188705123710_nat_a @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_736_fmla_Orel__cong,axiom,
! [X: relati3061873246650996333_nat_b,Ya2: relati3061873246650996333_nat_b,Y3: relati7126052417554554232at_nat,Xa2: relati7126052417554554232at_nat,R1: nat > nat > $o,R1a: nat > nat > $o,R2: b > nat > $o,R2a: b > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: b,Y22: nat] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya2 ) )
=> ( ( member_nat @ Y22 @ ( relati2567137625159299127at_nat @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati8642234053338007585_b_nat @ R1 @ R2 @ X @ Y3 )
= ( relati8642234053338007585_b_nat @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_737_fmla_Orel__cong,axiom,
! [X: relati3061873246650996333_nat_b,Ya2: relati3061873246650996333_nat_b,Y3: relati3061873246650996333_nat_b,Xa2: relati3061873246650996333_nat_b,R1: nat > nat > $o,R1a: nat > nat > $o,R2: b > b > $o,R2a: b > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: b,Y22: b] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya2 ) )
=> ( ( member_b @ Y22 @ ( relati410893084775174744_nat_b @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati4008535345494810862at_b_b @ R1 @ R2 @ X @ Y3 )
= ( relati4008535345494810862at_b_b @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_738_fmla_Orel__cong,axiom,
! [X: relati3061873246650996333_nat_b,Ya2: relati3061873246650996333_nat_b,Y3: relati3061873242347767532_nat_a,Xa2: relati3061873242347767532_nat_a,R1: nat > nat > $o,R1a: nat > nat > $o,R2: b > a > $o,R2a: b > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: b,Y22: a] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya2 ) )
=> ( ( member_a @ Y22 @ ( relati410893084775174743_nat_a @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati4008535345494810861at_b_a @ R1 @ R2 @ X @ Y3 )
= ( relati4008535345494810861at_b_a @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_739_fmla_Orel__cong,axiom,
! [X: relati3061873242347767532_nat_a,Ya2: relati3061873242347767532_nat_a,Y3: relati7126052417554554232at_nat,Xa2: relati7126052417554554232at_nat,R1: nat > nat > $o,R1a: nat > nat > $o,R2: a > nat > $o,R2a: a > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: a,Y22: nat] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya2 ) )
=> ( ( member_nat @ Y22 @ ( relati2567137625159299127at_nat @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati7406789724381613088_a_nat @ R1 @ R2 @ X @ Y3 )
= ( relati7406789724381613088_a_nat @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_740_fmla_Orel__cong,axiom,
! [X: relati3061873242347767532_nat_a,Ya2: relati3061873242347767532_nat_a,Y3: relati3061873246650996333_nat_b,Xa2: relati3061873246650996333_nat_b,R1: nat > nat > $o,R1a: nat > nat > $o,R2: a > b > $o,R2a: a > b > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: a,Y22: b] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya2 ) )
=> ( ( member_b @ Y22 @ ( relati410893084775174744_nat_b @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati6795990927467486895at_a_b @ R1 @ R2 @ X @ Y3 )
= ( relati6795990927467486895at_a_b @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_741_fmla_Orel__cong,axiom,
! [X: relati3061873242347767532_nat_a,Ya2: relati3061873242347767532_nat_a,Y3: relati3061873242347767532_nat_a,Xa2: relati3061873242347767532_nat_a,R1: nat > nat > $o,R1a: nat > nat > $o,R2: a > a > $o,R2a: a > a > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ Ya2 ) )
=> ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: a,Y22: a] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya2 ) )
=> ( ( member_a @ Y22 @ ( relati410893084775174743_nat_a @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati6795990927467486894at_a_a @ R1 @ R2 @ X @ Y3 )
= ( relati6795990927467486894at_a_a @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_742_fmla_Orel__cong,axiom,
! [X: relati7126052417554554232at_nat,Ya2: relati7126052417554554232at_nat,Y3: relati1059154107580485063_b_nat,Xa2: relati1059154107580485063_b_nat,R1: nat > b > $o,R1a: nat > b > $o,R2: nat > nat > $o,R2a: nat > nat > $o] :
( ( X = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: nat,Y1: b] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ Ya2 ) )
=> ( ( member_b @ Y1 @ ( relati700162154543277371_b_nat @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z22: nat,Y22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya2 ) )
=> ( ( member_nat @ Y22 @ ( relati6837777949408058618_b_nat @ Xa2 ) )
=> ( ( R2 @ Z22 @ Y22 )
= ( R2a @ Z22 @ Y22 ) ) ) )
=> ( ( relati8728868609221888707at_nat @ R1 @ R2 @ X @ Y3 )
= ( relati8728868609221888707at_nat @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% fmla.rel_cong
thf(fact_743_fmla_Omap__ident__strong,axiom,
! [T: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati9000828793121449555at_nat @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_744_fmla_Omap__ident__strong,axiom,
! [T: relati3061873246650996333_nat_b,F1: nat > nat,F2: b > b] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati4279548223302543473at_b_b @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_745_fmla_Omap__ident__strong,axiom,
! [T: relati3061873242347767532_nat_a,F1: nat > nat,F2: a > a] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati7067003805275219505at_a_a @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_746_fmla_Omap__ident__strong,axiom,
! [T: relati1059154107580485063_b_nat,F1: b > b,F2: nat > nat] :
( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati700162154543277371_b_nat @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati7072134983273611633at_nat @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_747_fmla_Omap__ident__strong,axiom,
! [T: relational_fmla_b_b,F1: b > b,F2: b > b] :
( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459988la_b_b @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati2381659108026109071_b_b_b @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_748_fmla_Omap__ident__strong,axiom,
! [T: relational_fmla_b_a,F1: b > b,F2: a > a] :
( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459987la_b_a @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati5169114689998785103_b_a_a @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_749_fmla_Omap__ident__strong,axiom,
! [T: relati9047081815478866374_a_nat,F1: a > a,F2: nat > nat] :
( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati8688089862441658682_a_nat @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati1332168654638169905at_nat @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_750_fmla_Omap__ident__strong,axiom,
! [T: relational_fmla_a_a,F1: a > a,F2: a > a] :
( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136020la_a_a @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati7308306074370631695_a_a_a @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_751_fmla_Omap__ident__strong,axiom,
! [T: relational_fmla_a_b,F1: a > a,F2: b > b] :
( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136021la_a_b @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_752_fmla_Omap__ident__strong,axiom,
! [T: relati6521690034043994866list_a,F1: nat > nat,F2: list_a > list_a] :
( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3899910203474895390list_a @ T ) )
=> ( ( F1 @ Z1 )
= Z1 ) )
=> ( ! [Z22: list_a] :
( ( member_list_a @ Z22 @ ( relati3314577606465187421list_a @ T ) )
=> ( ( F2 @ Z22 )
= Z22 ) )
=> ( ( relati4590563632004032561list_a @ F1 @ F2 @ T )
= T ) ) ) ).
% fmla.map_ident_strong
thf(fact_753_fmla_Oinj__map__strong,axiom,
! [X: relational_fmla_a_b,Xa2: relational_fmla_a_b,F1: a > a,F1a: a > a,F2: b > b,F2a: b > b] :
( ! [Z1: a,Z1a: a] :
( ( member_a @ Z1 @ ( relati3071123380395136021la_a_b @ X ) )
=> ( ( member_a @ Z1a @ ( relati3071123380395136021la_a_b @ Xa2 ) )
=> ( ( ( F1 @ Z1 )
= ( F1a @ Z1a ) )
=> ( Z1 = Z1a ) ) ) )
=> ( ! [Z22: b,Z2a: b] :
( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X ) )
=> ( ( member_b @ Z2a @ ( relati8924981150291758614la_a_b @ Xa2 ) )
=> ( ( ( F2 @ Z22 )
= ( F2a @ Z2a ) )
=> ( Z22 = Z2a ) ) ) )
=> ( ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X )
= ( relati4520850492397955663_a_b_b @ F1a @ F2a @ Xa2 ) )
=> ( X = Xa2 ) ) ) ) ).
% fmla.inj_map_strong
thf(fact_754_fmla_Omap__cong0,axiom,
! [X: relational_fmla_a_b,F1: a > a,G1: a > a,F2: b > b,G22: b > b] :
( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136021la_a_b @ X ) )
=> ( ( F1 @ Z1 )
= ( G1 @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X ) )
=> ( ( F2 @ Z22 )
= ( G22 @ Z22 ) ) )
=> ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X )
= ( relati4520850492397955663_a_b_b @ G1 @ G22 @ X ) ) ) ) ).
% fmla.map_cong0
thf(fact_755_fmla_Omap__cong,axiom,
! [X: relational_fmla_a_b,Ya2: relational_fmla_a_b,F1: a > a,G1: a > a,F2: b > b,G22: b > b] :
( ( X = Ya2 )
=> ( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136021la_a_b @ Ya2 ) )
=> ( ( F1 @ Z1 )
= ( G1 @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ Ya2 ) )
=> ( ( F2 @ Z22 )
= ( G22 @ Z22 ) ) )
=> ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X )
= ( relati4520850492397955663_a_b_b @ G1 @ G22 @ Ya2 ) ) ) ) ) ).
% fmla.map_cong
thf(fact_756_fmla_Oset__sel_I7_J,axiom,
! [A: relational_fmla_a_b,Xk: a] :
( ( relati5350680195807439568sj_a_b @ A )
=> ( ( member_a @ Xk @ ( relati3071123380395136021la_a_b @ ( relati8930481278502636917j2_a_b @ A ) ) )
=> ( member_a @ Xk @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).
% fmla.set_sel(7)
thf(fact_757_fmla_Oset__sel_I6_J,axiom,
! [A: relational_fmla_a_b,Xi: a] :
( ( relati5350680195807439568sj_a_b @ A )
=> ( ( member_a @ Xi @ ( relati3071123380395136021la_a_b @ ( relati3334262663314506228j1_a_b @ A ) ) )
=> ( member_a @ Xi @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).
% fmla.set_sel(6)
thf(fact_758_fmla_Oset__sel_I5_J,axiom,
! [A: relational_fmla_a_b,Xg: a] :
( ( relati8168519172193746908nj_a_b @ A )
=> ( ( member_a @ Xg @ ( relati3071123380395136021la_a_b @ ( relati1527130600461089641j2_a_b @ A ) ) )
=> ( member_a @ Xg @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).
% fmla.set_sel(5)
thf(fact_759_fmla_Oset__sel_I4_J,axiom,
! [A: relational_fmla_a_b,Xe: a] :
( ( relati8168519172193746908nj_a_b @ A )
=> ( ( member_a @ Xe @ ( relati3071123380395136021la_a_b @ ( relati5154284022127734760j1_a_b @ A ) ) )
=> ( member_a @ Xe @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).
% fmla.set_sel(4)
thf(fact_760_fmla_Oset__sel_I3_J,axiom,
! [A: relational_fmla_a_b,Xc: a] :
( ( relati4321004860440572638eg_a_b @ A )
=> ( ( member_a @ Xc @ ( relati3071123380395136021la_a_b @ ( relati5982302313924697647eg_a_b @ A ) ) )
=> ( member_a @ Xc @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).
% fmla.set_sel(3)
thf(fact_761_fmla_Oset__sel_I8_J,axiom,
! [A: relational_fmla_a_b,Xm: a] :
( ( relati5212983245281121968ts_a_b @ A )
=> ( ( member_a @ Xm @ ( relati3071123380395136021la_a_b @ ( relati5591445451228332309s2_a_b @ A ) ) )
=> ( member_a @ Xm @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).
% fmla.set_sel(8)
thf(fact_762_Relational__Calculus_Oterm_Osimps_I16_J,axiom,
! [X2: nat] :
( ( relati7240241301533008341la_a_b @ ( relati2528351936964124430la_a_b @ X2 ) )
= bot_bo4495933725496725865la_a_b ) ).
% Relational_Calculus.term.simps(16)
thf(fact_763_Relational__Calculus_Oterm_Osimps_I16_J,axiom,
! [X2: nat] :
( ( relati2096729434547099209term_b @ ( relational_Var_b @ X2 ) )
= bot_bot_set_b ) ).
% Relational_Calculus.term.simps(16)
thf(fact_764_Relational__Calculus_Oterm_Osimps_I16_J,axiom,
! [X2: nat] :
( ( relati7416457470477713926rm_nat @ ( relational_Var_nat @ X2 ) )
= bot_bot_set_nat ) ).
% Relational_Calculus.term.simps(16)
thf(fact_765_Relational__Calculus_Oterm_Osimps_I16_J,axiom,
! [X2: nat] :
( ( relati2096729434547099208term_a @ ( relational_Var_a @ X2 ) )
= bot_bot_set_a ) ).
% Relational_Calculus.term.simps(16)
thf(fact_766_term_Oset__map,axiom,
! [F: relational_fmla_a_b > relational_fmla_a_b,V: relati112041753218324778la_a_b] :
( ( relati7240241301533008341la_a_b @ ( relati8623550108501193999la_a_b @ F @ V ) )
= ( image_6790371041703824709la_a_b @ F @ ( relati7240241301533008341la_a_b @ V ) ) ) ).
% term.set_map
thf(fact_767_term_Oset__map,axiom,
! [F: a > a,V: relational_term_a] :
( ( relati2096729434547099208term_a @ ( relati3585320759856631375rm_a_a @ F @ V ) )
= ( image_a_a @ F @ ( relati2096729434547099208term_a @ V ) ) ) ).
% term.set_map
thf(fact_768_Relational__Calculus_Oterm_Osimps_I15_J,axiom,
! [X13: relational_fmla_a_b] :
( ( relati7240241301533008341la_a_b @ ( relati3340789340644911146la_a_b @ X13 ) )
= ( insert7010464514620295119la_a_b @ X13 @ bot_bo4495933725496725865la_a_b ) ) ).
% Relational_Calculus.term.simps(15)
thf(fact_769_Relational__Calculus_Oterm_Osimps_I15_J,axiom,
! [X13: b] :
( ( relati2096729434547099209term_b @ ( relational_Const_b @ X13 ) )
= ( insert_b @ X13 @ bot_bot_set_b ) ) ).
% Relational_Calculus.term.simps(15)
thf(fact_770_Relational__Calculus_Oterm_Osimps_I15_J,axiom,
! [X13: nat] :
( ( relati7416457470477713926rm_nat @ ( relational_Const_nat @ X13 ) )
= ( insert_nat @ X13 @ bot_bot_set_nat ) ) ).
% Relational_Calculus.term.simps(15)
thf(fact_771_Relational__Calculus_Oterm_Osimps_I15_J,axiom,
! [X13: a] :
( ( relati2096729434547099208term_a @ ( relational_Const_a @ X13 ) )
= ( insert_a @ X13 @ bot_bot_set_a ) ) ).
% Relational_Calculus.term.simps(15)
thf(fact_772_Relational__Calculus_Oequiv__def,axiom,
( relational_equiv_a_b
= ( ^ [Q13: relational_fmla_a_b,Q24: relational_fmla_a_b] :
! [I4: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
( ( finite_finite_a @ ( relational_adom_b_a @ I4 ) )
=> ( ( relational_sat_a_b @ Q13 @ I4 @ Sigma3 )
= ( relational_sat_a_b @ Q24 @ I4 @ Sigma3 ) ) ) ) ) ).
% Relational_Calculus.equiv_def
thf(fact_773_finite__fv__term__set,axiom,
! [T: relational_term_a] : ( finite_finite_nat @ ( relati6004689760767320788_set_a @ T ) ) ).
% finite_fv_term_set
thf(fact_774_finite__fv,axiom,
! [Phi2: relational_fmla_a_b] : ( finite_finite_nat @ ( relational_fv_a_b @ Phi2 ) ) ).
% finite_fv
thf(fact_775_finite__fv__terms__set,axiom,
! [Ts: list_R6823256787227418703term_a] : ( finite_finite_nat @ ( relati4569515538964159125_set_a @ Ts ) ) ).
% finite_fv_terms_set
thf(fact_776_sat_Opelims_I3_J,axiom,
! [X: relati7206184916280974613la_a_b,Xa2: produc7366699395886430672_b_nat > set_list_a,Xb: nat > a] :
( ~ ( relati5954879512608767636la_a_b @ X @ Xa2 @ Xb )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ X @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: relational_fmla_a_b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( produc4282057684358614024_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati3586412934113010954la_a_b @ B3 ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati3586412934113010954la_a_b @ B3 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> B3 ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relati4858397885352678280la_a_b @ X5 @ T3 ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati4858397885352678280la_a_b @ X5 @ T3 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati3276862304027480822la_a_b @ Phi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati3276862304027480822la_a_b @ Phi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2925905614403835404la_a_b @ Phi @ Psi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati2925905614403835404la_a_b @ Phi @ Psi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
& ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2923897639004875288la_a_b @ Phi @ Psi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati2923897639004875288la_a_b @ Phi @ Psi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
| ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ~ ! [Z3: nat,Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati8887572811940184376la_a_b @ Z3 @ Phi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati8887572811940184376la_a_b @ Z3 @ Phi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ? [X7: a] : ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(3)
thf(fact_777_sat_Opelims_I3_J,axiom,
! [X: relati9047081815478866374_a_nat,Xa2: product_prod_nat_nat > set_list_a,Xb: nat > a] :
( ~ ( relational_sat_a_nat @ X @ Xa2 @ Xb )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ X @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: nat,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati9034565498597818939_a_nat @ B3 ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9034565498597818939_a_nat @ B3 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> B3 ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_nat @ X5 @ T3 ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Eq_a_nat @ X5 @ T3 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relational_Neg_a_nat @ Phi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Neg_a_nat @ Phi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( relational_sat_a_nat @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati2542520632142267709_a_nat @ Phi @ Psi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati2542520632142267709_a_nat @ Phi @ Psi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati9106205213788308809_a_nat @ Phi @ Psi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9106205213788308809_a_nat @ Phi @ Psi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) ) )
=> ~ ! [Z3: nat,Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relati6314223733442460777_a_nat @ Z3 @ Phi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6314223733442460777_a_nat @ Z3 @ Phi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ? [X7: a] : ( relational_sat_a_nat @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(3)
thf(fact_778_sat_Opelims_I3_J,axiom,
! [X: relational_fmla_a_b,Xa2: product_prod_b_nat > set_list_a,Xb: nat > a] :
( ~ ( relational_sat_a_b @ X @ Xa2 @ Xb )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ X @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ R3 @ Ts2 ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts2 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B3 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> B3 ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X5 @ T3 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( relational_sat_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ? [X7: a] : ( relational_sat_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(3)
thf(fact_779_sat_Ocases,axiom,
! [X: produc1132964494702330949_nat_a] :
( ! [R3: b,Ts2: list_R6823256787227418703term_a,I5: product_prod_b_nat > set_list_a,Sigma4: nat > a] :
( X
!= ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts2 ) @ ( produc2895298938842563487_nat_a @ I5 @ Sigma4 ) ) )
=> ( ! [B3: $o,I5: product_prod_b_nat > set_list_a,Sigma4: nat > a] :
( X
!= ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B3 ) @ ( produc2895298938842563487_nat_a @ I5 @ Sigma4 ) ) )
=> ( ! [X5: nat,T3: relational_term_a,I5: product_prod_b_nat > set_list_a,Sigma4: nat > a] :
( X
!= ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X5 @ T3 ) @ ( produc2895298938842563487_nat_a @ I5 @ Sigma4 ) ) )
=> ( ! [Phi: relational_fmla_a_b,I5: product_prod_b_nat > set_list_a,Sigma4: nat > a] :
( X
!= ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi ) @ ( produc2895298938842563487_nat_a @ I5 @ Sigma4 ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b,I5: product_prod_b_nat > set_list_a,Sigma4: nat > a] :
( X
!= ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ I5 @ Sigma4 ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b,I5: product_prod_b_nat > set_list_a,Sigma4: nat > a] :
( X
!= ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ I5 @ Sigma4 ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b,I5: product_prod_b_nat > set_list_a,Sigma4: nat > a] :
( X
!= ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi ) @ ( produc2895298938842563487_nat_a @ I5 @ Sigma4 ) ) ) ) ) ) ) ) ) ).
% sat.cases
thf(fact_780_sat_Opelims_I1_J,axiom,
! [X: relati7206184916280974613la_a_b,Xa2: produc7366699395886430672_b_nat > set_list_a,Xb: nat > a,Y3: $o] :
( ( ( relati5954879512608767636la_a_b @ X @ Xa2 @ Xb )
= Y3 )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ X @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: relational_fmla_a_b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) )
=> ( ( Y3
= ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( produc4282057684358614024_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ~ ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati3586412934113010954la_a_b @ B3 ) )
=> ( ( Y3 = B3 )
=> ~ ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati3586412934113010954la_a_b @ B3 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relati4858397885352678280la_a_b @ X5 @ T3 ) )
=> ( ( Y3
= ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ~ ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati4858397885352678280la_a_b @ X5 @ T3 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati3276862304027480822la_a_b @ Phi ) )
=> ( ( Y3
= ( ~ ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati3276862304027480822la_a_b @ Phi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2925905614403835404la_a_b @ Phi @ Psi ) )
=> ( ( Y3
= ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
& ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati2925905614403835404la_a_b @ Phi @ Psi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2923897639004875288la_a_b @ Phi @ Psi ) )
=> ( ( Y3
= ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
| ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati2923897639004875288la_a_b @ Phi @ Psi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [Z3: nat,Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati8887572811940184376la_a_b @ Z3 @ Phi ) )
=> ( ( Y3
= ( ? [X3: a] : ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X3 ) ) ) )
=> ~ ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati8887572811940184376la_a_b @ Z3 @ Phi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(1)
thf(fact_781_sat_Opelims_I1_J,axiom,
! [X: relati9047081815478866374_a_nat,Xa2: product_prod_nat_nat > set_list_a,Xb: nat > a,Y3: $o] :
( ( ( relational_sat_a_nat @ X @ Xa2 @ Xb )
= Y3 )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ X @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: nat,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) )
=> ( ( Y3
= ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati9034565498597818939_a_nat @ B3 ) )
=> ( ( Y3 = B3 )
=> ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9034565498597818939_a_nat @ B3 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_nat @ X5 @ T3 ) )
=> ( ( Y3
= ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Eq_a_nat @ X5 @ T3 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relational_Neg_a_nat @ Phi ) )
=> ( ( Y3
= ( ~ ( relational_sat_a_nat @ Phi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Neg_a_nat @ Phi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati2542520632142267709_a_nat @ Phi @ Psi ) )
=> ( ( Y3
= ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati2542520632142267709_a_nat @ Phi @ Psi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati9106205213788308809_a_nat @ Phi @ Psi ) )
=> ( ( Y3
= ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9106205213788308809_a_nat @ Phi @ Psi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [Z3: nat,Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relati6314223733442460777_a_nat @ Z3 @ Phi ) )
=> ( ( Y3
= ( ? [X3: a] : ( relational_sat_a_nat @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X3 ) ) ) )
=> ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6314223733442460777_a_nat @ Z3 @ Phi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(1)
thf(fact_782_sat_Opelims_I1_J,axiom,
! [X: relational_fmla_a_b,Xa2: product_prod_b_nat > set_list_a,Xb: nat > a,Y3: $o] :
( ( ( relational_sat_a_b @ X @ Xa2 @ Xb )
= Y3 )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ X @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ R3 @ Ts2 ) )
=> ( ( Y3
= ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) )
=> ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts2 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ( ( Y3 = B3 )
=> ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B3 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( ( Y3
= ( ( Xb @ X5 )
= ( relati1177013128715261720term_a @ Xb @ T3 ) ) )
=> ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X5 @ T3 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ( ( Y3
= ( ~ ( relational_sat_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( ( Y3
= ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ( ( Y3
= ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) )
=> ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ( ( Y3
= ( ? [X3: a] : ( relational_sat_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X3 ) ) ) )
=> ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(1)
thf(fact_783_sat_Opelims_I2_J,axiom,
! [X: relati7206184916280974613la_a_b,Xa2: produc7366699395886430672_b_nat > set_list_a,Xb: nat > a] :
( ( relati5954879512608767636la_a_b @ X @ Xa2 @ Xb )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ X @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: relational_fmla_a_b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati1568360951651578835_a_b_a @ R3 @ Ts2 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( produc4282057684358614024_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati3586412934113010954la_a_b @ B3 ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati3586412934113010954la_a_b @ B3 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ~ B3 ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relati4858397885352678280la_a_b @ X5 @ T3 ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati4858397885352678280la_a_b @ X5 @ T3 ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati3276862304027480822la_a_b @ Phi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati3276862304027480822la_a_b @ Phi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2925905614403835404la_a_b @ Phi @ Psi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati2925905614403835404la_a_b @ Phi @ Psi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
& ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ( ! [Phi: relati7206184916280974613la_a_b,Psi: relati7206184916280974613la_a_b] :
( ( X
= ( relati2923897639004875288la_a_b @ Phi @ Psi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati2923897639004875288la_a_b @ Phi @ Psi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ Xb )
| ( relati5954879512608767636la_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ~ ! [Z3: nat,Phi: relati7206184916280974613la_a_b] :
( ( X
= ( relati8887572811940184376la_a_b @ Z3 @ Phi ) )
=> ( ( accp_P932837839904948380_nat_a @ relati3587375677737501741la_a_b @ ( produc1809642229787647839_nat_a @ ( relati8887572811940184376la_a_b @ Z3 @ Phi ) @ ( produc4684437433003574739_nat_a @ Xa2 @ Xb ) ) )
=> ~ ? [X5: a] : ( relati5954879512608767636la_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(2)
thf(fact_784_sat_Opelims_I2_J,axiom,
! [X: relati9047081815478866374_a_nat,Xa2: product_prod_nat_nat > set_list_a,Xb: nat > a] :
( ( relational_sat_a_nat @ X @ Xa2 @ Xb )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ X @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: nat,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6362048942677509346_nat_a @ R3 @ Ts2 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relati9034565498597818939_a_nat @ B3 ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9034565498597818939_a_nat @ B3 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ~ B3 ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_nat @ X5 @ T3 ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Eq_a_nat @ X5 @ T3 ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relational_Neg_a_nat @ Phi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Neg_a_nat @ Phi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ( relational_sat_a_nat @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati2542520632142267709_a_nat @ Phi @ Psi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati2542520632142267709_a_nat @ Phi @ Psi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) ) )
=> ( ! [Phi: relati9047081815478866374_a_nat,Psi: relati9047081815478866374_a_nat] :
( ( X
= ( relati9106205213788308809_a_nat @ Phi @ Psi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9106205213788308809_a_nat @ Phi @ Psi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( ( relational_sat_a_nat @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_nat @ Psi @ Xa2 @ Xb ) ) ) )
=> ~ ! [Z3: nat,Phi: relati9047081815478866374_a_nat] :
( ( X
= ( relati6314223733442460777_a_nat @ Z3 @ Phi ) )
=> ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6314223733442460777_a_nat @ Z3 @ Phi ) @ ( produc4953239424914856836_nat_a @ Xa2 @ Xb ) ) )
=> ~ ? [X5: a] : ( relational_sat_a_nat @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(2)
thf(fact_785_sat_Opelims_I2_J,axiom,
! [X: relational_fmla_a_b,Xa2: product_prod_b_nat > set_list_a,Xb: nat > a] :
( ( relational_sat_a_b @ X @ Xa2 @ Xb )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ X @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( ! [R3: b,Ts2: list_R6823256787227418703term_a] :
( ( X
= ( relational_Pred_b_a @ R3 @ Ts2 ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts2 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts2 ) @ ( Xa2 @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) )
=> ( ! [B3: $o] :
( ( X
= ( relational_Bool_a_b @ B3 ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B3 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ~ B3 ) )
=> ( ! [X5: nat,T3: relational_term_a] :
( ( X
= ( relational_Eq_a_b @ X5 @ T3 ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X5 @ T3 ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( ( Xb @ X5 )
!= ( relati1177013128715261720term_a @ Xb @ T3 ) ) ) )
=> ( ! [Phi: relational_fmla_a_b] :
( ( X
= ( relational_Neg_a_b @ Phi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ( relational_sat_a_b @ Phi @ Xa2 @ Xb ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Conj_a_b @ Phi @ Psi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
& ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ( ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
( ( X
= ( relational_Disj_a_b @ Phi @ Psi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi @ Psi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ~ ( ( relational_sat_a_b @ Phi @ Xa2 @ Xb )
| ( relational_sat_a_b @ Psi @ Xa2 @ Xb ) ) ) )
=> ~ ! [Z3: nat,Phi: relational_fmla_a_b] :
( ( X
= ( relati591517084277583526ts_a_b @ Z3 @ Phi ) )
=> ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi ) @ ( produc2895298938842563487_nat_a @ Xa2 @ Xb ) ) )
=> ~ ? [X5: a] : ( relational_sat_a_b @ Phi @ Xa2 @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ).
% sat.pelims(2)
thf(fact_786_fv__fo__term__list_Osimps_I2_J,axiom,
! [V: a] :
( ( relati2314952831343875613list_a @ ( relational_Const_a @ V ) )
= nil_nat ) ).
% fv_fo_term_list.simps(2)
thf(fact_787_foldr1_Oelims,axiom,
! [X: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,Xa2: list_R8263082107343818799la_a_b,Xb: relational_fmla_a_b,Y3: relational_fmla_a_b] :
( ( ( relati1724936043867567613la_a_b @ X @ Xa2 @ Xb )
= Y3 )
=> ( ! [X5: relational_fmla_a_b,Xs2: list_R8263082107343818799la_a_b] :
( ( Xa2
= ( cons_R4161027894713053801la_a_b @ X5 @ Xs2 ) )
=> ( Y3
!= ( foldr_789212930732525799la_a_b @ X @ Xs2 @ X5 ) ) )
=> ~ ( ( Xa2 = nil_Re6358386334527539737la_a_b )
=> ( Y3 != Xb ) ) ) ) ).
% foldr1.elims
thf(fact_788_subst__term_Ocases,axiom,
! [X: produc6058688428250151583at_nat] :
( ! [Z3: nat,X5: nat,Y5: nat] :
( X
!= ( produc2180204704594896271at_nat @ ( relational_Var_a @ Z3 ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
=> ~ ! [C: a,X5: nat,Y5: nat] :
( X
!= ( produc2180204704594896271at_nat @ ( relational_Const_a @ C ) @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) ) ) ).
% subst_term.cases
thf(fact_789_fv__fo__term__list_Oelims,axiom,
! [X: relational_term_a,Y3: list_nat] :
( ( ( relati2314952831343875613list_a @ X )
= Y3 )
=> ( ! [N2: nat] :
( ( X
= ( relational_Var_a @ N2 ) )
=> ( Y3
!= ( cons_nat @ N2 @ nil_nat ) ) )
=> ~ ( ? [V2: a] :
( X
= ( relational_Const_a @ V2 ) )
=> ( Y3 != nil_nat ) ) ) ) ).
% fv_fo_term_list.elims
thf(fact_790_fv__fo__term__list_Osimps_I1_J,axiom,
! [N: nat] :
( ( relati2314952831343875613list_a @ ( relational_Var_a @ N ) )
= ( cons_nat @ N @ nil_nat ) ) ).
% fv_fo_term_list.simps(1)
thf(fact_791_list__all2__Cons2,axiom,
! [P: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a,Y3: relational_term_a,Ys: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ Xs @ ( cons_R2133480724479300095term_a @ Y3 @ Ys ) )
= ( ? [Z4: relational_term_a,Zs: list_R6823256787227418703term_a] :
( ( Xs
= ( cons_R2133480724479300095term_a @ Z4 @ Zs ) )
& ( P @ Z4 @ Y3 )
& ( list_a3533670403825157575term_a @ P @ Zs @ Ys ) ) ) ) ).
% list_all2_Cons2
thf(fact_792_list__all2__Cons1,axiom,
! [P: relational_term_a > relational_term_a > $o,X: relational_term_a,Xs: list_R6823256787227418703term_a,Ys: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ ( cons_R2133480724479300095term_a @ X @ Xs ) @ Ys )
= ( ? [Z4: relational_term_a,Zs: list_R6823256787227418703term_a] :
( ( Ys
= ( cons_R2133480724479300095term_a @ Z4 @ Zs ) )
& ( P @ X @ Z4 )
& ( list_a3533670403825157575term_a @ P @ Xs @ Zs ) ) ) ) ).
% list_all2_Cons1
thf(fact_793_list__all2__Cons,axiom,
! [P: relational_term_a > relational_term_a > $o,X: relational_term_a,Xs: list_R6823256787227418703term_a,Y3: relational_term_a,Ys: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ P @ ( cons_R2133480724479300095term_a @ X @ Xs ) @ ( cons_R2133480724479300095term_a @ Y3 @ Ys ) )
= ( ( P @ X @ Y3 )
& ( list_a3533670403825157575term_a @ P @ Xs @ Ys ) ) ) ).
% list_all2_Cons
thf(fact_794_list_Orel__intros_I2_J,axiom,
! [R: relational_term_a > relational_term_a > $o,X21: relational_term_a,Y21: relational_term_a,X222: list_R6823256787227418703term_a,Y222: list_R6823256787227418703term_a] :
( ( R @ X21 @ Y21 )
=> ( ( list_a3533670403825157575term_a @ R @ X222 @ Y222 )
=> ( list_a3533670403825157575term_a @ R @ ( cons_R2133480724479300095term_a @ X21 @ X222 ) @ ( cons_R2133480724479300095term_a @ Y21 @ Y222 ) ) ) ) ).
% list.rel_intros(2)
thf(fact_795_list_Orel__inject_I2_J,axiom,
! [R: relational_term_a > relational_term_a > $o,X21: relational_term_a,X222: list_R6823256787227418703term_a,Y21: relational_term_a,Y222: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ R @ ( cons_R2133480724479300095term_a @ X21 @ X222 ) @ ( cons_R2133480724479300095term_a @ Y21 @ Y222 ) )
= ( ( R @ X21 @ Y21 )
& ( list_a3533670403825157575term_a @ R @ X222 @ Y222 ) ) ) ).
% list.rel_inject(2)
thf(fact_796_list__all2__induct,axiom,
! [P: relational_term_a > relational_term_a > $o,Xs: list_R6823256787227418703term_a,Ys: list_R6823256787227418703term_a,R: list_R6823256787227418703term_a > list_R6823256787227418703term_a > $o] :
( ( list_a3533670403825157575term_a @ P @ Xs @ Ys )
=> ( ( R @ nil_Re7785829565976577615term_a @ nil_Re7785829565976577615term_a )
=> ( ! [X5: relational_term_a,Xs2: list_R6823256787227418703term_a,Y5: relational_term_a,Ys2: list_R6823256787227418703term_a] :
( ( P @ X5 @ Y5 )
=> ( ( list_a3533670403825157575term_a @ P @ Xs2 @ Ys2 )
=> ( ( R @ Xs2 @ Ys2 )
=> ( R @ ( cons_R2133480724479300095term_a @ X5 @ Xs2 ) @ ( cons_R2133480724479300095term_a @ Y5 @ Ys2 ) ) ) ) )
=> ( R @ Xs @ Ys ) ) ) ) ).
% list_all2_induct
thf(fact_797_list_Orel__induct,axiom,
! [R: relational_term_a > relational_term_a > $o,X: list_R6823256787227418703term_a,Y3: list_R6823256787227418703term_a,Q: list_R6823256787227418703term_a > list_R6823256787227418703term_a > $o] :
( ( list_a3533670403825157575term_a @ R @ X @ Y3 )
=> ( ( Q @ nil_Re7785829565976577615term_a @ nil_Re7785829565976577615term_a )
=> ( ! [A21: relational_term_a,A222: list_R6823256787227418703term_a,B21: relational_term_a,B22: list_R6823256787227418703term_a] :
( ( R @ A21 @ B21 )
=> ( ( Q @ A222 @ B22 )
=> ( Q @ ( cons_R2133480724479300095term_a @ A21 @ A222 ) @ ( cons_R2133480724479300095term_a @ B21 @ B22 ) ) ) )
=> ( Q @ X @ Y3 ) ) ) ) ).
% list.rel_induct
thf(fact_798_list_Orel__cases,axiom,
! [R: relational_term_a > relational_term_a > $o,A: list_R6823256787227418703term_a,B: list_R6823256787227418703term_a] :
( ( list_a3533670403825157575term_a @ R @ A @ B )
=> ( ( ( A = nil_Re7785829565976577615term_a )
=> ( B != nil_Re7785829565976577615term_a ) )
=> ~ ! [X1: relational_term_a,X23: list_R6823256787227418703term_a] :
( ( A
= ( cons_R2133480724479300095term_a @ X1 @ X23 ) )
=> ! [Y1: relational_term_a,Y22: list_R6823256787227418703term_a] :
( ( B
= ( cons_R2133480724479300095term_a @ Y1 @ Y22 ) )
=> ( ( R @ X1 @ Y1 )
=> ~ ( list_a3533670403825157575term_a @ R @ X23 @ Y22 ) ) ) ) ) ) ).
% list.rel_cases
thf(fact_799_list_Orel__distinct_I1_J,axiom,
! [R: relational_term_a > relational_term_a > $o,Y21: relational_term_a,Y222: list_R6823256787227418703term_a] :
~ ( list_a3533670403825157575term_a @ R @ nil_Re7785829565976577615term_a @ ( cons_R2133480724479300095term_a @ Y21 @ Y222 ) ) ).
% list.rel_distinct(1)
thf(fact_800_list_Orel__distinct_I2_J,axiom,
! [R: relational_term_a > relational_term_a > $o,Y21: relational_term_a,Y222: list_R6823256787227418703term_a] :
~ ( list_a3533670403825157575term_a @ R @ ( cons_R2133480724479300095term_a @ Y21 @ Y222 ) @ nil_Re7785829565976577615term_a ) ).
% list.rel_distinct(2)
thf(fact_801_foldr1_Osimps_I1_J,axiom,
! [F: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,X: relational_fmla_a_b,Xs: list_R8263082107343818799la_a_b,Z2: relational_fmla_a_b] :
( ( relati1724936043867567613la_a_b @ F @ ( cons_R4161027894713053801la_a_b @ X @ Xs ) @ Z2 )
= ( foldr_789212930732525799la_a_b @ F @ Xs @ X ) ) ).
% foldr1.simps(1)
thf(fact_802_fv__fo__term__list_Opelims,axiom,
! [X: relational_term_a,Y3: list_nat] :
( ( ( relati2314952831343875613list_a @ X )
= Y3 )
=> ( ( accp_R1925461290012245842term_a @ relati4401960826742192740_rel_a @ X )
=> ( ! [N2: nat] :
( ( X
= ( relational_Var_a @ N2 ) )
=> ( ( Y3
= ( cons_nat @ N2 @ nil_nat ) )
=> ~ ( accp_R1925461290012245842term_a @ relati4401960826742192740_rel_a @ ( relational_Var_a @ N2 ) ) ) )
=> ~ ! [V2: a] :
( ( X
= ( relational_Const_a @ V2 ) )
=> ( ( Y3 = nil_nat )
=> ~ ( accp_R1925461290012245842term_a @ relati4401960826742192740_rel_a @ ( relational_Const_a @ V2 ) ) ) ) ) ) ) ).
% fv_fo_term_list.pelims
thf(fact_803_subst__term_Opelims,axiom,
! [X: relational_term_a,Xa2: nat,Xb: nat,Y3: relational_term_a] :
( ( ( relati7175845559408349773term_a @ X @ Xa2 @ Xb )
= Y3 )
=> ( ( accp_P7512640865500879912at_nat @ relati1089594453538404916_rel_a @ ( produc2180204704594896271at_nat @ X @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) )
=> ( ! [Z3: nat] :
( ( X
= ( relational_Var_a @ Z3 ) )
=> ( ( Y3
= ( relational_Var_a @ ( if_nat @ ( Xa2 = Z3 ) @ Xb @ Z3 ) ) )
=> ~ ( accp_P7512640865500879912at_nat @ relati1089594453538404916_rel_a @ ( produc2180204704594896271at_nat @ ( relational_Var_a @ Z3 ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) )
=> ~ ! [C: a] :
( ( X
= ( relational_Const_a @ C ) )
=> ( ( Y3
= ( relational_Const_a @ C ) )
=> ~ ( accp_P7512640865500879912at_nat @ relati1089594453538404916_rel_a @ ( produc2180204704594896271at_nat @ ( relational_Const_a @ C ) @ ( product_Pair_nat_nat @ Xa2 @ Xb ) ) ) ) ) ) ) ) ).
% subst_term.pelims
thf(fact_804_substs__bd_Oelims,axiom,
! [X: nat,Xa2: list_nat,Xb: list_nat,Xc: relational_fmla_a_b,Y3: nat] :
( ( ( relati3061153751618241490bd_a_b @ X @ Xa2 @ Xb @ Xc )
= Y3 )
=> ( ! [X5: nat,Xs2: list_nat] :
( ( Xa2
= ( cons_nat @ X5 @ Xs2 ) )
=> ! [Y5: nat,Ys2: list_nat] :
( ( Xb
= ( cons_nat @ Y5 @ Ys2 ) )
=> ~ ( ( ( X5 = X )
=> ( Y3
= ( relati3061153751618241490bd_a_b @ X @ Xs2 @ Ys2 @ Xc ) ) )
& ( ( X5 != X )
=> ( ( ( X = Y5 )
=> ( Y3
= ( relati3061153751618241490bd_a_b @ ( relati2677767559083392098h2_a_b @ X5 @ Y5 @ Xc ) @ Xs2 @ Ys2 @ ( relational_subst_a_b @ ( relational_subst_a_b @ Xc @ Y5 @ ( relati2677767559083392098h2_a_b @ X5 @ Y5 @ Xc ) ) @ X5 @ Y5 ) ) ) )
& ( ( X != Y5 )
=> ( Y3
= ( relati3061153751618241490bd_a_b @ X @ Xs2 @ Ys2 @ ( relational_subst_a_b @ Xc @ X5 @ Y5 ) ) ) ) ) ) ) ) )
=> ( ( ( Xa2 = nil_nat )
=> ( Y3 != X ) )
=> ~ ( ( Xb = nil_nat )
=> ( Y3 != X ) ) ) ) ) ).
% substs_bd.elims
thf(fact_805_substs__bd_Osimps_I1_J,axiom,
! [X: nat,Z2: nat,Xs: list_nat,Y3: nat,Ys: list_nat,Q: relational_fmla_a_b] :
( ( ( X = Z2 )
=> ( ( relati3061153751618241490bd_a_b @ Z2 @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y3 @ Ys ) @ Q )
= ( relati3061153751618241490bd_a_b @ Z2 @ Xs @ Ys @ Q ) ) )
& ( ( X != Z2 )
=> ( ( ( Z2 = Y3 )
=> ( ( relati3061153751618241490bd_a_b @ Z2 @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y3 @ Ys ) @ Q )
= ( relati3061153751618241490bd_a_b @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) @ Xs @ Ys @ ( relational_subst_a_b @ ( relational_subst_a_b @ Q @ Y3 @ ( relati2677767559083392098h2_a_b @ X @ Y3 @ Q ) ) @ X @ Y3 ) ) ) )
& ( ( Z2 != Y3 )
=> ( ( relati3061153751618241490bd_a_b @ Z2 @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y3 @ Ys ) @ Q )
= ( relati3061153751618241490bd_a_b @ Z2 @ Xs @ Ys @ ( relational_subst_a_b @ Q @ X @ Y3 ) ) ) ) ) ) ) ).
% substs_bd.simps(1)
thf(fact_806_un__Bool__def,axiom,
( relati2638701775882563405ol_a_b
= ( relati6637215556741570915_b_a_o
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefined_o
@ ^ [X22: $o] : X22
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefined_o
@ ^ [Uu4: relational_fmla_a_b] : undefined_o
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_o
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_o
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefined_o ) ) ).
% un_Bool_def
thf(fact_807_un__Pred1__def,axiom,
( relati91604085239814319d1_a_b
= ( relati4214321532279288650_b_a_b
@ ^ [X112: b,X122: list_R6823256787227418703term_a] : X112
@ ^ [Uu4: $o] : undefined_b
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefined_b
@ ^ [Uu4: relational_fmla_a_b] : undefined_b
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_b
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_b
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefined_b ) ) ).
% un_Pred1_def
thf(fact_808_un__Neg__def,axiom,
( relati5982302313924697647eg_a_b
= ( relati5004271986839035796la_a_b
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: $o] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
@ ^ [X42: relational_fmla_a_b] : X42
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).
% un_Neg_def
thf(fact_809_un__Conj1__def,axiom,
( relati5154284022127734760j1_a_b
= ( relati5004271986839035796la_a_b
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: $o] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [X512: relational_fmla_a_b,X522: relational_fmla_a_b] : X512
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).
% un_Conj1_def
thf(fact_810_un__Conj2__def,axiom,
( relati1527130600461089641j2_a_b
= ( relati5004271986839035796la_a_b
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: $o] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [X512: relational_fmla_a_b,X522: relational_fmla_a_b] : X522
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).
% un_Conj2_def
thf(fact_811_un__Disj1__def,axiom,
( relati3334262663314506228j1_a_b
= ( relati5004271986839035796la_a_b
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: $o] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [X612: relational_fmla_a_b,X622: relational_fmla_a_b] : X612
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).
% un_Disj1_def
thf(fact_812_un__Disj2__def,axiom,
( relati8930481278502636917j2_a_b
= ( relati5004271986839035796la_a_b
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: $o] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [X612: relational_fmla_a_b,X622: relational_fmla_a_b] : X622
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).
% un_Disj2_def
thf(fact_813_un__Exists2__def,axiom,
( relati5591445451228332309s2_a_b
= ( relati5004271986839035796la_a_b
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: $o] : undefi1992772029223621943la_a_b
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
@ ^ [X712: nat,X722: relational_fmla_a_b] : X722 ) ) ).
% un_Exists2_def
thf(fact_814_un__Eq2__def,axiom,
( relati1832481647827092069q2_a_b
= ( relati8448653393198995860term_a
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefi4938429376670434993term_a
@ ^ [Uu4: $o] : undefi4938429376670434993term_a
@ ^ [X313: nat,X323: relational_term_a] : X323
@ ^ [Uu4: relational_fmla_a_b] : undefi4938429376670434993term_a
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi4938429376670434993term_a
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi4938429376670434993term_a
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefi4938429376670434993term_a ) ) ).
% un_Eq2_def
thf(fact_815_un__Pred2__def,axiom,
( relati5687822700427945008d2_a_b
= ( relati130711325911436314term_a
@ ^ [X112: b,X122: list_R6823256787227418703term_a] : X122
@ ^ [Uu4: $o] : undefi8139585145400706743term_a
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefi8139585145400706743term_a
@ ^ [Uu4: relational_fmla_a_b] : undefi8139585145400706743term_a
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi8139585145400706743term_a
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi8139585145400706743term_a
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefi8139585145400706743term_a ) ) ).
% un_Pred2_def
thf(fact_816_un__Eq1__def,axiom,
( relati5459635069493737188q1_a_b
= ( relati5872380936867403461_a_nat
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefined_nat
@ ^ [Uu4: $o] : undefined_nat
@ ^ [X313: nat,X323: relational_term_a] : X313
@ ^ [Uu4: relational_fmla_a_b] : undefined_nat
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
@ ^ [Uu4: nat,Uv2: relational_fmla_a_b] : undefined_nat ) ) ).
% un_Eq1_def
thf(fact_817_un__Exists1__def,axiom,
( relati9218598872894977428s1_a_b
= ( relati5872380936867403461_a_nat
@ ^ [Uu4: b,Uv2: list_R6823256787227418703term_a] : undefined_nat
@ ^ [Uu4: $o] : undefined_nat
@ ^ [Uu4: nat,Uv2: relational_term_a] : undefined_nat
@ ^ [Uu4: relational_fmla_a_b] : undefined_nat
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
@ ^ [Uu4: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
@ ^ [X712: nat,X722: relational_fmla_a_b] : X712 ) ) ).
% un_Exists1_def
thf(fact_818_size__subst__term,axiom,
! [T: relational_term_a,X: nat,Y3: nat] :
( ( size_s49661629988129973term_a @ ( relati7175845559408349773term_a @ T @ X @ Y3 ) )
= ( size_s49661629988129973term_a @ T ) ) ).
% size_subst_term
thf(fact_819_fmla_Orel__Grp,axiom,
! [A15: set_a,F1: a > a,A25: set_b,F2: b > b] :
( ( relati8459511609072445516_a_b_b @ ( bNF_Grp_a_a @ A15 @ F1 ) @ ( bNF_Grp_b_b @ A25 @ F2 ) )
= ( bNF_Gr5077645004228818574la_a_b
@ ( collec3419995626248312948la_a_b
@ ^ [X3: relational_fmla_a_b] :
( ( ord_less_eq_set_a @ ( relati3071123380395136021la_a_b @ X3 ) @ A15 )
& ( ord_less_eq_set_b @ ( relati8924981150291758614la_a_b @ X3 ) @ A25 ) ) )
@ ( relati4520850492397955663_a_b_b @ F1 @ F2 ) ) ) ).
% fmla.rel_Grp
thf(fact_820_EXISTS__def,axiom,
( relati7004044288120072026TS_a_b
= ( fold_n2260362839379620988la_a_b @ relati591517084277583526ts_a_b ) ) ).
% EXISTS_def
thf(fact_821_list_Orel__Grp,axiom,
! [A2: set_Re5178783185447174953term_a,F: relational_term_a > relational_term_a] :
( ( list_a3533670403825157575term_a @ ( bNF_Gr6379633379135635214term_a @ A2 @ F ) )
= ( bNF_Gr1063844525067465614term_a
@ ( collec8200894614646537018term_a
@ ^ [X3: list_R6823256787227418703term_a] : ( ord_le6173019262470748873term_a @ ( set_Re3569617851344498910term_a @ X3 ) @ A2 ) )
@ ( map_Re5736185711816362116term_a @ F ) ) ) ).
% list.rel_Grp
thf(fact_822_term_Orel__Grp,axiom,
! [A2: set_a,F: a > a] :
( ( relati3163788165526728396rm_a_a @ ( bNF_Grp_a_a @ A2 @ F ) )
= ( bNF_Gr6379633379135635214term_a
@ ( collec7376311432011962548term_a
@ ^ [X3: relational_term_a] : ( ord_less_eq_set_a @ ( relati2096729434547099208term_a @ X3 ) @ A2 ) )
@ ( relati3585320759856631375rm_a_a @ F ) ) ) ).
% term.rel_Grp
thf(fact_823_fmla_Opred__mono__strong,axiom,
! [P1: nat > $o,P22: nat > $o,X: relati7126052417554554232at_nat,P1a: nat > $o,P2a: nat > $o] :
( ( relati6725209092851823240at_nat @ P1 @ P22 @ X )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati6725209092851823240at_nat @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_824_fmla_Opred__mono__strong,axiom,
! [P1: nat > $o,P22: b > $o,X: relati3061873246650996333_nat_b,P1a: nat > $o,P2a: b > $o] :
( ( relati2149557458355847751_nat_b @ P1 @ P22 @ X )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati2149557458355847751_nat_b @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_825_fmla_Opred__mono__strong,axiom,
! [P1: nat > $o,P22: a > $o,X: relati3061873242347767532_nat_a,P1a: nat > $o,P2a: a > $o] :
( ( relati2149557458355847750_nat_a @ P1 @ P22 @ X )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati2149557458355847750_nat_a @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_826_fmla_Opred__mono__strong,axiom,
! [P1: b > $o,P22: nat > $o,X: relati1059154107580485063_b_nat,P1a: b > $o,P2a: nat > $o] :
( ( relati8576442322988731625_b_nat @ P1 @ P22 @ X )
=> ( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati700162154543277371_b_nat @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati8576442322988731625_b_nat @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_827_fmla_Opred__mono__strong,axiom,
! [P1: b > $o,P22: b > $o,X: relational_fmla_b_b,P1a: b > $o,P2a: b > $o] :
( ( relati872579602796707366la_b_b @ P1 @ P22 @ X )
=> ( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459988la_b_b @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati872579602796707366la_b_b @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_828_fmla_Opred__mono__strong,axiom,
! [P1: b > $o,P22: a > $o,X: relational_fmla_b_a,P1a: b > $o,P2a: a > $o] :
( ( relati872579602796707365la_b_a @ P1 @ P22 @ X )
=> ( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459987la_b_a @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati872579602796707365la_b_a @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_829_fmla_Opred__mono__strong,axiom,
! [P1: a > $o,P22: nat > $o,X: relati9047081815478866374_a_nat,P1a: a > $o,P2a: nat > $o] :
( ( relati7340997994032337128_a_nat @ P1 @ P22 @ X )
=> ( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati8688089862441658682_a_nat @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati7340997994032337128_a_nat @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_830_fmla_Opred__mono__strong,axiom,
! [P1: a > $o,P22: a > $o,X: relational_fmla_a_a,P1a: a > $o,P2a: a > $o] :
( ( relati3660035184769383398la_a_a @ P1 @ P22 @ X )
=> ( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136020la_a_a @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati3660035184769383398la_a_a @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_831_fmla_Opred__mono__strong,axiom,
! [P1: a > $o,P22: b > $o,X: relational_fmla_a_b,P1a: a > $o,P2a: b > $o] :
( ( relati3660035184769383399la_a_b @ P1 @ P22 @ X )
=> ( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136021la_a_b @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati3660035184769383399la_a_b @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_832_fmla_Opred__mono__strong,axiom,
! [P1: nat > $o,P22: list_a > $o,X: relati6521690034043994866list_a,P1a: nat > $o,P2a: list_a > $o] :
( ( relati1651932441426877132list_a @ P1 @ P22 @ X )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3899910203474895390list_a @ X ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z22: list_a] :
( ( member_list_a @ Z22 @ ( relati3314577606465187421list_a @ X ) )
=> ( ( P22 @ Z22 )
=> ( P2a @ Z22 ) ) )
=> ( relati1651932441426877132list_a @ P1a @ P2a @ X ) ) ) ) ).
% fmla.pred_mono_strong
thf(fact_833_fmla_Opred__inject_I4_J,axiom,
! [P1: a > $o,P22: b > $o,A: relational_fmla_a_b] :
( ( relati3660035184769383399la_a_b @ P1 @ P22 @ ( relational_Neg_a_b @ A ) )
= ( relati3660035184769383399la_a_b @ P1 @ P22 @ A ) ) ).
% fmla.pred_inject(4)
thf(fact_834_fmla_Opred__inject_I6_J,axiom,
! [P1: a > $o,P22: b > $o,A: relational_fmla_a_b,Aa: relational_fmla_a_b] :
( ( relati3660035184769383399la_a_b @ P1 @ P22 @ ( relational_Disj_a_b @ A @ Aa ) )
= ( ( relati3660035184769383399la_a_b @ P1 @ P22 @ A )
& ( relati3660035184769383399la_a_b @ P1 @ P22 @ Aa ) ) ) ).
% fmla.pred_inject(6)
thf(fact_835_fmla_Opred__inject_I5_J,axiom,
! [P1: a > $o,P22: b > $o,A: relational_fmla_a_b,Aa: relational_fmla_a_b] :
( ( relati3660035184769383399la_a_b @ P1 @ P22 @ ( relational_Conj_a_b @ A @ Aa ) )
= ( ( relati3660035184769383399la_a_b @ P1 @ P22 @ A )
& ( relati3660035184769383399la_a_b @ P1 @ P22 @ Aa ) ) ) ).
% fmla.pred_inject(5)
thf(fact_836_fmla_Opred__inject_I7_J,axiom,
! [P1: a > $o,P22: b > $o,A: nat,Aa: relational_fmla_a_b] :
( ( relati3660035184769383399la_a_b @ P1 @ P22 @ ( relati591517084277583526ts_a_b @ A @ Aa ) )
= ( relati3660035184769383399la_a_b @ P1 @ P22 @ Aa ) ) ).
% fmla.pred_inject(7)
thf(fact_837_fmla_Opred__map,axiom,
! [Q1: a > $o,Q22: b > $o,F1: a > a,F2: b > b,X: relational_fmla_a_b] :
( ( relati3660035184769383399la_a_b @ Q1 @ Q22 @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X ) )
= ( relati3660035184769383399la_a_b @ ( comp_a_o_a @ Q1 @ F1 ) @ ( comp_b_o_b @ Q22 @ F2 ) @ X ) ) ).
% fmla.pred_map
thf(fact_838_fmla_Omap__cong__pred,axiom,
! [X: relational_fmla_a_b,Ya2: relational_fmla_a_b,F1: a > a,G1: a > a,F2: b > b,G22: b > b] :
( ( X = Ya2 )
=> ( ( relati3660035184769383399la_a_b
@ ^ [Z12: a] :
( ( F1 @ Z12 )
= ( G1 @ Z12 ) )
@ ^ [Z23: b] :
( ( F2 @ Z23 )
= ( G22 @ Z23 ) )
@ Ya2 )
=> ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X )
= ( relati4520850492397955663_a_b_b @ G1 @ G22 @ Ya2 ) ) ) ) ).
% fmla.map_cong_pred
thf(fact_839_fmla_Opred__cong,axiom,
! [X: relati7126052417554554232at_nat,Ya2: relati7126052417554554232at_nat,P1: nat > $o,P1a: nat > $o,P22: nat > $o,P2a: nat > $o] :
( ( X = Ya2 )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati6321887899146193334at_nat @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati6725209092851823240at_nat @ P1 @ P22 @ X )
= ( relati6725209092851823240at_nat @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_840_fmla_Opred__cong,axiom,
! [X: relati3061873246650996333_nat_b,Ya2: relati3061873246650996333_nat_b,P1: nat > $o,P1a: nat > $o,P22: b > $o,P2a: b > $o] :
( ( X = Ya2 )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169305_nat_b @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati2149557458355847751_nat_b @ P1 @ P22 @ X )
= ( relati2149557458355847751_nat_b @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_841_fmla_Opred__cong,axiom,
! [X: relati3061873242347767532_nat_a,Ya2: relati3061873242347767532_nat_a,P1: nat > $o,P1a: nat > $o,P22: a > $o,P2a: a > $o] :
( ( X = Ya2 )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3496649326765169304_nat_a @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati2149557458355847750_nat_a @ P1 @ P22 @ X )
= ( relati2149557458355847750_nat_a @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_842_fmla_Opred__cong,axiom,
! [X: relati1059154107580485063_b_nat,Ya2: relati1059154107580485063_b_nat,P1: b > $o,P1a: b > $o,P22: nat > $o,P2a: nat > $o] :
( ( X = Ya2 )
=> ( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati700162154543277371_b_nat @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati8576442322988731625_b_nat @ P1 @ P22 @ X )
= ( relati8576442322988731625_b_nat @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_843_fmla_Opred__cong,axiom,
! [X: relational_fmla_b_b,Ya2: relational_fmla_b_b,P1: b > $o,P1a: b > $o,P22: b > $o,P2a: b > $o] :
( ( X = Ya2 )
=> ( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459988la_b_b @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati872579602796707366la_b_b @ P1 @ P22 @ X )
= ( relati872579602796707366la_b_b @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_844_fmla_Opred__cong,axiom,
! [X: relational_fmla_b_a,Ya2: relational_fmla_b_a,P1: b > $o,P1a: b > $o,P22: a > $o,P2a: a > $o] :
( ( X = Ya2 )
=> ( ! [Z1: b] :
( ( member_b @ Z1 @ ( relati283667798422459987la_b_a @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati872579602796707365la_b_a @ P1 @ P22 @ X )
= ( relati872579602796707365la_b_a @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_845_fmla_Opred__cong,axiom,
! [X: relati9047081815478866374_a_nat,Ya2: relati9047081815478866374_a_nat,P1: a > $o,P1a: a > $o,P22: nat > $o,P2a: nat > $o] :
( ( X = Ya2 )
=> ( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati8688089862441658682_a_nat @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: nat] :
( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati7340997994032337128_a_nat @ P1 @ P22 @ X )
= ( relati7340997994032337128_a_nat @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_846_fmla_Opred__cong,axiom,
! [X: relational_fmla_a_a,Ya2: relational_fmla_a_a,P1: a > $o,P1a: a > $o,P22: a > $o,P2a: a > $o] :
( ( X = Ya2 )
=> ( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136020la_a_a @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: a] :
( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati3660035184769383398la_a_a @ P1 @ P22 @ X )
= ( relati3660035184769383398la_a_a @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_847_fmla_Opred__cong,axiom,
! [X: relational_fmla_a_b,Ya2: relational_fmla_a_b,P1: a > $o,P1a: a > $o,P22: b > $o,P2a: b > $o] :
( ( X = Ya2 )
=> ( ! [Z1: a] :
( ( member_a @ Z1 @ ( relati3071123380395136021la_a_b @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: b] :
( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati3660035184769383399la_a_b @ P1 @ P22 @ X )
= ( relati3660035184769383399la_a_b @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_848_fmla_Opred__cong,axiom,
! [X: relati6521690034043994866list_a,Ya2: relati6521690034043994866list_a,P1: nat > $o,P1a: nat > $o,P22: list_a > $o,P2a: list_a > $o] :
( ( X = Ya2 )
=> ( ! [Z1: nat] :
( ( member_nat @ Z1 @ ( relati3899910203474895390list_a @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z22: list_a] :
( ( member_list_a @ Z22 @ ( relati3314577606465187421list_a @ Ya2 ) )
=> ( ( P22 @ Z22 )
= ( P2a @ Z22 ) ) )
=> ( ( relati1651932441426877132list_a @ P1 @ P22 @ X )
= ( relati1651932441426877132list_a @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% fmla.pred_cong
thf(fact_849_fmla_Opred__inject_I3_J,axiom,
! [P1: a > $o,P22: b > $o,A: nat,Aa: relational_term_a] :
( ( relati3660035184769383399la_a_b @ P1 @ P22 @ ( relational_Eq_a_b @ A @ Aa ) )
= ( relati6920953664156333207term_a @ P1 @ Aa ) ) ).
% fmla.pred_inject(3)
thf(fact_850_fmla_Osize__gen__o__map,axiom,
! [F: a > nat,Fa: b > nat,G2: a > a,Ga: b > b] :
( ( comp_R8034543168650949107la_a_b @ ( relati8658001423745148871la_a_b @ F @ Fa ) @ ( relati4520850492397955663_a_b_b @ G2 @ Ga ) )
= ( relati8658001423745148871la_a_b @ ( comp_a_nat_a @ F @ G2 ) @ ( comp_b_nat_b @ Fa @ Ga ) ) ) ).
% fmla.size_gen_o_map
thf(fact_851_term_Opred__inject_I1_J,axiom,
! [P: a > $o,A: a] :
( ( relati6920953664156333207term_a @ P @ ( relational_Const_a @ A ) )
= ( P @ A ) ) ).
% term.pred_inject(1)
thf(fact_852_term_Opred__mono__strong,axiom,
! [P: relational_fmla_a_b > $o,X: relati112041753218324778la_a_b,Pa: relational_fmla_a_b > $o] :
( ( relati9173353072008103110la_a_b @ P @ X )
=> ( ! [Z3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ Z3 @ ( relati7240241301533008341la_a_b @ X ) )
=> ( ( P @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( relati9173353072008103110la_a_b @ Pa @ X ) ) ) ).
% term.pred_mono_strong
thf(fact_853_term_Opred__mono__strong,axiom,
! [P: nat > $o,X: relational_term_nat,Pa: nat > $o] :
( ( relati2679609588974042615rm_nat @ P @ X )
=> ( ! [Z3: nat] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X ) )
=> ( ( P @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( relati2679609588974042615rm_nat @ Pa @ X ) ) ) ).
% term.pred_mono_strong
thf(fact_854_term_Opred__mono__strong,axiom,
! [P: b > $o,X: relational_term_b,Pa: b > $o] :
( ( relati6920953664156333208term_b @ P @ X )
=> ( ! [Z3: b] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X ) )
=> ( ( P @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( relati6920953664156333208term_b @ Pa @ X ) ) ) ).
% term.pred_mono_strong
thf(fact_855_term_Opred__mono__strong,axiom,
! [P: list_a > $o,X: relati383187284260386255list_a,Pa: list_a > $o] :
( ( relati4353722553127530653list_a @ P @ X )
=> ( ! [Z3: list_a] :
( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ X ) )
=> ( ( P @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( relati4353722553127530653list_a @ Pa @ X ) ) ) ).
% term.pred_mono_strong
thf(fact_856_term_Opred__mono__strong,axiom,
! [P: a > $o,X: relational_term_a,Pa: a > $o] :
( ( relati6920953664156333207term_a @ P @ X )
=> ( ! [Z3: a] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X ) )
=> ( ( P @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( relati6920953664156333207term_a @ Pa @ X ) ) ) ).
% term.pred_mono_strong
thf(fact_857_term_Opred__cong,axiom,
! [X: relati112041753218324778la_a_b,Ya2: relati112041753218324778la_a_b,P: relational_fmla_a_b > $o,Pa: relational_fmla_a_b > $o] :
( ( X = Ya2 )
=> ( ! [Z3: relational_fmla_a_b] :
( ( member4680049679412964150la_a_b @ Z3 @ ( relati7240241301533008341la_a_b @ Ya2 ) )
=> ( ( P @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( relati9173353072008103110la_a_b @ P @ X )
= ( relati9173353072008103110la_a_b @ Pa @ Ya2 ) ) ) ) ).
% term.pred_cong
thf(fact_858_term_Opred__cong,axiom,
! [X: relational_term_nat,Ya2: relational_term_nat,P: nat > $o,Pa: nat > $o] :
( ( X = Ya2 )
=> ( ! [Z3: nat] :
( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya2 ) )
=> ( ( P @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( relati2679609588974042615rm_nat @ P @ X )
= ( relati2679609588974042615rm_nat @ Pa @ Ya2 ) ) ) ) ).
% term.pred_cong
thf(fact_859_term_Opred__cong,axiom,
! [X: relational_term_b,Ya2: relational_term_b,P: b > $o,Pa: b > $o] :
( ( X = Ya2 )
=> ( ! [Z3: b] :
( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya2 ) )
=> ( ( P @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( relati6920953664156333208term_b @ P @ X )
= ( relati6920953664156333208term_b @ Pa @ Ya2 ) ) ) ) ).
% term.pred_cong
thf(fact_860_term_Opred__cong,axiom,
! [X: relati383187284260386255list_a,Ya2: relati383187284260386255list_a,P: list_a > $o,Pa: list_a > $o] :
( ( X = Ya2 )
=> ( ! [Z3: list_a] :
( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ Ya2 ) )
=> ( ( P @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( relati4353722553127530653list_a @ P @ X )
= ( relati4353722553127530653list_a @ Pa @ Ya2 ) ) ) ) ).
% term.pred_cong
thf(fact_861_term_Opred__cong,axiom,
! [X: relational_term_a,Ya2: relational_term_a,P: a > $o,Pa: a > $o] :
( ( X = Ya2 )
=> ( ! [Z3: a] :
( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya2 ) )
=> ( ( P @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( relati6920953664156333207term_a @ P @ X )
= ( relati6920953664156333207term_a @ Pa @ Ya2 ) ) ) ) ).
% term.pred_cong
thf(fact_862_fmla_Opred__inject_I1_J,axiom,
! [P1: a > $o,P22: b > $o,A: b,Aa: list_R6823256787227418703term_a] :
( ( relati3660035184769383399la_a_b @ P1 @ P22 @ ( relational_Pred_b_a @ A @ Aa ) )
= ( ( P22 @ A )
& ( list_a1394079704683284733term_a @ ( relati6920953664156333207term_a @ P1 ) @ Aa ) ) ) ).
% fmla.pred_inject(1)
thf(fact_863_fmla_Opred__set,axiom,
( relati3660035184769383399la_a_b
= ( ^ [P12: a > $o,P23: b > $o,X3: relational_fmla_a_b] :
( ! [Y6: a] :
( ( member_a @ Y6 @ ( relati3071123380395136021la_a_b @ X3 ) )
=> ( P12 @ Y6 ) )
& ! [Y6: b] :
( ( member_b @ Y6 @ ( relati8924981150291758614la_a_b @ X3 ) )
=> ( P23 @ Y6 ) ) ) ) ) ).
% fmla.pred_set
thf(fact_864_term_Opred__set,axiom,
( relati6920953664156333207term_a
= ( ^ [P5: a > $o,X3: relational_term_a] :
! [Y6: a] :
( ( member_a @ Y6 @ ( relati2096729434547099208term_a @ X3 ) )
=> ( P5 @ Y6 ) ) ) ) ).
% term.pred_set
thf(fact_865_comparator__term__simps_I1_J,axiom,
! [Comp_a: a > a > order,X: a,Y3: a] :
( ( relati3061618831195317182term_a @ Comp_a @ ( relational_Const_a @ X ) @ ( relational_Const_a @ Y3 ) )
= ( Comp_a @ X @ Y3 ) ) ).
% comparator_term_simps(1)
thf(fact_866_term_Opred__inject_I2_J,axiom,
! [P: a > $o,A: nat] :
( ( relati6920953664156333207term_a @ P @ ( relational_Var_a @ A ) )
= ( top_top_nat_o @ A ) ) ).
% term.pred_inject(2)
thf(fact_867_comparator__term__simps_I4_J,axiom,
! [Comp_a: a > a > order,X: nat,Ya2: nat] :
( ( relati3061618831195317182term_a @ Comp_a @ ( relational_Var_a @ X ) @ ( relational_Var_a @ Ya2 ) )
= ( linord2364297732936386151of_nat @ X @ Ya2 ) ) ).
% comparator_term_simps(4)
thf(fact_868_comparator__term__simps_I3_J,axiom,
! [Comp_a: a > a > order,X: nat,Y3: a] :
( ( relati3061618831195317182term_a @ Comp_a @ ( relational_Var_a @ X ) @ ( relational_Const_a @ Y3 ) )
= gt ) ).
% comparator_term_simps(3)
thf(fact_869_comparator__term__simps_I2_J,axiom,
! [Comp_a: a > a > order,X: a,Ya2: nat] :
( ( relati3061618831195317182term_a @ Comp_a @ ( relational_Const_a @ X ) @ ( relational_Var_a @ Ya2 ) )
= lt ) ).
% comparator_term_simps(2)
thf(fact_870_comparator__fmla__simps_I15_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_term_a,Y3: b,Ya2: list_R6823256787227418703term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Eq_a_b @ X @ Xa2 ) @ ( relational_Pred_b_a @ Y3 @ Ya2 ) )
= gt ) ).
% comparator_fmla_simps(15)
thf(fact_871_comparator__fmla__simps_I25_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Ye: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Neg_a_b @ X ) @ ( relational_Neg_a_b @ Ye ) )
= ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ X @ Ye ) ) ).
% comparator_fmla_simps(25)
thf(fact_872_comparator__fmla__simps_I27_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Yh: relational_fmla_a_b,Yi: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Neg_a_b @ X ) @ ( relational_Disj_a_b @ Yh @ Yi ) )
= lt ) ).
% comparator_fmla_simps(27)
thf(fact_873_comparator__fmla__simps_I26_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Yf: relational_fmla_a_b,Yg: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Neg_a_b @ X ) @ ( relational_Conj_a_b @ Yf @ Yg ) )
= lt ) ).
% comparator_fmla_simps(26)
thf(fact_874_comparator__fmla__simps_I39_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Ye: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Disj_a_b @ X @ Xa2 ) @ ( relational_Neg_a_b @ Ye ) )
= gt ) ).
% comparator_fmla_simps(39)
thf(fact_875_comparator__fmla__simps_I28_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Yj: nat,Yk: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Neg_a_b @ X ) @ ( relati591517084277583526ts_a_b @ Yj @ Yk ) )
= lt ) ).
% comparator_fmla_simps(28)
thf(fact_876_comparator__fmla__simps_I32_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Ye: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Conj_a_b @ X @ Xa2 ) @ ( relational_Neg_a_b @ Ye ) )
= gt ) ).
% comparator_fmla_simps(32)
thf(fact_877_comparator__fmla__simps_I34_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yh: relational_fmla_a_b,Yi: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Conj_a_b @ X @ Xa2 ) @ ( relational_Disj_a_b @ Yh @ Yi ) )
= lt ) ).
% comparator_fmla_simps(34)
thf(fact_878_comparator__fmla__simps_I11_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: $o,Ye: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Bool_a_b @ X ) @ ( relational_Neg_a_b @ Ye ) )
= lt ) ).
% comparator_fmla_simps(11)
thf(fact_879_comparator__fmla__simps_I18_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_term_a,Ye: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Eq_a_b @ X @ Xa2 ) @ ( relational_Neg_a_b @ Ye ) )
= lt ) ).
% comparator_fmla_simps(18)
thf(fact_880_comparator__fmla__simps_I46_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_fmla_a_b,Ye: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relati591517084277583526ts_a_b @ X @ Xa2 ) @ ( relational_Neg_a_b @ Ye ) )
= gt ) ).
% comparator_fmla_simps(46)
thf(fact_881_comparator__fmla__simps_I42_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yj: nat,Yk: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Disj_a_b @ X @ Xa2 ) @ ( relati591517084277583526ts_a_b @ Yj @ Yk ) )
= lt ) ).
% comparator_fmla_simps(42)
thf(fact_882_comparator__fmla__simps_I40_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yf: relational_fmla_a_b,Yg: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Disj_a_b @ X @ Xa2 ) @ ( relational_Conj_a_b @ Yf @ Yg ) )
= gt ) ).
% comparator_fmla_simps(40)
thf(fact_883_comparator__fmla__simps_I23_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Yb2: $o] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Neg_a_b @ X ) @ ( relational_Bool_a_b @ Yb2 ) )
= gt ) ).
% comparator_fmla_simps(23)
thf(fact_884_comparator__fmla__simps_I24_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Yc: nat,Yd: relational_term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Neg_a_b @ X ) @ ( relational_Eq_a_b @ Yc @ Yd ) )
= gt ) ).
% comparator_fmla_simps(24)
thf(fact_885_comparator__fmla__simps_I35_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yj: nat,Yk: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Conj_a_b @ X @ Xa2 ) @ ( relati591517084277583526ts_a_b @ Yj @ Yk ) )
= lt ) ).
% comparator_fmla_simps(35)
thf(fact_886_comparator__fmla__simps_I13_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: $o,Yh: relational_fmla_a_b,Yi: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Bool_a_b @ X ) @ ( relational_Disj_a_b @ Yh @ Yi ) )
= lt ) ).
% comparator_fmla_simps(13)
thf(fact_887_comparator__fmla__simps_I20_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_term_a,Yh: relational_fmla_a_b,Yi: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Eq_a_b @ X @ Xa2 ) @ ( relational_Disj_a_b @ Yh @ Yi ) )
= lt ) ).
% comparator_fmla_simps(20)
thf(fact_888_comparator__fmla__simps_I48_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_fmla_a_b,Yh: relational_fmla_a_b,Yi: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relati591517084277583526ts_a_b @ X @ Xa2 ) @ ( relational_Disj_a_b @ Yh @ Yi ) )
= gt ) ).
% comparator_fmla_simps(48)
thf(fact_889_comparator__fmla__simps_I12_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: $o,Yf: relational_fmla_a_b,Yg: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Bool_a_b @ X ) @ ( relational_Conj_a_b @ Yf @ Yg ) )
= lt ) ).
% comparator_fmla_simps(12)
thf(fact_890_comparator__fmla__simps_I19_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_term_a,Yf: relational_fmla_a_b,Yg: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Eq_a_b @ X @ Xa2 ) @ ( relational_Conj_a_b @ Yf @ Yg ) )
= lt ) ).
% comparator_fmla_simps(19)
thf(fact_891_comparator__fmla__simps_I47_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_fmla_a_b,Yf: relational_fmla_a_b,Yg: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relati591517084277583526ts_a_b @ X @ Xa2 ) @ ( relational_Conj_a_b @ Yf @ Yg ) )
= gt ) ).
% comparator_fmla_simps(47)
thf(fact_892_comparator__fmla__simps_I37_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yb2: $o] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Disj_a_b @ X @ Xa2 ) @ ( relational_Bool_a_b @ Yb2 ) )
= gt ) ).
% comparator_fmla_simps(37)
thf(fact_893_comparator__fmla__simps_I38_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yc: nat,Yd: relational_term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Disj_a_b @ X @ Xa2 ) @ ( relational_Eq_a_b @ Yc @ Yd ) )
= gt ) ).
% comparator_fmla_simps(38)
thf(fact_894_comparator__fmla__simps_I14_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: $o,Yj: nat,Yk: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Bool_a_b @ X ) @ ( relati591517084277583526ts_a_b @ Yj @ Yk ) )
= lt ) ).
% comparator_fmla_simps(14)
thf(fact_895_comparator__fmla__simps_I30_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yb2: $o] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Conj_a_b @ X @ Xa2 ) @ ( relational_Bool_a_b @ Yb2 ) )
= gt ) ).
% comparator_fmla_simps(30)
thf(fact_896_comparator__fmla__simps_I21_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_term_a,Yj: nat,Yk: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Eq_a_b @ X @ Xa2 ) @ ( relati591517084277583526ts_a_b @ Yj @ Yk ) )
= lt ) ).
% comparator_fmla_simps(21)
thf(fact_897_comparator__fmla__simps_I31_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yc: nat,Yd: relational_term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Conj_a_b @ X @ Xa2 ) @ ( relational_Eq_a_b @ Yc @ Yd ) )
= gt ) ).
% comparator_fmla_simps(31)
thf(fact_898_comparator__fmla__simps_I4_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: b,Xa2: list_R6823256787227418703term_a,Ye: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Pred_b_a @ X @ Xa2 ) @ ( relational_Neg_a_b @ Ye ) )
= lt ) ).
% comparator_fmla_simps(4)
thf(fact_899_comparator__fmla__simps_I10_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: $o,Yc: nat,Yd: relational_term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Bool_a_b @ X ) @ ( relational_Eq_a_b @ Yc @ Yd ) )
= lt ) ).
% comparator_fmla_simps(10)
thf(fact_900_comparator__fmla__simps_I44_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_fmla_a_b,Yb2: $o] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relati591517084277583526ts_a_b @ X @ Xa2 ) @ ( relational_Bool_a_b @ Yb2 ) )
= gt ) ).
% comparator_fmla_simps(44)
thf(fact_901_comparator__fmla__simps_I45_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_fmla_a_b,Yc: nat,Yd: relational_term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relati591517084277583526ts_a_b @ X @ Xa2 ) @ ( relational_Eq_a_b @ Yc @ Yd ) )
= gt ) ).
% comparator_fmla_simps(45)
thf(fact_902_comparator__fmla__simps_I22_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Y3: b,Ya2: list_R6823256787227418703term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Neg_a_b @ X ) @ ( relational_Pred_b_a @ Y3 @ Ya2 ) )
= gt ) ).
% comparator_fmla_simps(22)
thf(fact_903_comparator__fmla__simps_I16_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_term_a,Yb2: $o] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Eq_a_b @ X @ Xa2 ) @ ( relational_Bool_a_b @ Yb2 ) )
= gt ) ).
% comparator_fmla_simps(16)
thf(fact_904_comparator__fmla__simps_I6_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: b,Xa2: list_R6823256787227418703term_a,Yh: relational_fmla_a_b,Yi: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Pred_b_a @ X @ Xa2 ) @ ( relational_Disj_a_b @ Yh @ Yi ) )
= lt ) ).
% comparator_fmla_simps(6)
thf(fact_905_comparator__fmla__simps_I5_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: b,Xa2: list_R6823256787227418703term_a,Yf: relational_fmla_a_b,Yg: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Pred_b_a @ X @ Xa2 ) @ ( relational_Conj_a_b @ Yf @ Yg ) )
= lt ) ).
% comparator_fmla_simps(5)
thf(fact_906_comparator__fmla__simps_I36_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Y3: b,Ya2: list_R6823256787227418703term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Disj_a_b @ X @ Xa2 ) @ ( relational_Pred_b_a @ Y3 @ Ya2 ) )
= gt ) ).
% comparator_fmla_simps(36)
thf(fact_907_comparator__fmla__simps_I7_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: b,Xa2: list_R6823256787227418703term_a,Yj: nat,Yk: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Pred_b_a @ X @ Xa2 ) @ ( relati591517084277583526ts_a_b @ Yj @ Yk ) )
= lt ) ).
% comparator_fmla_simps(7)
thf(fact_908_comparator__fmla__simps_I29_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Y3: b,Ya2: list_R6823256787227418703term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Conj_a_b @ X @ Xa2 ) @ ( relational_Pred_b_a @ Y3 @ Ya2 ) )
= gt ) ).
% comparator_fmla_simps(29)
thf(fact_909_comparator__fmla__simps_I2_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: b,Xa2: list_R6823256787227418703term_a,Yb2: $o] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Pred_b_a @ X @ Xa2 ) @ ( relational_Bool_a_b @ Yb2 ) )
= lt ) ).
% comparator_fmla_simps(2)
thf(fact_910_comparator__fmla__simps_I3_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: b,Xa2: list_R6823256787227418703term_a,Yc: nat,Yd: relational_term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Pred_b_a @ X @ Xa2 ) @ ( relational_Eq_a_b @ Yc @ Yd ) )
= lt ) ).
% comparator_fmla_simps(3)
thf(fact_911_comparator__fmla__simps_I43_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_fmla_a_b,Y3: b,Ya2: list_R6823256787227418703term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relati591517084277583526ts_a_b @ X @ Xa2 ) @ ( relational_Pred_b_a @ Y3 @ Ya2 ) )
= gt ) ).
% comparator_fmla_simps(43)
thf(fact_912_comparator__fmla__simps_I8_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: $o,Y3: b,Ya2: list_R6823256787227418703term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Bool_a_b @ X ) @ ( relational_Pred_b_a @ Y3 @ Ya2 ) )
= gt ) ).
% comparator_fmla_simps(8)
thf(fact_913_comparator__fmla__simps_I17_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_term_a,Yc: nat,Yd: relational_term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Eq_a_b @ X @ Xa2 ) @ ( relational_Eq_a_b @ Yc @ Yd ) )
= ( case_order_order @ ( relati3061618831195317182term_a @ Comp_a @ Xa2 @ Yd ) @ lt @ gt @ ( linord2364297732936386151of_nat @ X @ Yc ) ) ) ).
% comparator_fmla_simps(17)
thf(fact_914_comparator__fmla__simps_I49_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: nat,Xa2: relational_fmla_a_b,Yj: nat,Yk: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relati591517084277583526ts_a_b @ X @ Xa2 ) @ ( relati591517084277583526ts_a_b @ Yj @ Yk ) )
= ( case_order_order @ ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ Xa2 @ Yk ) @ lt @ gt @ ( linord2364297732936386151of_nat @ X @ Yj ) ) ) ).
% comparator_fmla_simps(49)
thf(fact_915_comparator__fmla__simps_I41_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yh: relational_fmla_a_b,Yi: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Disj_a_b @ X @ Xa2 ) @ ( relational_Disj_a_b @ Yh @ Yi ) )
= ( case_order_order @ ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ Xa2 @ Yi ) @ lt @ gt @ ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ X @ Yh ) ) ) ).
% comparator_fmla_simps(41)
thf(fact_916_comparator__fmla__simps_I33_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: relational_fmla_a_b,Xa2: relational_fmla_a_b,Yf: relational_fmla_a_b,Yg: relational_fmla_a_b] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Conj_a_b @ X @ Xa2 ) @ ( relational_Conj_a_b @ Yf @ Yg ) )
= ( case_order_order @ ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ Xa2 @ Yg ) @ lt @ gt @ ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ X @ Yf ) ) ) ).
% comparator_fmla_simps(33)
thf(fact_917_comparator__fmla__simps_I1_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: b,Xa2: list_R6823256787227418703term_a,Y3: b,Ya2: list_R6823256787227418703term_a] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Pred_b_a @ X @ Xa2 ) @ ( relational_Pred_b_a @ Y3 @ Ya2 ) )
= ( case_order_order @ ( compar345322307989717423term_a @ ( relati3061618831195317182term_a @ Comp_a ) @ Xa2 @ Ya2 ) @ lt @ gt @ ( Comp_b @ X @ Y3 ) ) ) ).
% comparator_fmla_simps(1)
thf(fact_918_comparator__fmla__simps_I9_J,axiom,
! [Comp_a: a > a > order,Comp_b: b > b > order,X: $o,Yb2: $o] :
( ( relati7279129871493024880la_a_b @ Comp_a @ Comp_b @ ( relational_Bool_a_b @ X ) @ ( relational_Bool_a_b @ Yb2 ) )
= ( compar7506081026712146693r_bool @ X @ Yb2 ) ) ).
% comparator_fmla_simps(9)
thf(fact_919_fmla_Omap__id,axiom,
! [T: relational_fmla_a_b] :
( ( relati4520850492397955663_a_b_b @ id_a @ id_b @ T )
= T ) ).
% fmla.map_id
thf(fact_920_fmla_Omap__id0,axiom,
( ( relati4520850492397955663_a_b_b @ id_a @ id_b )
= id_Rel8561829368999054574la_a_b ) ).
% fmla.map_id0
thf(fact_921_comparator__fmla__def,axiom,
( relati7279129871493024880la_a_b
= ( ^ [Comp_a2: a > a > order,Comp_b2: b > b > order] : ( comp_R3016128876294075703la_a_b @ relati8601483800347945207la_a_b @ ( relati6560747122616347791_order @ Comp_a2 @ Comp_b2 ) ) ) ) ).
% comparator_fmla_def
% Helper facts (5)
thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y3: nat] :
( ( if_nat @ $false @ X @ Y3 )
= Y3 ) ).
thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y3: nat] :
( ( if_nat @ $true @ X @ Y3 )
= X ) ).
thf(help_If_3_1_If_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_T,axiom,
! [X: relational_fmla_a_b,Y3: relational_fmla_a_b] :
( ( if_Rel1279876242545935705la_a_b @ $false @ X @ Y3 )
= Y3 ) ).
thf(help_If_1_1_If_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_T,axiom,
! [X: relational_fmla_a_b,Y3: relational_fmla_a_b] :
( ( if_Rel1279876242545935705la_a_b @ $true @ X @ Y3 )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
relational_rrb_a_b @ ( relational_Bool_a_b @ b2 ) ).
%------------------------------------------------------------------------------